CON] 



First Aid 



Radii of ( 
Tangents 
Conversic 




>ATA 



CfiEffilGHT DEPOSm 



460 



346 
349 
297 



Volumes 51g 

Volume of Excavauon oiae xxiii jLrocauous 286-296 



Required Depth of Maeadam on Different Soils 

Table of Macadam Quantities 

Square Yards of Pavement per 100' 

Weights of Cast Iron Pipe 

Weights of Corrugated Iron Pipe 

Weights of Vitrified Pipe 

Steel Bar Reinforcement 

Metal Mesh Reinforcement 

Thickness of Concrete Bridge Slabs 

Material Required per Cti. Td. Concrete 



152 
543 
543 
558 
559 
560 
556 
555 
565 
623 



General Tables and Formulae 825-956 



»/ 



HANDBOOK FOR 
HIGHWAY ENGINEERS 



4 




Vlk QrawOlillBock & 7m 

PUDLISWERS OF BOOKS F O R^ 

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lIBj gMPMrM^^^ 



HANDBOOK 

FOR 

HIGHWAY ENGINEERS 

CONTAINING INFORMATION ORDINARILY USED 

IN THE DESIGN AND CONSTRUCTION 

OF RURAL HIGHWAYS 



Part I. Principles of Design. 

Part II. Practice of Design and Construction. 

Part III. Specifications. 

Part IV. General Tables. 

Appendix. Traffic Rules and Regulations. 



BY 

WILSON G. HARGER, C. E. 

AND 

EDMUND A. BONNEY 

SUPERVISING ENGINEER, N. Y. ^TATE DEPARTMENT OF HIGHWAYS 



Third Edition 

Entirely Revised, Enlarged and Reset 



McGRAW-HILL BOOK COMPANY, Inc. 
239 WEST 39TH STREET. NEW YORK 



LONDON: HILL PUBLISHING CO., Ltd. 
6 & 8 BOUVERIE ST., E. C. 

1919 



'^'^% 

^(\\ \ 



Copyright, 1919, by the 
McGraw-Hill Book Company, Inc. 



Copyright, 1912, 1916, by the 
McGraw-Hill Book Company, Inc. 



(via- iq lOiq %:' 

■a: 

©CI.A515659 



THB MAPIiBJ PRSSS Y O K K I» A 



i\ 



PREFACE TO THIRD EDITION 

The present revision was undertaken in response to the sugges- 
tions and requests of many users of the earlier editions. The 
practical value of the Handbook is increased by the addition of 
approximately 350 pages of new material covering mountain road 
location and design, camp equipment, medical notes, notes on pho- 
tography, the selected soil and gravel treatment of moderate traffic 
roads, and the more recent developments of hard surfaced types. 
There is no change in the general scheme of the publication, which 
is primarily a compact collection of reference data and time saving 
tables. For the benefit of men not entirely familiar with the road 
problem, the discussion of principles has been retained, and in some 
cases where it has been shown that certain arguments in the previ- 
ous editions have failed to make the impression warranted by their 
importance, the discussion has been amplified and illustrated by 
examples of construction and design. We wish particularly to 
emphatize gradeline design, which is not at present receiving the 
attention to which it is entitled, and also point out the practically 
universal lack of adequate maintenance. 

The costs given in the body of the text are for comparative pur- 
poses only and are based on labor at from $0,175 to $0.20 per hour 
and material costs of the period 1912 to 1915. 

For the improvement of future editions we request your cooper- 
ation in the correction of typographical errors, and the addition 
of any omitted data generally useful in road work. 

Very few highway engineers are satisfied with the road legislation 
or technical practice of today or believe that it can be applied as it 
stands to solve the highway problem in this country in the next 
fifty years, but the data that has been collected from experience 
serves as a basis for future improvement. There is every reason 
to be optimistic in regard to road development provided the prob- 
lem is approached with constructive imagination and encourage- 
ment is given to departure from methods whose main defense lies 
in precedent or habit. 

The work of revision for this edition is entirely that of W. G. 
Harger. 

W. G. H. 
E. A. B. 

Rochester, N. Y., January, 1919. 



PREFACE TO SECOND EDITION 

Since the pubKcation of the first edition of this book four years 
ago, considerable progress has been made in the practice of road 
design and construction. To meet this advance, this handbook has 
been revised by bringing the material on top courses up-to-date, 
and by adding considerable data on tests, designs, costs, mainte- 
nance and specifications. Not only has much of the old material 
been revised, but new material, totahng approximately loo pages, 
has been added. The criticisms and suggestions of many who have 
used the book in the field and office have aided the authors in this 
revision. 

A more complete and systematic index has been prepared by Mr. 
Percy Waller. 

The general arrangement of the book remains untouched. 

W. G. H. 
E. A. B. 

Rochester, N.Y., May, 19 16. 



PREFACE TO PIRST EDITION 

The purpose of this book is to collect, in a compact and conven- 
ient form, information ordinarily required in the field and office 
practice of road design and construction. 

The book is designed to meet the requirements of both experienced 
and inexperienced road men. The material on the relative impor- 
tance of the different parts of the design, and the possibihties of 
economy, without impairing the efficiency of the road, are primarily 
for the inexperienced engineer. The collection of cost data and the 
tables will be useful to any one engaged in road work. 

As it is difficult to avoid clerical errors and mistakes in proof- 
reading in first editions, we shall appreciate the cooperation of read- 
ers in caUing our attention to any errors. 

W. G. H. 
E. A. B. 
Rochester, N.Y., April, 19 12. 



TABLE OF CONTENTS 

Page 

Preface v 

Introduction and General Analysis 1-9 

General i 

Engineering design 2-5 

Pioneer roads . 3 

High type roads 4 

Maintenance and renewals 5 

Road bonds . 6 

General summary 6 

Value of engineering advice 8 

PART I. PRINCIPLES OF DESIGN 

Chapter I. Grades and Alignment 10-35 

Maximum Grades 10-26 

Effect of horse and automobile traffic on design ... 10 

Effect of grade on load 11 

Effect of length of grade on load 16 

Theoretical advantages of different grades 22 

Practical selection of maximum grades . 22 

Effect of ruling grade on cost 24 

Intermediate Grades 26-28 

Controlling points 26 

Flexibility 26 

^'Rolling Profile^^ 26 

Effect of careful design on cost 26 

Effect of arbitrary limitations on cost 28 

Minimum Grades 28-29 

On hard surfaced roads 28 

On earth roads 29 

Level Grades 28 

Adverse Grades 29 

Proper and improper use 29 

Summary of Grades . .' 29 

Alignment 33~35 

In well settled districts (ordinary topography) .... 7,^ 

Sight distance and minimum radius 33 

Mountain road conditions . 33 

Minimum radius 34 

Effect of alignment on grade 34 

Effect of alignment on cost 34 

Railroad grade crossing eliminations 35 

ix 



X TABLE OF CONTENTS 

Page 

Chapter II. Sections 36-73 

High Type Roads (Inordinary Topography) 36-62 

Conditions that sections must fulfil 36 

Premises of design 36-41 

Safe slopes for driving 36 

Comfortable slope for driving 36 

Required slope for surface drainage . 36 

Crowns 36 

Stable cut and fill slopes 36 and 40 

Widths of pavement 36 and 42 

Widths of roading between ditches 38 

Effect of grading width on cost 39 

Effect of pavement width on cost 42 

Examples of typical sections •. . . . 43-62 

Banked curves 45 

Widening at curves 45 and 62 

Mountain Road Sections 63-73 

Requirements 63 

One way crown on unprotected roads 63 

Effect of width on cost 6^ 

Minimum allowable widths 64 

Turnouts 65 

Typical Sections 66 

Side hill balanced section 66 

Through cut section 66 

Through fill section . 66 

Turnpike 66 

Wall sections 66 

Intercepting ditches 66 

Examples of typical sections . 68-73 

Chapter III. Drainage 74-127 

General Discussion 

Location of structures 74 

Spacing of relief culverts 74 

Design 74-77 

Size of opening 75 

Live and dead loads 76 

Width of roadway 77 

Type of structures 77 

Rates of rainfall 78 

Tables of runoff 79-^2 

Examples of railroad practice in sizes of opening for 

small drainage areas 80, 83 

Discharge capacity of small culverts 84 

Culverts 

Types. . .^ 83 

Size of opening 85 



I 



TABLE OF CONTENTS Xl 

Page 

Plugging of culverts by ice and snow 85 

Plugging of culverts by silt 85 

Side culverts 86 

Village culverts 86 

Private drive pipes 87 

Relative cost 87 

Examples of current practice in culvert design . . . 89-97 

Small Span Bridges 89 

Safe load on foundation soils . 89 and 98 

Safe pile loads 98 

Scour 98 

Rip rap 98 

Fords 99 

Examples of current practice 100-124 

Underdrains 

Porous tile 125 

Open throat 125 

Location and outlets 126 

Summary of the chapter 127 

Chapter IV. Eauth, Sand-clay, and Gravel Roads 

Limitation of practical satisfactory use 128 

Earth Roads 130-131 

Rut roads 130 

Ordinary turnpike roads 130 

Approx. cost 131 

Examples of current practice in sections 131 

Sand-clay Roads 

Principle of construction 131 

Mixtures 131 

Examples of current practice 134 

Approx. cost 137 

Gravel Roads 

Requirements of construction 137 

Suitable gravels 138 

Sizing 138 

Loam content 138 

Manipulation of gravel 139 

Typical specification 139 

Typical example of gravel sections 140-142 

Approx. cost 143 

Miscellaneous Special Cases 

Alaskan conditions 144 

Arid regions 146 



xii TABLE OF CONTENTS 

Page 

Chapter V. Gravel and Stone Foundation Courses. 147-162 

Bearing Power of Surface Soils .......... 147 

Concentrated Wheel Loads 148-150 

Regulation of loads 148 

Reasonable limits of load 148 

Ordinary present day loads 149-150 

Military ordinance 149 

Commercial trucks 150 

Farm wagons 150 

Thickness of Road Metal Required on Different Soils. 150-152 

Diferent Types of Foundation Courses 153-158 

Broken stone bottom course 153 

Screened gravel bottom course 154 

Pit run gravel bottom course 156 

Field stone sub-base 154 

Gravel sub- base 155 

Field stone sub- base bottom course 155 

Gravel sub-base bottom course 156 

Telford foundation course 157 

Distribution of Stone in Foundations 158 

Single track roads (8-12' wide) 158 

Double track roads (16-22' wide) 158 

Special Foundation Designs. ^ 158 

Enconomical Foundation Design 161 

Conclusion 161 



Chapter VI. Macadam Top Courses and Rigid 
Pavements 163-191 

Relative merits of macadam and rigid pavements. . 163 

Classification of traffic 164 

Traffic census, value of in design 164 

Types of Pavement 165-186 

Waterbound macadam 165 

Treated with calcium chloride , . . . 166 

Oil or tar 167 

Glutrin 167 

Bituminous macadams 169 

Penetration method 169 

Mixing method 171 

Topeka mix 171 

Natural rock asphalt . . . . . . ..... . . . 172 

Amiesite .- 172 

Sheet asphalt 1 73 

Brick pavement i73 

Stone block pavement 175 

Asphalt block pavement 176 

Concrete pavements i77 



TABLE OF CONTENTS xm 

Page 

Small cube surfaces 

Kleinpflaster • i8i 

McClintock cube pavement 182 

Rocmac 184 

Conclusion of Chapter 

Classification of pavements as safe for high speed 

traffic 186 

Classification of pavements as safe on steep hills . . 186 

Recommendation of pavements for different locations 186 

Common causes of failure *. 187 

Capitalized cost of different pavements under dif- 
ferent traffic 190 

Chapter VII. Maintenance 192-214 

Earth roads 192 

Sandy clay roads 197 

Gravel roads 197 

Macadam roads 199 

Rigid pavements 203 

General organization methods 205 

General costs 205 

Detail typical costs 212 

Chapter VIII. Minor Points 215-228 

Right-of-way width 215 

Clearing widths . . . 215 

Guard-rail 216 

Wooden 216 

Concrete 216 

Steel cable 218 

Snow fences 218 

Bridge rail 219 

Retaining walls 220 

Toe walls 222 

Curbs 223 

Guide and danger signs 224 

Rip rap 225 

Dykes 225 

Cobble gutters 226 

Refacing old walls . 226 

Storm sewers on hills ; 227 

Special drainage ditches . 228 

Cattle guards .- 228 

Chapter IX. Materials . . ... 229-265 

Top course. Macadam stone (tests and properties). . 229-239 

Screenings 239 



xiv TABLE OF CONTENTS 

Page 

Bottom course. Macadam stone 240 

Fillers 240 

Brick 240 

Bituminous Binders 241-253 

Concrete Materials 253-265 

Cement 252 

Sand 253 

Stone 254 

Gravel 254 

Slag 254 

.Water 262 

PART II 

Chapter X. Preliminary Investigations 266-322 

General Costs 266 

High Type Roads in Populous Districts 266-282 

Scope of investigation 266 

Field methods 267 

Sampling materials 269 

Estimates of cost . 273 

Sample report 274-282 

Pioneer Roads in Unsettled Districts. 282-320 

Scope of investigation 282 

Equipment 282 

Field methods 282 

Estimates of cost 283 

Tabular Compilation of Useful Information in Con- 
nection with Investigations of this Character . . 285-308 

Excavation amounts 285-296 

Grades expressed in degrees 297 

Right-of-way acreages 297 

Unit prices. , 297 

Masonry quantities . . . . 299 

Rule for computing ft. B.M. in logs 300 

Steel in bridges 301 

Magnetic declination 300-308 

Sample preliminary report 309-320 

Reconnaissance Surveys 321-322 

Methods 321 

Cost 321 

Chapter XL The Survey . 323-422 

High Type Roads (Improvement of Existing Roads) . . 323-384 

Center line ^ 323 

Levels and cross sections 325 

Drainage 327 

Topography ._ 328 

Traffic reports 329 

Foundation soils . . . 330 



TABLE OF CONTENTS XV 

Page 

Location and character of materials 331 

Right of way 333 

Stadia reduction tables 335 

Diversion lines 343 

Adjustment of instruments 343 

Curve tables and formulae 345 

Examples of curve problems 376 

Pioneer Roads (Nqw LocBitions) 384-422 

Cost and organization 384 

Equipment 385 

Base line 387 

7 Levels and cross sections 388 

Drainage 392 

Topography ^ 392 

Materials 394 

Survey report 394 

Meridian Determination] 

By polaris 394 

By direct solar 402 

Stadia work 416 

Chapter XII. Photography, Camp Equipment and 
Notes on Camp Medicine. 

Photography 423-435 

Equipment 424 

Time and aperture 425-430 

Effect of use of tripod 426 

Motion of object 426 

Altitude . 427 

Latitude .• 427 

Season of the year 427 

Light and phase 428 

Time chart 429 

Exposure record 430 

Developing 431 

Printing 433 

Camp Equipment 436-444 

List of articles 

Tableware 436 

Cooking utensils 436 

Hardware 437 

Tents and miscellaneous 438 

Sketches of handy equipment 439 

Camp Medicine and First Aid for Accidents . . . . . . 455-501 

Personal hygiene 445 

Clothing 445 

Bedding 445 

Diet 445 



xvi TABLE OF CONTENTS 

Page 

Baths 445 

Care of mouth and teeth 445 

Care of feet 446 

Fly and mosquito dopes 447 

Insect bites and stings 447 

Cures for vermin pests 447 

Medical and surgical supplies 449 

List of remedies and their use ]452 

Common Sickness (Symptoms and Treatment) , . . . 455 

Stomach and Bowels 

Constipation 455 

Colic 455 

Diarrhea 455 

Dysentery . 455 

Fevers 

Typhoid fever 456 

Malarial fever 456 

Throat and Lungs 

Sore throat 457 

Influenza . -. . 457 

Pneumonia 458 

Miscellaneous 

Headache 458 

Sunstroke 458 

Poison ivy 458 

Rheumatism 459 

Gonorrhea 460 

Nephritis 460 

Piles 460 

Accidents 

Minor Accidents 

Bruises 461 

Sprains 461 

Foreign matter in eyes, ears, nose or throat . . . 462 

Serious Accidents 

Snake bites 464 

Bad cuts 464 

Burns and frost bite 471 

Wounds. . 472 

Drowning and electric shock 476 

Poisons 481 

Fractures and dislocations 483 

Chapter XIIL Office Practice .......... 502-584 

For the Improvement of Existing Roads {High Types) . . 503-567 
Mapping the Preliminary Survey 

Scales. 503 



TABLE OF CONTENTS xvii 

Mapping {continued) Page 

Plotting center line 504 

Table of sight distances 504 

Plotting topography 505 

Bench level computations 505 

Cross-section level computations 505 

Plotting cross-sections 506 

Plotting profile 506 

The Design 

Maximum grades different pavements 507 

Shrinkage of earthwork 507 

Templets ^ 509 

Economical grade line design 509 

Vertical curves 

Formulae 511 

Sight distance . 513 

Radii for plotting 513 

Planimeter work 514 

Methods 514 

Accuracy . 514 

Substitute method 514 

Computation of earthwork (tables) SiS'SS? 

Overhaul 539 

Mass diagram 539 

Sample final design report 544 

Grade crossing elimination data 547 

Grade crossing alignment restrictions 549 

Right of way computations 549 

Summary of economical design 552 

Tables of quantities (stone, macadam, oil, sq. yards 

of pavement, etc.) . ^ . 540-554 

Tables of dimensions and sizes (pipe, mesh, steel, 

etc.) 555-560 

Tables of strength of materials (I-beams, concrete 

slabs, wooden beams and long columns) .... 561-567 
{h) Office Practice for Pioneer Road Design 

General methods (graphic or analytic) 567 

Drafting room instructions 568 

Drafting room supplies 568 

Detail design instructions 569-584 

Reasonable speed of design 569 

Reasonable cost of design 570 

Detail manipulation (organization and methods) . 570 

Progress report 578 

Sample estimate forms 581 

Chapter XIV. Cost Data and Estimates 585-661 

Macadam Roads 585-603 

Earth excavation 585 

Rock excavation 586 

\ 



xviii TABLE OF CONTENTS 

Page 

Unloading broken stone 586 

Hauling. 588 

Loading fence stone 590 

Spreading crushed stone 590 

Placing boulder stone 591 

Ratio of loose to consolidated depths . 591 

Amounts of filler and binder 591 

Loading filler sand and spreading . 591 

Spreading filler and binder. 592 

Rolling 592 

Crushing 593-599 

Cost of ......... 593-599 

Proportions of different sizes in output 594-599 

Sledging boulders for crusher 597 

Dustless screenings 599 

Stone fill, bottom course 599 

Sub-base, bottom course 600 

Applying bituminous binder 600 

Kentucky rock asphalt 602 

Puddling waterbound roads 602 

Pavements (Miscellaneous) 

McClintock cube surfacing 603 

Amiesite 604 

Topeka mix 607 

Hassam concrete pavement 607 

Mixed concrete pavement . 608-621 

Asphalt block pavement 610 

Concrete Culvert Work 621-625 

, Miscellaneous, 
Guard rail 

Wooden ; 625 

Concrete 626 

Cobble gutter 626 

Vitrified pipe 626 

Organization \ 

Speed of work 627 

Plant and payroll 627-631 

Forms for Estimate^ 

Sample estimate macadam construction ...... 632-640 

Unit Prices Minor Items 640 

Sample average haul forms of estimate 641 

Brick Pavements on Country Roads 647-653 

Excavation 647 

Concrete base 648 

Preparing cushion 649 

Laying brick 649 

Grouting brick 649 



TABLE OF CONTENTS xix 

Page 

Expansion joints 649 

Edging 648 

Unloading brick 650 

Hauling brick 650 

Form of estimate 651 

Sample estimate 651 

Maintenance and Repair 653-661 

Cold oiling 653 

Hot oiling 655 

Calcium chloride 655 

Recapping 655 

Scarifying and reshaping 658 

Patrol maintenance 660 

Automobile maintenance truck 660 

Distribution of maintenance charges (actual cost one 

year) 661 

Chapter XV. Notes on Construction (Inspection) 662-697 

Staking out 662 

Rough grading 664 

Fine grading 666 

Sub-base 667 

Bottom stone 669 

Top courses (macadams) 670 

Hassam concrete pavement 672 

Mixed concrete pavement 673 

Sheet asphalt pavement 677 

Brick roads 679 

Pipe culverts 683 

Concrete culverts ^ 685 

PART III 

■ Specifications 698-824 

Discussion of requirements 698 

General Outline of Clauses (U. S. Office of Public 

Roads) 699-709 

Examples of Current Practice (Roads and Pavements) 

General clauses (U. S. Forest Road Specifications) . 710-717 
Materials 

Portland cement (New York State Specifications). 717 

Water for concrete (New York State Specifications) 718 

. Concrete sand (New York State Specifications).. . 718 

Grout sand (New York State Specifications) ... 719 

Cushion sand (New York State Specifications)*".. . 719 
Coarse aggregate for concrete (New York State 

Specifications) 719 

Stone and gravel for pavements (New York State 

Specifications) . 720 



XX TABLE OF CONTENTS 

Page 
Bituminous materials (New York State Specifi- 
cations) 721 

Brick (New York State Specifications) 730 

Stone block (New York State Specifications) . . . 735 

Asphalt block (New York State Specifications) . . 787 

Wood block (New York State Specifications) . . . 790 

Cast iron pipe (New York State Specifications) . 736 

Reinforcement (New York State Specifications) . 736 

Cast iron (New York State Specifications) .... 736 

Wrought iron (New York State Specifications) . . 736 

Steel (New York State Specifications) 73 7 

Vitrified pipe (New York State Specifications) . . 737 

Concrete pipe (U. S. Forest Road Specifications) . . 738 

Corrugated pipe (U. S. Forest Road Specifications) 739 

Porous tile (N.^ Y. State) . , . . 740 

Timber (Washington State Specifications) .... 740 

Piles 740 and 804 

Construction Methods 

Pipe culverts (U. S. Forest Road Specifications) . . 737 
Log culverts and Bridges (U. S. Forest Road 

Specifications) 740 

Clearing and grubbing (State of Washington 

Specifications) 742 

Excavation (New York State Specifications) . . . 743 
Overhaul (New York State Specifications) .... 745 
Tiles and underdrains (New York State Specifi- 
cations) 745 

Leaching basins (New York State Specifications) . 746 
Catch basins (New York State Specifications) . . 747 
Cast-iron pipe culverts (New York State Specifi- 
cations) 747 

Stone fill (New York State Specifications) .... 748 

Piles (New York State Specifications) 748 

Timber and lumber (New York State Specifications) 748 

Riprap (New York State Specifications) 749 

Concrete masonry (New York State Specifications) 749 
Stone masonry (New York State Specifications) . 752 
Stone curbing (New York State Specifications) . . 753 
Concrete curbing (New York State Specifications) 754 
Concrete edging (New York State Specifications) . 754 
Cobble gutters (New York State Specifications) . 754 
Concrete gutters (New York State Specifications). 755 
Brick gutters (New York State Specifications) . . ,755 
Concrete reinforcement (New York State Speci- 
fications) 755 

Guard rail (New York State Specifications) ... 75^ 

Guide signs (New York State Specifications) ... 757 

Sign posts (New York State Specifications) .... 75^ 

Loose stone (New York State Specifications) ... 75^ 



TABLE OF CONTENTS xxi 

Page 

Sub- base courses (New York State Specifications) . 759 

Telford (New York State Specifications) 759 

Bottom course (Gravel and macadam) (New York 

State Specifications) 760 

Bottom courses (concrete base) (New York State 

Specifications) 761 

Earth road construction (Iowa Specifications) . . 763 

Gravel road construction (Iowa Specifications) . . 766 

Chert roads (Alabama Specifications) 771 

Gravel roads (Alabama Specifications) 772 

Sand clay roads (Alabama Specifications) .... 773 
Waterbound Macadam pavement (New York 

State Specifications) 774 

Scarifying and reshaping (New York State Speci- 
fications) .... 776 

Bituminous surface treatments (New York State 

Specifications) .777 

Bituminous macadams (New York State Speci- 
fications) ... 778 

Bitulithic pavement (New York State Specifications) 782 

Amiesite pavement (New York State Specifications) 783 
Hassam concrete pavement (New York State 

Specifications) 784 

Mixed concrete pavement (New York State 

Specifications) 785 

Glutrin 786 

Wood block pavement (New York State Speci- 
fications) 787 

Asphalt block pavement (New York State Speci- 
fications) 790 

Brick pavement (sand cushion) (New York State 

Specifications) 791 

Brick pavement (cement sand cushion) (Dunn Wire 

Cut Lug Specifications) 794 

Stone block pavement (City of Rochester Specifi- 
cations) 799 

Highway Bridge Specifications (State of Iowa) 

Giving materials and manipulation 800-824 

Widths of bridges 807 

Standard loadings 805-806 

Standard stresses 807-808 

Floorings, etc 805, 821 

PART IV 

General Tables and Formulce. 
Table No. 

68. Conversion of units of measure 825 

69. Conversion inches to decimals of a foot .... 826 



xxii TABLE OF CONTENTS 

Page 

70. Areas and volumes 828 

71. Squares, cubes, square roots, cube roots circum- 
ferences and circular areas i to 520 830 

72. Trigonometric functions and formulae 843 

73. Table of natural tangents and cotangents . . . 845 

Table of natural sines and cosines 857 

Table of natural secants and cosecants 868 

74. Table of logarithms of numbers 880 

75. Table of logarithmic sines, cosines, tangents and 
cotangents 905 

76. Weights of materials 950 

77. Strength of materials . 951 

78. Flexure formulae of beams 952 

79. Centers of gravity 954 

80. Moments of inertia 955 

Appendix A 

Traffic Rules and Regulations J Stale of Ohio 957 

Traffic Rules and Regulations, State of New York . . . 968 

Index 971 



HANDBOOK 

FOR 

HIGHWAY ENGINEERS 



INTRODUCTION AND GENERAL ANALYSIS 

The highway question can not be treated as a local issue, as with 
limited funds it is often impossible to make improvements that 
are necessary to pioneer development, or that are suitable for 
modern long distance traffic. The national importance of the 
problem is recognized by the steady growth of State and Federal 
aid, which has already done much to improve engineering control 
and to increase financial resources. In many localities, however, 
it is still impossible to obtain enough money for proper design, 
and for these cases any solution is more or less ,unsatisf actory from 
an engineering standpoint. 

Road design ranges from the low type earth roads of sparsely 
settled districts to the hard surfaced pavements of densely popu- 
lated sections. For these extreme conditions the issues are clear 
cut; the first requires the greatest possible mileage with limited 
funds, and the last the most suitable design regardless of first cost. 
Intermediate cases are handled by merging the requirements pre- 
sented by the extremes. A reasonable design for any case depends 
on the needs and resources of the local community, considered in 
connection with the importance of the improvement to the general 
transportation scheme of the country and the aid that will be 
granted on account of its general importance. 

High type pavements should never be designed unless the 
community is able to provide its share of the construction cost by 
either direct appropriation, or short term, or serial bonds based on 
the probable life of the pavement, and in addition, to raise by 
some form of vehicle tax or direct appropriation its part of an 
annual maintenance and renewal fund of from $500 to $1000 per 
mile. States similar to New York, with an assessed valuation 
averaging $240,000 per square mile and a population averaging 
210^ per square mile have demonstrated their willingness and 
ability to raise any amount required for the construction of the 
most suitable types of road, considering traffic conditions and 
economy of maintenance, but even these states have not yet made 
adequate provision for maintenance and renewal . States similar 



2 INTRODUCTION AND GENERAL ANALYSIS 

to Wyoming, with an assessed valuation of $2000 per square mile, 
and a population of 2 per square mile, can not handle road con- 
struction in a conclusive way. They must adopt the method of 
progressive improvement. This represents the pioneer condition 
where the road question is most vital. Highways are a necessity 
to their development, and are considered primarily as a means 
of communication, not as pleasure routes, nor their improvement 
as a refinement to reduce the cost of transportation to a minimum. 
The people are willing to provide all the money they can afford, 
but expect some form of construction which will complete a line 
of communication to the point desired; a pack trail will do, a 
wagon trail is better, and an ordinary earth road will generally be 
accepted without question. 

The same engineering principles apply to both conditions but 
the emphasis is different. Where the funds are practically un- 
limited, the problem is comparatively easy and is strictly technical. 
Where the funds are limited to inadequate amounts, the solution 
is more difficult; the engineer must decide where technical require- 
ments should be retained and where ignored; he must plan the 
work so that whatever is done will become, if possible, a useful 
part of any future improvement, but above all a line of communica- 
tion must be opened. In the design of high type roads the engineer- 
ing emphasis is placed on safety, ease and economy of travel and 
maintenance. On pioneer roads the emphasis is placed on the 
selection of the best natural economic and engineering location 
and the greatest mileage for the funds. 

We have therefore arranged the discussion of design practice from 
standpoints required for each case, and have indicated in the 
chapters on Grade, Alignment, Sections, etc., the road value of 
different limiting engineering requirements with their effect on 
construction cost. 

ENGINEERING DESIGN 

Functions of Grades, Alignments, etc. — A well-proportioned 
design considers the relative value and the object of the different 
engineering elements of the problem. In this connection we may 
say that grades, alignment and section are the most permanent and 
fundamental features of construction. The ruling grade largely 
controls the loads that can be hauled; section, grade and alignment 
combined determine the convenience of the road and the economy 
of earthwork, while alignment and section affect the safety and are 
also important factors in the appearance of the highway. For 
these reasons these three points must be ranked as equal and first 
in importance. 

The next elements to be considered are drainage, foundation 
and top course, which keep the section firm and intact under traffic 
and weather action. Washouts are prevented and the bearing 
power of the soil is increased by surface and sub-surface drainage; 
the heavy concentrated wheel loads of vehicles are spread over 
a safe area of the sub-grade by the foundation course; the top 
course provides a surface that will withstand the abrasive action of 



ENGINEERING DESIGN 3 

wheels and horses' shoes, that gives a good footing and offers slight 
rolling resistance. At the present time the problem of the top course 
is troublesome, on account of the conflicting demands of horse and 
automobile traffic. There is so much discussion of this one fea- 
ture that it is easy to give it too much weight and there is a tendency 
to economize on the more permanent elements of construction 
in order to get a higher grade top. In the writer's opinion this is a 
mistake. The different top courses will be discussed in detail, but 
no definite conclusions can be drawn, as this part of the design is 
subject to constant change and improvement. 



The Application of the Order of Importance of the Elements of 
Design to General Cases 

Pioneer Roads. — Considering the policy of progressive improve- 
ment, limited funds should be expended as far as possible for 
essentials which will eventually become integral parts of the 
complete and finished design. The engineering requirements 
are listed below in their order of importance. 

First. — Selection of the best general route, 

(a) Best location for the development of the territory. 
(&) Longest open season, 
(c) Least rise and fall. 
{d) Length and cost. 

Second. — Selection of the most natural engineering location follow- 
ing the desired general route. 

(a) Reasonable grades. 

(b) Exposure. Avoid north exposure and areas of deep 
snow. 

(c) Character of excavation. Avoid rock, slides, etc. 

(d) Drainage problems. Avoid flood areas, stream cross- 
ings, etc. 

(e) Avoid artificial restrictions such as section line locations, 
etc. 

Third. — Detail requirements of design. 

(a) Reasonable maximum grade. 

(b) Economical intermediate grades. 

(c) Safe and economical alignment. 

(d) Width of roadway safe for trafiic. 

{e) Width of roadway convenient for traffic. 

if) Sufficient culverts and bridges to protect the roadway. 

ig) Permanent construction of these culverts and bridges. 

(h) Sufficient width of clearing for sun to reach road. 

(i) Safety provisions. Protection for traffic at dangerous 

places. 
ij) Provision of liberal width of right-of-way considering 

future widenings and development. 



4 INTRODUCTION AND GENERAL ANALYSIS 

Fourth. — Improvement of the road surface. 
(a) By selective soil treatment. 
{h) By gravel, chert, caliche, etc. 
(c) By hard surfaced pavements. 

The following typical cases illustrate the usual problems that 
occur, and indicate their general solutions. 

Where no road exists and the funds are entirely too small for 
good construction, a sufficiently cheap design is used to complete 
the entire length. Under these conditions the only requirement 
that must be met is the proper selection of general route, although 
it is probable that for the greater part of the distance the final 
engineering location can be followed. Considerable work of this 
kind has been done in New Mexico under the direction of State 
Engineer James A. French, and the solutions are ingenious. Satis- 
factory wagon and automobile trails have been constructed under 
favorable conditions for as low as $5.00 per mile (see page 130), 
while in difficult locations advantage has been taken of all possible 
expedients to keep the cost down. 

Where a poor but usable road exists between the terminal points, 
or for a portion of the distance, either the uncompleted or worst 
sections of the route are first considered. Under such circum- 
stances the funds are generally sufficient to permit a moderately 
good engineering design, which must provide for the proper final 
grade and drainage scheme on the improved sections, although 
the drainage structures may be cheap and temporary and the road- 
way narrow. 

Where a fair road has been previously built over the entire route, 
no improvement should be attempted unless it provides for the 
best engineering design of grades, alignment, section and permanent 
drainage structures. 

Where a first-class natural soil road is in use, the next step in 
progressive improvement requires either selected soil, gravel or 
hard surfaced construction of the traveled way. 

Order of Work Pioneer Road Design. — The methods employed 
for the field and office work are described in Chapters X, XI and 
XIII. Engineering of this nature forms the most interesting 
class of highway work, and is handled in three stages. 

A preliminary investigation is made to determine the general 
route, the best engineering location and the approximate cost of 
construction. It forms the basis for the general scheme of financing 
and design. It is the most important feature of new road location, 
and if well done insures the completion of a reasonable program 
of construction with the funds at hand. It also prevents wasteful 
expenditure on ill considered or unsuitable location surveys and 
plans. The detail location survey based on the preliminary 
conclusions is next made to secure the data for the final ofiice 
design, which carries out in detail the recommendations of the first 
report and completes the work preliminary to construction. 

Relative Order of Importance of Design Detail for Hard Surfaced 
Roads. — High type pavements in populous districts are necessary 



MAINTENANCE AND RENEWAL 5 

to meet heavy traffic requirements. They reduce the cost of 
hauling and increase the ease and safety of light and heavy traffic. 
The parts of the design are more or less important in proportion 
to their necessity for the fulfillment of these purposes, and may be 
ranked as follows: 

1. <jrades. 

2. Alignment. 

3. Sections. 

4. Drainage. 

5. Foundations. 

6. Top courses. 

7. Minor details. 

It can be seen by comparison that the details of hard surfaced 
road design have the same order of importance as for low type 
roads. The order of engineering procedure is also the same. The 
character of the information for the preliminary investigation is 
different, but the object is identical; namely, to provide a basis for 
appropriations and reasonable design. The preliminary data deals 
largely with probable traffic, available local materials and the 
most suitable and economical pavement type. The location sur- 
vey provides the essential data for design, using somewhat better 
methods than for mountain conditions, and the office work is more 
detailed and complete. The methods are described in Chapters 
X, XI and XIII. 

The application of the order of importance of design elements 
for hard surfaced pavement work can be shown by three cases: 

Under the most favorable conditions outlined in the introduction, 
the improvement is considered final and its design is based on an 
effort to obtain the most useful, and in the end the most econom- 
ical form of construction regardless of first cost. In this case all the 
engineering requirements may be fulfilled. 

In many communities, however, the funds are only sufficient to 
build a moderately good pavement, which will have to be bettered 
by reconstruction in a few years, to meet the demands of the traffic. 
An improvement of this kind should be permanently and com- 
pletely designed for proper grades, alignment, section, drainage and 
safety provisions, and the balance of the money spent on the best 
type of hard surface that can be afforded. 

The third case is reconstruction, which usually confines the 
problem to considerations of the most suitable type of re-surfacing, 
utilizing previous work to the best advantage. 

Maintenance and Renewal. — In presenting construction design 
for the approval of a community the cost of maintenance and the 
renewal of its temporary features should be fully explained in order 
that the cost of such work may be provided for. The amount re- 
quired for adequate maintenance is rarely appreciated and the 
comparatively short life of any road surface is not a matter of 
general knowledge. Maintenance costs are discussed in Chapter 
VIII and the following Table No. i supplemented by Tables 
No. 21 and 22, Chapter VI, page 190, give a rough idea of the cost 
and length of life of the temporary features of typical hard pave- 



INTRODUCTION AND GENERAL ANALYSIS 



ment types. Table No. i is based on 200 miles of 16 ft. width 
macadam and brick in Western New York. A well-designed earth 
road can be considered as 90% permanent. 

Table i 



Brick 



Cost 
per 
mile 



% Total 
Cost 



Bit. Mac. 



Cost 
per 
mile 



% Total 
Cost 



Water Mac. 



Cost 
per 
mile 



% Total 
Cost 



•Excavation 

•Drainage Structures. , 

•Foundations and sub- 
base 

, Surfacing 

.Edging 

. Minor points 

•Total Permanent fea- 
tures 

" Temporary fea- 
tures 

. Probable life " 



$2200 
700 

6300 

I 14700 

500 

9200 

15200 



9.0 

2.8 

25-9 

60. 1 

2 .2 

37-7 
62.3 



10 to 25 years 



II900 
700 


15 

5 


9 
3 


3300 


27 





5900 


47 


S 


500 


4 


3 


5900 


48 


2 


6400 


SI 


8 



6 to 12 years 



$1900 
700 

3300 

4000 

500 

5900 

4500 



18.3 
6.7 

31.7 
38.5 

4.8 

56.7 
43-3 



5 to 10 years, 



Road Bonds. — Extensive road programs are usually financed by 
long term bonds, fifty-year bonds being very generally used. 
This practice has been justly criticized, as large amounts of money 
will be required for construction renewals before the original 
bonds expire, except in the case of dirt roads. Serial or short 
term bonds, based on the probable life of the pavement, are more 
rational. 

General Summary. — The general analysis may be summarized 
as follows: 

The details of economic highway design are everywhere a local 
problem depending on the available materials, climatic conditions 
and traffic requirements. We know of no one who has had enough 
personal experience in the design, construction and maintenance of 
the various types under different sectional requirements to pose 
as an expert over any extended part of the country except on very 
general lines. 

The chief factors which govern the cost of a highway system 
are legislative and finance programs which should provide the nec- 
essary money at the proper time; an engineering design which at 
all times should strive to use local materials to advantage, and a 
construction staff to insist on good workmanship. (The costs 
given below are based on labor and material costs prevailing from 
1912 to 1916.) 

I. The financing of many State systems of highways has never 
been well worked out for either construction or maintenance; 
what applies to them we believe is true of a large percentage of 
cases. A reasonable finance program depends on compliance with 
the following facts: The permanent features of a highway im- 



GENERAL SUMMARY 7 

provement are the grading, drainage and foundation. The sur- 
facing is temporary even for the so-called "permanent " types. The 
rigid pavements such as brick, asphalt, concrete, etc. need resur- 
facing in from ten to twenty years; the macadam in from five to 
twelve years. The ordinary maintenance for the rigid types will 
run about $150 per mile per year with a resurfacing charge of 
$10,000 to $15,000 per mile at intervals of about 15 years. The 
ordinary maintenance on macadams is about $500 per mile per year 
with a resurfacing charge of $4000 to $6000 at intervals of seven to 
ten years. The ordinary maintenance of earth and sand clay roads 
runs from $30 to $150 per mile per year. The ordinary main- 
tenance of gravel roads from $100 to $500 per mile per year. The 
yearly cost of maintenance and renewals amounts to from $50 
to $500 per mile for earth, sand-clay and gravel roads and from 
$700 to $1000 per mile for macadams and rigid pavements. Pro- 
vision for the necessary amounts is rarely made which results in a 
gradual deterioration of the roads and will finally occasion an un- 
necessarily large expenditure to put the systems back in good 
condition. Proper provision should be made for maintenance and 
renewal or a large future waste is certain to occur. ^ A foresighted 
policy in this particular would save the community more than 
any economies of the design. 

2. The engineering design rests on the consideration of con- 
struction, maintenance and renewal costs. In discussing this 
problem most of the current literature and highway speakers empha- 
size and confine economies to the selection of pavement type. 
This is a natural result of the exploitation of various materials and 
patent processes. As a matter of fact our experience indicates 
that for 75 to 80% of the roads the final cost is not greatly affected 
by the selection of type except as it governs the use of local materials. 

In general the high and low-priced pavements cost about the 
same, considering interest on first cost, maintenance and renewals. 
What is saved on first cost is spent on maintenance. The real 
engineering economies are limited to a careful grading and safe 
foundation design utilizing local materials, and to a selection of 
the cheapest first cost type of pavement of the general class re- 
quired by the traffic; that is a rigid type for very heavy traffic and 
for all ordinary roads any type which will utilize local materials 
to their best advantage. On from 75 to 80% of the mileage of most 
State systems, any standard type of construction which will satisfy 
the traffic and which is the cheapest in first cost will generally be 
the cheapest in the end. 

3. The inspection of construction has a marked effect on final 
cost and on public work there is a great variation in the care and 
knowledge of the inspectors. Well built macadams are much 
cheaper in the end than poorly constructed brick or concrete. 
The problem of improving inspection is a difficult one and the 
results appear to be spasmodic. If good inspection is not reason- 
ably certain, the more nearly "fool proof" macadams are the most 
economical form of construction. 



8 INTRODUCTION AND GENERAL ANAI.YSIS 

Value and Cost of Engineering Advice. — Sound financial and 
construction programs must be based on technical data and judg- 
ment. As a rule engineering advice is solicited and followed for 
the minor details of design and construction but is too often ignored 
or dispensed with in deciding on the general plan of action. This 
has resulted in patchwork systems; in poor legislative programs 
for maintenance and sometimes in a complete set back for high- 
way improvements for a number of years. 

The details of grade, alignment, section and drainage are usually 
solved on engineering principles except that in sotaie localities 
the influence of patented culvert propoganda overcomes sub- 
stantial design. The selection of pavement type however is often 
determined by popular vote or by the choice of non- technical boards. 
It is an unfortunate fact that very often communities, officials and 
engineers are susceptible to a continuous well planned advertising 
campaign and to the more or less proper and improper methods of 
approach of material salesmen, patented pavement promoters and 
influencial citizens. Current engineering literature is full of 
inspired articles and the rosy hued optimism is to use a slang phrase 
''pure bunk.'' Each well established pavement has certain ad- 
vantages which are desirable under different conditions but the 
proper selection is a difficult matter which can be handled by an ex- 
perienced engineer with better chances of success than if left to the 
limited knowledge of the community influenced by the silver ton- 
gued persuasiveness of the man with something to sell. 

What, however, is more important is the preliminary layout of a 
comprehensive scheme of complete future improvement and the 
designing of each separate construction job as a part of the whole 
scheme rather than as a problem by itself. Hardly less necessary is 
the inauguration of a foresighted plan for obtaining enough yearly 
upkeep funds to prevent the partial or total loss of such improve- 
ments. This requires thorough preliminary study and the expendi- 
ture of considerable money for which there is apparently no imme- 
diate return, but so many ill considered, disappointing programs 
have resulted from the lack of this work that we can not over- 
emphasize its importance. 

At the present time road expenditures in the United States 
amount to approximately $300,000,000 per year and it can be 
said without undue criticism that the problem is entitled to more 
intelligent planning than it is now receiving. It is well worth the 
best engineering talent and sufficient initial expenditure to assure 
a workable scheme. Careless or inadequate investigation, survey 
and design are worse than useless and tend to discredit the value of 
engineering in connection with highway improvements. There is 
no doubt that any amount of money that may be required for 
thorough planning is justified by the resultant saving in construc- 
tion cost and by the increased usefulness of the improvement but 
there is also no doubt that much of the money spent for inadequate 
engineering is absolutely wasted. This fact is recognized by the 
State and Government Departments which are conducting an 
educational campaign to raise the standard of highway work. 



VALUE OF ENGINEERING ADVICE 9 

Satisfactory preliminary engineering costs from $100 to $300 per 
mile and amounts to about the same whether the proposed road is 
to cost $1000 per mile or $30,000 per mile. This is regarded with 
suspicion by men accustomed to figuring the cost of engineering as 
2%, 4% or 6% of the construction cost but it should be borne in 
mind that it is more a mileage proposition than a percentage of 
construction proposition; that the cost is largely necessary for the 
location and grading design which is the same for low and high 
cost roads; that pioneer road location must consider the future 
development of the country and that the engineering cost in com- 
parison with the amount of money which will immediately be 
spent on construction is of no importance whatever provided a 
proper location is made. Many of the older well settled com- 
munities are now suffering from originally poor road locations and 
it is hoped by all concerned that these mistakes will not be repeated 
in the construction of the new roads in the West. 

Highway engineering in this country is still in the infant stage 
but growing lustily. It represents the systematic element of the 
road movement. The road improvement programs as expressed 
by current legislation are not logical nor could they reasonably be 
expected to be efficient as they represent a compromise between 
the conflicting ideas of earnest and flippant folks and profiteers. 
They contain a large element of humor and camouflage and a 
dash of efficiency. It is undoubtedly desirable to increase the 
percentage of efficiency somewhat but too much of that quality 
is not pleasing as popularly expressed by an unknown genius, 

"Who is it takes the joy from Hfe and makes existence Hell, 
Who'll fire a real good looking one because she can not spell, ' 
Who'll substitute a dictaphone for a coral tinted ear 
The penny chasing, dollar wasting efficiency engineer." 

However, the fact remains that tax-payers desire to have their 
money spent with care and as there is rarely much difficulty in 
inaugurating a road program up to the limit of the financial ability 
of the community it seems well worth while to get the best results 
that are possible. 



PART I 

PRINCIPLES OF DESIGN 

Order of Discussion.— The detail discussion of design will be 
taken up in the following chapters in their order of importance 
indicated on page 5 as follows: 

Grades and Alignment. 

Sections. 

Drainage 

Foundations. 

Top Courses. 

Minor Points. 

CHAPTER I 

GRADES AND ALIGNMENT 

The subject of "Grades" may be treated under sub-headings 
of ''Maximum/' ''Minimum," "Intermediate" and "Adverse." 

MAXIMUM OR RULING GRADES 

The following considerations govern the design of ruling grades : 

1. The relative importance of horse and automobile traffic. 

2. The difficulty of ascent and the ease and safety of descent. 

3. The effect of length of grade on maximum load. 

4. The theoretical advantage of certain grades. 

5. The ruling grades in ordinary use and practical considerations 
governing their selection. 

6. The effect of ruling grade on cost. 

I. Relative Importance of Horse and Automobile Traffic in 
the Selection of Grade. — The remarkable development of me- 
chanical transportation on rural highways entitles this class of 
traffic to every consideration within reason, but at the present time 
and for a long future period may reasons indicate that horse traffic 
will govern the selection of grade in most cases. This conclu- 
sion is based on the greater adaptability of team hauling to adverse 
conditions; on the probability that as long as stock is used for or- 
dinary farm work it will be utilized to some extent for hauling 
even under conditions favorable for trucks; and on the fact that 
grades suitable for horses afford no hardship to mechanical out- 
fits. All of the trucks and tractors in use have sufficient power to 
haul their loads on firm surfaced roads up any grade that would 
be selected for horse traffic and while a reduction in grade below 
these rates would reduce operating costs slightly, this consideration 
would hardly warrant any large expenditure at this time. The theo- 
retical discussion is therefore developed on the basis of horse traffic . 



ASCENT AND DESCENT li 

2. Difficulty of Ascent and Safety of Descent. — The factors 
controlling ease and safety of ascent and descent have different 
values for different surfaces, but as most of the roads will in time 
be hard surfaced and as all parts of the design should fit into the 
final improvement, this part of the grade argument is made 
primarily for hard surfaced conditions. 

European observers claim that on a stone road 5 % is the maxi- 
mum grade that can be descended safely by a trotting team with- 
I out brakes and that 12% is the maximum that can be safely de- 
scended with brakes. By the use of the sliding shoe or locked 
wheels freighters in the Rockies descend 20% grades without 
much difficulty on ordinary natural soil roads. Safe descent with 
brakes need not be considered except in rare cases as it would 
result in a grade far beyond ordinary practice. Safe and easy 
descent without breaks is more important for light rigs than for 
heavy hauling but as this class of traffic has been practically elimi- 
nated by cheap automobiles it need not be given much weight. 
Descent, therefore, plays only a minor part in grade selection. 

The writer knows of no careful records of actual maximum 
loads that can be hauled up different hard surfaced grades by an 
ordinary team; it is probably better to discuss this point theo- 
^ retically as any experiments would be affected by too many vari- 
j able local conditions to be worth much as a basis of comparison. 
I As a check on the theoretical discussion records of loads on ex- 
' treme mountain grades are given on page 16 which show that for 
' all practical purposes, Table No. 7 of theoretical loads is fairly 
, close and is on the safe side. 

' A summary of Prof. I. O. Baker's discussion of maximum team 
I loads is given below, and through his courtesy we are enabled to 
include a collection of tables taken from his work, "Roads and 
i Pavements." _ 

Various trials have determined that the normal tractive power 
of a horse traveling three miles per hour for ten hours a day is 
approximately one- tenth of its weight; that when hauling up a 
steep grade it can exert one-fourth of its weight for a short time; 
that for a continuous exertion of one-fourth, the grade should not 
be over 1200 feet long and if over that, resting places should be 
provided every 600 to 800 feet; that in starting and for a distance 
of 50 to 100 feet, one-half of its weight can be used; and that the 
net tractive power ordinarily exerted by a horse on a grade equals 
(J^ its weight) — (the effort required to lift itself) or approximately 
(0.25 W) — (WX % of grade expressed in hundredths) i.e. (0.25 W— 
0.04 W) for a 4% grade. This undoubtedly gives a reasonable 
basis for ordinary hauling conditions but from data obtained by the 
author in connection with freight hauling in mountain regions it 
is evident that a good draft horse will exert more than 0.25 W 
on moderately short sharp pitches of a long climb if allowed to 
rest at intervals of 200' to 300'. The evidence indicates that a 
value of 0.35 W is about right for such conditions. 

Table 2 shows the effective power developed by an ordinary 
team of 1200 pound horses with moderate exertion and Table 2 A 



12 



GRADES AND ALIGNMENT 



the power of a first class team of 1600 pound horses exerting their 
full strength. 

Table 2. — Ordinary Stock Moderate Exertion 





Grade 


Theoretical Net Tractive Effort 
Tractive Effort in Pounds 


W = weight of team, 
2400 lb 


Level 

2i % 

4 % 

5 % 

6 % 

7 % 

8 % 

9 % 
10 % 


O.IO W 

0.25 W-PW 
0.25 W-PW 
0.25 TF-PTF 
0.25 W-PW 
0.25 W-PW 
0.25 TF-PT^ 
0.25 TF-PPF 
0.25 TF-PTF 


240 
540 
504 
480 
456 
432 
408 

384 
360 


P = per cent, of 
grade in hun- 
dredths 



Table 2A. — Draft Stock Full Power 





Grade 


Theoretical Net 
Tractive Effort 


Tractive Effort 
in Pounds 


W = weight of team, 
3200 lb 

P = per cent, of 
grade in hun- 
dredths 


5% 

6% 

7% 

8% 

10% 

12% 

14% 

16% 

18% 

20% 

22% 


0.35 W-PW 
0.35 W-PW 
0,35 W-PW 
0.35 W-PW 
0.35 W-PW 
0.35 W-PW 
0.3s W-PW 
0.35 W-PW 
0.3s W-PW 
0.35 W-PW 
0.35 W-PW 


960 

928 

896 

864 

800 ■ 

736 

672 

608 

544 
480 
416 





This power is used in overcoming axle friction, gravity resistance 
and rolling resistance. 

The axle friction is small amounting to three or four pounds per 
ton for American farm wagons. 

Grade resistance (gravity) equals (load X per cent, of grade 
expressed in hundredths) and expressed in pounds per ton of load 
equals (2000 X P). 

The rolling resistance varies for different surfaces and for each 
surface depends on the diameter of wheel, width of tire, speed of 
travel and the presence or absence of springs on the wagon. The 
best diameter of wheels, best width of tires and the use of springs 
as they affect the ease of hauling for both farm and road use are 
problems for the wagon manufacturers. 



TRACTIVE RESISTANCE 



13 



Morin a French engineer concluded, from a series of careful 
experiments that the harder the surface of the road the less effect 
width of tire had on rolling resistance. We are arguing from the 
standpoint of comparatively hard surfacing and are dealing with 
small dififerences in wheel diameter and can disregard these fac- 
tors. As a matter of interest Tables 3, 4 and 5 are included to 
show the results of experiments on different soils and roads. 

The question of wide tires affects road design chiefly in connection 
with the distribution of load over a safe area and will be taken up 
under "Foundations." 

Table 3. — Effect of Width of Tire upon Tractive Powers 
Resistances in Pounds per Ton 



Ref. 
No. 


Description of the 
Road Surface 


Diameters of the Front & Rear Wheels respectively 


S'-S" & 3-6'' & 
3-10" 1 3-10'' 


3-8'' & 
4'-6'' 


3'-6» & 

3-icy 


3-8" & 
4'-6'' 


i^- 


4" 


Wi 


dth 

4" 


c 
If' 

236 
141 

83 
35 


f 

254 
168 

80 
46 


Ti 

i|'' 

283 
152 


res 
3" 

239 

152 

54 


189 
265 

66 

28 


3" 

228 
114 
228 

76 
38 


I 
2 
3 
4 
5 
6 
7 


Sod 

Earth road (hard) . . . 

" " (muddy) 
Sand " (hard) .... 

(deep) 

Gravel road (good) . . 
Wood Block (round) 


199 

371 

51 


108 

162 
351 

49 


268 
171 

98 
6i 


304 
164 

117 
70 



1 Pamphlet by Studebaker Brothers Manufacturing Company, 1892. 

Table 4. — Effect of Size of Wheels on Tractive 
Resistance 1 Pounds per ton 



Ref. 

No. 


Description of Road Surface 


Mean Diameter of 
Front & Rear Wheels 


SO" 


38- 


26" 


I 
2 
3 

4 
5 
6 
7 
8 

9 
10 


Macadam, slightly worn, fair condition 

Gravel road, sand 1" deep, loose stones 

" " upgrade 2.2%, one-half inch wet 
sand, frozen below 


57 
84 

69 

lOI 

132 
173 
178 
252 


61 
90 

132 
75 
119 
145 
203 
201 
303 


70 
no 

173 
79 
139 
179 
281 
265 
374 


Earth road. Dry and hard 


" " h'^ sticky mud, frozen below 

Timothy & blue grass sod, dry grass cut 

" " " " " wet & spongy 

Cornfield; flat culture across rows, dry 

Plowed ground; not harrowed, dry & cloddy . . 
Average Value of Tractive Power 


130 


148 


186 





1 Experiments of Mr. T. I. Mairs at the Missouri Agricultural Experiment Station. 



14 



GRADES AND ALIGNMENT 






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TRACTIVE RESISTANCE 



IS 



Table 6 gives the average rolling resistance in pounds per ton of 
load on different pavements for the ordinary farm wagon driven 
at ordinary speeds. 



Table 6^ 



Kind of Pavement 


Rolling Resistance in Lbs. 
per Ton of Load 


Asphalt 


30 to 70 
15 to 40 
50 to 100 
50 to 200 
50 to 100 
20 to 100 
30 to 50 
30 to 80 
30 to 50 


Brick 


Cobble Stones 

Earth Roads 


Gravel Roads 


Macadam Roads 

Plank 


Stone Block 


Wood Block 





1 Baker's "Roads and Pavements." 

For a comparative estimate we will take a value of forty pounds 
per ton of load, including axle friction, on Macadams and Rigid 
Pavements and one hundred pounds per ton for earth roads in fair 
shape. The resistance to the effective tractive power of the team 
per ton of load is therefore 40 + (2000 X P) on hard surfaced roads, 
and iQo + (2000 X P) for earth roads, and the maximum load 
expressed in tons for any grade equals 

(Effective tractive power of team for that grade\ 
Resistance per ton of load for that grade / 

Using the tractive powers of the ordinary team shown in Table 
2, the following table is constructed. It is chiefly useful for a 
comparison of the effect of grade on load but all evidence indicates 
that the loads given correspond closely to practice. Table 7A 
shows loads for extreme team exertion as compiled in Table 2A. 
The loads given include weight of wagon. 

Table 7 







Improved Roads 


Earth Roads I 




Effective 
Tractive 










Grade 


Resistance in 


Maximum 








Effort 


lbs. per Ton 
of Load 


Load in 
Tons 


Resistance 


Max. Load 


Level 


240 lbs. 


40 lbs. 


6.0 tons 


100 lbs. 


2.4 tons 


2W0 


540 " 


90 " 


6.0 " 


150 " 


^\ I 


4% 


S04 " 


120 *• 


4.2 " 


180 " 


2.8 " 


5 % 


480 « 


140 " 


3-4 " 


200 " 


2.4 " 


6 % 


456 " 


160 " 


2.9 " 


220 " 


2.1 " 


432 " 


180 " 


2.4 " 


240 " 


1.8 " 


8 % 


408 " 


200 " 


2.0 " 


260 


1.6 " 


9 % 


384 ;; 


220 " 


^•7 !! 


280 " 


1.4 " 


10 % 


360 " 


240 " 


1.5 " 


300 " 


\.2 



i6 



GRADES AND ALIGNMENT 





Table 7A 


. — Draft Stock Extreme Exertion 






Hard Surfaced Roads 


Earth Roads 




Effective 
Tractive 






Grade 


Resistance 


Maximum 


Resistance 


Maximum 




Effort 


in lbs. per 


Load in 


in lbs. per 


Load in 






Ton 


Tons 


Ton 


Tons 


5% 


960 lbs. 


140 lbs. 


6 . 8 tons 


200 lbs. 


4.8 tons 


6% 


928 " 


160 " 


5.8 " 


220 ' 




4.2 " 


7% 


896 " 


180 " 


50 " 


240 ' 




3-7 " 


8% 


864 " 


200 " 


4-3 " 


260 ' 




3-3 " 


10% 


800 " 


240 " 


3-3 " 


300 ' 




2.7 " 


12% 


736 " 


280 " 


3.0 " 


340 ' 




2.2 *' 


14% 


672 " 






380 ' 




1.6 " 


i6% 


608 " 






420 ' 




1.4 " 


i8% 


544 " 






460 ' 




1.2 " 


20% 


480 " 






500 ' 




I.O " 


22% 


416 






540 " 


0.8 •* 



3. Effect of Length of Grade on Maximum Load. — In moun- 
tain road design where a long ruling grade is used it is often eco- 
nomical to introduce short stretches of steeper grade to avoid 
extremely expensive construction. In order to determine the maxi- 
mum short grade (not exceeding 300 feet in length) that can be 
used in connection with a long ruling grade without reducing the 
team load we have compiled Table 7B for a 2400 pound team. 



Table 7B. — Equivalent Long and Short Grades for Hard 
Surfaced Conditions 



Long Ruling Grades 

Tractive Effort 0.25W 

2400-LB. Team 


Short Maximum Grades 

Tractive Effort 0.35W 

2400-LB. Team 


Grade 


Maximum Load 


Grade 


Maximum Load 


5% 
6% 

7% 
8% 


3 . 4 tons 

-9 :: 
2.4 
2.0 '' 


7% 

9% 

10% 

*I2% 


3 . 7 tons 

2.8 " 
2-5 " 

2.0 " 


* 12 % is the practical limit (on account of safe descent) on any road of 
sufficient importance to be considered from an engineering standpoint. 1 



This principle can also be applied to a long cut and fill grade 
reduction with a very material saving in cost but if used the steeper 
rate should not be over 250 to 300 feet long and should be at the 
bottom of the hill. 

Records of Team Loads 

We are indebted to Mr. H. G. McPheters and F. F. Roberts 
for the following data on team freighting in the Rocky Mountain 



TEAM LOADS 1 7 

region. It is practical data obtained from personal experience 
and strengthens the force of the theoretical discussion. The 
loads given are net and do not include wagon weights. They 
represent usual freighting loads which are practical maxima. 

HEBER FRUITLAND ROAD, STATE OF UTAH 
Daniels Canyon Section 

Earth road in fair shape. 

Long 8% grades. 

Short 15% grades. 

Net load for four horse team 3500 lb. (during summer). 

GALENA SUMMIT ROAD, STATE OF IDAHO 

Natural soil road in fair shape. 

Maximum grade (Salmon River side) 20%. 

Maximum grade (Wood River side) 17%. 

Load for one team 1800 lb. (during summer). 

Load for two team 4000 lb. (during summer). 

Load for three teams (six horses and two wagons loaded 5000 
lb. on lead wagon and 4000 lb. on trail taking one wagon at a trip 
up the mountain). 

TRAIL CREEK SUMMIT ROAD, STATE OF IDAHO 

Natural soil road (fair condition during summer). 

Maximum grade 22%. 

Load one team 1200 lb. 

Load two team 2500 lb. 

When freighting by teams was the principle mode of transporta- 
tion, there were used on this road several outfits of twenty-four 
mules hooked to four wagons loaded about as follows: Lead 
14,000 lb.; lead swing 10,000 lb.; swing 8000 lb. and trail 4000 lb. 
Two men handled the whole outfit which was certainly a man's job. 

ROCKY BAR ATLANTA ROAD OVER BALD MOUNTAIN 

Natural soil. 

Maximum grade 16%. 

Load for one team 2000 lb. 

Load for two teams 4000 lb. 

A large amount of freight is carried over this road by auto 
trucks at the present time. 

Record of Truck Performance. — We are indebted to the Pierce 
Arrow Motor Car Company for the following charts which show 
the ability of their trucks to pull on different kinds of road surfaces 
and different grades when running on direct drive. This data con- 
firms the previous statement that modern trucks have sufficient 
power to easily handle their full loads on any grade that would be 
selected for horse traffic on improved roads. 
2 



i8 



GRADES AND ALIGNMENT 




^UQQja^ ut ^uaipisi*) 



TRUCK LOADS 19 



OPTIONAL GEARING ON FIVE-TON MODEL 

The first option is ou'i* standard gearing and will be supplied on all orders 
unless otherwise specified. This gearing should be used where the truck is 
to traverse good hard roads at all times, and where the grades do not ex- 
ceed 10%. 

The second option gives great pulling power on the low speeds, and the 
standard speed of 14 miles per hour on high gear. This gearing should be 
used only where the truck has to pull through a very short portion of poor 
road and the great majority of the running is done on direct drive. This 
option is popular with contractors, etc. 

The third option is especially suited for districts where by nature of roads 
or trafl&c conditions a high speed is undesirable, or in hilly country, where the 
road surfaces are good. This gearing is standard equipment on the long 
wheel base model. 

The fourth option should only be used where the road surfaces are ex- 
ceedingly poor, and the country very hilly. We do not advise using this 
gearing except in extreme cases. 



20 



GRADES AND ALIGNMENT 



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TRUCK LOADS 21 



OPTIONAL GEARING ON FIVE TON MODEL 

The first option is our standard gearing and will be supplied on all orders 
unless otherwise specified. This gearing should be used where the truck is 
to traverse good hard roads at all times, and where the grades do not ex- 
ceed 10%. 

The second option gives great pulling power on the low speeds, and the 
standard speed of 14 miles per hour on high gear. This gearing should be 
used only where the truck has to pull through a very short portion of poor 
road and the great majority of the running is done on direct drive. This 
option is popular with contractors, etc. 

The .third option is especially suited for districts where by nature of roads 
or traffic conditions a high speed is undesirable, or in hilly country where 
the road surfaces are good. This gearing is standard equipment on the long 
wheel base model. 

The fourth option should only be used where the road surfaces are ex- 
ceedingly^ poor, and the country very hilly. We do not advise using this 
gearing except in extreme cases. 



2 2 GRADES AND ALIGNMENT 

4. The Theoretical Advantage of Certain Grades.— From Tables 
7, 7A, 7B and the previous discussion we can pick out the grades 
that theoretically fulfill certain trafiic requirements. 

I. On hard surfaced roads the same load that can be drawn up a 
2/^% grade by reasonable extra exertion of a team, can be hauled 
on a level with ease. This makes a perfectly balanced design from 
the standpoint of team hauling. The theoretical load*is six tons. 
For earth roads 5 % fulfills this same condition with a theoretical 
team load of 2.4 tons. 

II. 5% is the maximum grade that fulfills the requirement of 
safe descent at a trot without brakes. This is of little importance 
under modern traffic conditions. 

III. The same load that can be hauled up a 7 % hard surfaced 
grade can be drawn on a level dirt road in fair condition; a 7 % grade 
therefore does not reduce the load of a team which must travel 
over an earth road for part of the distance. The theoretical load 
is 2.4 tons. 

IV. The use of short maximum grades of greater rate than the 
long ruling grades does not reduce the maximum load provided they 
are proportioned as follows for hard pavements and do not exceed 
250 feet to 300 feet in length. 

Long 5% Short 7% 

" 6% " 9% 



7% " 10% 

">% " 12% 



V. 12% is the practical limit of grade for even unimportant 
roads on account of safe team descent with heavy loads. 

As a matter of fact the selection of grade depends more on the 
requirements of the traffic and the topography of the country than 
on these theoretical advantages. 

5. Ruling Grades in Ordinary use and the Practical Considera- 
tions Governing their Selection. — Various grades on country roads 
have been under observation for so many years that it is safer to be 
guided by present practice which is the result of such observation 
than to trust too much to a theoretical discussion. The adoption 
of the ruling grades shown in Table 8 has depended partly on the 
ease of maintenance as well as trafiic considerations. The maxi- 
mum grade on which different kinds of top courses can be safely 
used either on account of foothold for horses or the maintenance 
of the surface properly comes under a discussion of such courses 
and will be fully covered in Chapter VI. 

In regard to the matter of safe team footing, it is possible to 
select some type of pavement which will satisfy this condition 
for any grade used but a change in surfacing to meet this require- 
ment is often omitted on account of expense and more often omitted 
by careless design. Most of the rigid pavement types give satisfac- 
tory footing up to 5 % which is the practical limit without special 
design. Bituminous macadams can, by variations in manipulation, 
be made suitable for grades up to 8%. Plain macadams give good 



RULING GRADES 



23 



footing for any grade but are expensive to maintain over 5%. 
From the standpoint of footing 5% has a distinct advantage on 
main roads where rigid types are desirable, and 7% or 8% is a 
reasonable limit on side roads where some form of macadam or 
gravel will probably be used. 

Table 8. — Ruling Grades in Foreign Countries 



Location 


Mountainous 
Districts 


Hilly 
Districts 


Level 
Districts 


Prussia 

Hanover 

Baden 

Brunswick 

Holyrod Road in England . 


s % 

4 % 
8 % 

6 % 


4 % 
3H% 
6 % 
4 % 
3%% 


2M% 

s % 

3 % 


Military Highway 
over the Alps Italian side ... 4}^i% Swiss side 6 % 


Location 


National 
Roads 


Departmental 
Roads 


Subordinate 
Roads 


France 


3% 


4% 


6% 



Ruling Grades in the United States 



State 


Main Roads 


Side Roads 


Unusual Cases 




New York 

Massachusetts 

Connecticut 

New Jersey 

Michigan : . . 

Missouri 

Washington 

Illinois 


5% 
s% 

5% 
5% 
6% 
S&6% 
5% 
6% 


7&8% 
7% 

6&7% 

S% 


11% 
9% 

9% 


United States National Forest ^oads (Mountainous districts) 
First Class Roads Long Grades 5 % Short Grades 7 % 
Second " " " " 7% " " 10% 
Third " " '' '' 10% '' '' 12% 
State of Colorado (Main Mountain Roads) 6 % 



From the standpoint of accommodating ordinary farm team loads 
7 % is the logical ruling rate. This is based on a load of 5000 pounds 
for farm hauling which includes wagon weight. The records of 



24 GRADES AND ALIGNMENT 

produce dealers in the Eastern States show that the ordinary wagon 
weighs about 1350 pounds and that 3500 pounds is a large net load. 
This load of 2.4 tons corresponds with the maximum theoretical 
load for 7% hard surfaced grade. Team loads of six tons would 
be very unusual which means that the ideal teaming grade of 2 3^ % 
need not be considered except in level country where it can be 
obtained without much extra cost. 

From the standpoint of maintenance the cost of upkeep of 
ditches, shoulders and earth or gravel- surfacing increases rapidly 
on grades above 5%. 

From the standpoint of construction cost 5% to 7% can gen- 
erally be built without excessive expenditure even in hilly country. 

Practical considerations therefore indicate that for level country 
a 2j^% maximum is desirable but does not justify large expendi- 
tures and that any grade up to 5% will probably be satisfactory; 
that in hilly or mountainous regions on the main roads, a long 
ruling 5% grade is the most satisfactory rate and warrants con- 
siderable expenditure but that 6% or 7% are reasonable if the funds 
are limited; that short stretches of steep maximum grades are allow- 
able to reduce cost provided the element of safe footing is provided 
and the rate is properly proportioned and that on side roads 7% 
is generally satisfactory. 

Grades as high as 1 1 % have been constructed on State improved 
roads in New York and as high as 9% in New Jersey and Illinois 
but the general opinion of the Departments under which these 
grades were built is that they would not again use such a high rate 
except in villages where any material charge in street elevation 
would damage valuable properties. Outside of corporations it is 
bad practice to use long grades of greater rate than 7% for if any 
road is of sufficient importance to warrant engineering plans for 
the future it is certainly of sufficient importance to warrant a 
reduction in grade to a reasonable rate. 

In any case the design should be consistent. Take for example 
a road between two shipping points. It is first necessary to deter- 
mine the portion tributary to each terminal and then the practical 
grades on all the hills on each portion in order to decide what 
consistent ruling grade can be adopted without excessive cost 
(see example, page 329). There is no object in reducing a hill 
from 7% to 5% with a large expenditure if nearer the terminal 
there is a grade that cannot be reduced below 7%. It should be 
borne in mind, however, that the nearer you approach the shipping 
or market point, the more traffic the road will have, and if the 
hills are naturally flatter the ruling grade should be reduced. 
The direction of heavy traffic on each hill should be determined 
and considered. 

Effect of Ruling Grade on Cost. — Money spent on the reduction 
of ruling grade is never wasted although it is not good policy 
to spend large sums to reduce below 5% in hilly country or 2)'^% 
in level country. The effect on cost of the selection of a 5% in 
place of a 6% or a 6% in place of a 7% depends largely on the 
method af construction that must be used. Where locations are 



COST OF GRADES 



25 



fixed by well established right-of-ways and permanent structures 
and the cost of new right-of-way is very high grades are generally 
reduced by cut and fill. Under these conditions the effect of the 
selection of rate is very marked and no general relation can be 
established as each case is a law unto itself. To show the fluc- 
tuating amounts of excavation per mile for different improvements 
based on different rates of ruling grade where cut and fill was used, 
Table 9, page 30, has been compiled. 

Unfortunately many of the roads in the older states were not 
laid out on natural engineering locations and grade improvements 




Pig. I. — Balanced sidehill section. 

are expensive either on account of excessive cut and fill or the high 
cost of new right-of-way on a better location. In mountain road 
or ordinary locations in newly settled districts the question of 
right-of-way rarely handicaps the design and easy grades are 
obtained at moderate cost by natural locations which avoid steep 
adverse grades by going around a hill or develop moderate grades 
on a long cHmb by a longer distance. In climbing on a sidehill 
location the road section is generally what is known as a balanced 
section, that is, the cut just makes the fill by side displacement. 
The amount of excavation per mile is not affected by the rate 
of grade but usually the length of road is affected. 




^ Elevation 6OOO' 



A \Elevafion 5000' 
\< ^Miies.- 



^x 'P 




— Both Lines 6.0 Miles 



Fig. 2. 



Generalizing we can say that the effect of grade reduction on 
cost is not as marked as for cut and fill methods and that roughly 
the relation of cost to grade depends on the length which is often 
inversely proportional to the rate; that is, where cut and fill is 
used a 5% grade might easily cost three or four times as much 
as a 6% grade but where sidehill location is possible a 5% would 
rarely cost more than ^ as much as a 6 % . This is of course affected 
by all sorts of local conditions and may not apply at all but is 
true by and large and serves to illustrate the relation of rate to 



26 GRADES AND ALIGNMENT 

cost. To illustrate: If the difference in elevation between A 
and B is looo feet a 6% grade would require approximately ^}i 
miles of length and a 5% grade 4 miles to make the ascent. If 
the direct distance between A and B is less than 3 J'^ miles the lengths 
of the two lines will be approximately as given. If the distance 
from ^ to ^ is more than 4 miles there would be little difference 
in the length as it would merely mean that the 5 % started to climb 
sooner than the 6%. Under most conditions the cost would be 
more affected by the character of the excavation on the different 
locations and by the number of switchbacks required for the smaller 
rate. The difference in cost due to the difference in rate of ruling 
grade in mountain location does not often warrant the adoption of 
excessive grades. 

No criticism of wasteful expenditure on ruling grade can be made 
in regard to most of the plans as now designed but in many instances 
the profile feature of intermediate grades is not intelligently handled. 

Intermediate Grades. — Intermediate grades include all rates 
between the ruling and minimum grades for the particular job in 
question. They afford the greatest chance for reasonable economy 
of earthwork of any part of the grading design and usually receive 
the least attention. From the standpoint of traffic they have 
no road value; their proper use however controls the convenience 
and suitability of the road to abutting property and controlling 
conditions. In laying a profile grade the controlling points must 
first be considered; these are high water levels of flood areas, eleva- 
tions of existing bridges, railroad crossings, all points where deep 
cuts or high fills would damage the approaches to valuable property; 
connections with other highways, portions of the road previously 
improved and in villages the elevation that will permit future widen- 
ing and curbing that will fit the case. 

Current practice handles most of these controlling features 
intelligently with the exception of grades through villages which 
are-almost without exception too high for future widening and curb 
finish. Designers are cautioned to use city street methods and to 
make the elevation the same as if a full width curbed pavement 
was being designed. 

Effect of Intermediate Grades on Cost. — All of these controlling 
points must be satisfied but they usually affect only a small per- 
centage of the length of any improvement and on the greater portion 
of the road the most economical elevation and any intermediate 
rate of grade can be used. A grade so established that the cut 
in every cross-section would just make the fill at that point would 
result in the least possible excavation and the cheapest kind of 
grading methods. This condition can never be realized but the 
nearer it is approximated the nearer we get to the most economical 
grading design. Where intermediate grades are applicable there 
is no restriction on any combination of rates as they have no effect 
on traffic loads and by an intelligent selection the ideal solution 
can be closely approximated. The cheapest and most satisfactory 
profile can be obtained by the use of the ^'rolling grade;'' by this 
is meant a profile made up of a combination of simple, compound, 



ROLLING GRADES 



27 



or reverse vertical curves, connected by tangent grades only when 
the tangent grade is the most economical or is necessary to prevent 
a series of short humps and hollows. Long straight grades are 
not required a mistake easil}^ made by engineers trained in railroad 
work. Short grades are not objectionable and reverse vertical 
curves ride easily if well built. The rolling grade is also more 
pleasing in appearance than a straight profile if not carried to 
extremes. It appears that there is too much tendency to cut the 
top of each knoll and fill each hollow for it is certainly a waste of 
money to reduce a natural 4% grade to a 3.5% or a 3.5% natural 
grade to a 3 % if the ruling grade is 5 % . 

We can not overestimate the importance of this principle as the 
plans of about 2000 miles of road constructed in the last ten years 
which the writer has looked over in this connection show a needless 
expenditure of at least a million dollars for grading which had no 



^'Undulating Grade f Proper Use Saves Excavaf/on and is 
*^ at tiie Same Time an easy 

Riding Profile. 




E3 



^. hump of this Kind must be 
Disregarded 



5t "aig hr C '^rade Pi vper Us\ 



25 *€0 26 +55 27 



2& 



29 



30 



Illustrating Proper Use of 
Straight and Undulating Grades. 

FiG. 3. 



practical value whatever. This element of poor design in current 
practice is probably due to the fact that the savings are not spec- 
tacular at any one place but if the principle is consistently used the 
total result is spectacular. 

It is also undoubtedly true that the previous railroad training of 
most road engineers and college instructors has had a detrimental 
effect on intermediate profile design. The author has personally 
applied the "rolling grade" principle on construction work for the 
last seven years and found that the saving averaged about $500 
per mile. An intelligent grade line design will also often change 
the method of grading as well as reduce the yardage. To illustrate 
we will cite the Heber Fruitland Road in Utah. The original 
design used long straight railroad grades which required wagon 
haul; the redesign used a rolling grade which not only reduced the 
amount of excavation by about 30% but also practically eliminated 
wagon haul for most of the work and made it possible to handle 



28 GRADES AND ALIGNMENT 

the dirt with slip scrapers and road machine blade scrapers. This 
reduced the cost per cubic yard about 25%. The quantity re- 
duction plus the unit cost reductions amounted to approximately 
50%. 

The Effect of Arbitrary Profile Limitations on Cost. — A common 
grade line limitation calls for tangent grades drawn to intersection 
with simple vertical curves easing off the apex and insists on 100' 
of tangent grade between the ends of these vertical curves. This 
sounds scientific but has no practical value and is cited to illustrate 
the danger of ill considered limitations. A specification of this 
kind often increases the grading by from 500 to 1000 cu. yd. per 
mile an example of which is given below. 



PITTSFORD— N. HENRIETTA ROAD IN NEW YORK STATE 

Length 2.67 Miles 
Original Design Revised Design 

Maximum Grade 5 %. Maximum Grade 5 %. 

Profile. — Straight grades with Profile. — Rolling grade. 
100' of tangent between 
vertical curves. 

Original amount excavation Revised amount 9300 cu. yd 
11,450 cu. yd. 

(A saving of 800 yd. per mile.) 



I 



In conclusion we may say that the matter of intermediate 
grades needs more care than it is at present receiving. 



MINIMUM GRADES 

Hard Surfaced Pavements. — Most road books claim that level 
grades should not be used because of the liability of water standing 
in ruts and that a certain minimum grade should be adopted that 
will insure their longitudinal drainage. Baker states in his '' Roads 
and Pavements'' that for macadam roads English engineers use 
a minimum grade of 1.5%, French engineers 0.8% and that Ameri- 
can practice favors 0.5%, Let us see what this means. 

For a 1.5% grade the fall would be }i inch per foot 
For a 0.8% grade the fall would be J^f inch per foot 
For a 0.5% grade the fall would be He inch per foot 

The flattest crown that is ordinarily used even on bituminous 
macadam is %'' per foot or twice as much as the greatest longitudi- 
nal fall in the above list. For long ruts the longitudinal grade is of 
course effective but the patrol system of maintenance is supposed 
to prevent their formation and for short small depressions the crown 
slope must furnish the drainage. There seems to be no reason 



ADVERSE GRADES 29 

why level grades should not be used on hard surfaced roads; on 
such stretches the crown can be increased slightly to insure trans- 
verse drainage and the ditches given a minimum longitudinal 
fall of 0.2' to 0.5' per 100 ft. depending on the soil to insure the 
longitudinal drainage of the surface water. 

Earth Roads. — On earth or gravel roads attention should be 
given to minimum grades as for these types they have some value 
but not enough to warrant much expenditure. 

It is advisable to use a 0.4% to 0.5% grade where much snow or 
rain occurs but in the arid regions no minimum restriction should 
be specified. 

ADVERSE GRADES 

Adverse grades are defined as grades contrary to the general 
rise and fall of the road betw^een terminals or controlling points. 
It is important to avoid them on mountain road locations where the 
prime object is to gain elevation. They are not a drawback in 
ordinary rolling topography. This is so self-evident that it hardly 
seems necessary to state it. There is no serious objection to short 
adverse grades even on a long climb if by their use the alignment 
can be bettered and excavation saved in crossing a small gully; 
the main objection is to long adverse grades introducing consider- 
able additional rise and fall which could be avoided by a better 
engineering location. This point is generally considered in the 
selection of the general route and is covered by the comparison of 
routes in the preliminary investigation. 

Grades, Summary. — The discussion of grades may be summa- 
rized as follows: 

The road value of ruling grades can not be overestimated. 
Any expenditure on this feature is justified so long as it is consistent. 
The use of properly proportioned short maximum grades in con- 
nection with long ruling grades is the greatest source of justifiable 
economy. 

Minimum center line grades have no road value on hard surfaced 
roads and only a slight value on earth .roads. Minimum ditch 
grades are important. 

The traffic value of intermediate grades is negligible but their 
importance in economical design is large. The greatest faults of 
present practice are the needless reduction of light natural grades 
and the use of long straight railroad rates. 

Steep grades must be modified for sharp alignment which is 
discussed in the following text. 



so 



GRADES AND ALIGNMENT 



Table 9 

Part i. — Compiled from the 1908 and 1909 Reports of the 

New Jersey Highway Commission. 



Name of Road 



May's Landing 

Rivervale 

Westwood 

Franklin Turnpike. . . 

Summit 

Lamberton 

Westfield . .r 

Blue Anchor 

Malaga 

Whitehouse , 

English Creek 

Paterson Plank Road 

Yesler Way , 

Camden 

Evesham , 

Schellenger's Landing 

Goshen , 

Tuckahoe 

Hopewell 



Length 


Maximum 


Max. 


in 


Original 


Improved 


Miles 


Grade 


Grade 


14.0 


7-o% 
8.5% 


3.2% 


5.0 


5.0% 


1.2 




4.5% 


1.6 


8.0% 


2.8% 


1.9 


13-0% 


6.5% 


3-9 


2.8% 


2.8% 


3-1 


4-5% 


2.9% 


2.3 


^•5% 


2.0% 


S-7 


4.2% 


2.0% 


6.5 


12.5% 


5.0% 


6.7 


6.0% 


3.9% 


2.3 


Level 


Level 


2.7 


12.0% 


6.5% 


2.4 


6.7% 


4.0% 


2.4 


6.4% 


3.7% 


2.1 


3.4% 


1-1% 


2.6 


3-4% 


1.4% 


4.3 


4.1% 


1.6% 


2.0 


7.6% 


S.0% 



Excavation in 
cu. yds. per Mile 



2,220 
4,680 
2,500 
8,200 
S,2oo 
540 
6,500 
3,200 
1,700 
4,100 
2,000 
(Emb.) 50,000 
5,700 
5,200 
3,500 
5,000 
4,500 
8,100 
3,800 



Table 9 

Part 2. — Compiled from the Records of the New York 
State Highway Commission. 

Plans for 1911 


Name of Road 


Character 
of Country 


Maximum 

Improved 

Grade 


Width of 
Section 

between 
Ditches 


Exc. in 
cu. yds. 
per mi. 


Pittsford — North Henrietta' 

Indian Falls — Corfu 


Rolling 

Flat 

Hilly 

Hilly 

Hilly 

Hilly 

Hilly 
Rolling 

Hilly 

Rolling 

50% F'at 

50% Hilly 

Rolling 

Hilly 

Flat 


5.0% 
2.6% 

l-ol 

lol 
8.0% 

til 

1.5% 

5.0% 
10.0% 

6.0% 


24; 
24' 

32' 

11' 
26' 
28' 

32 & 

2^8132' 

22-30' 

32' 


2500 
2800 
3600 
5500 
4500 

6600 
3400 
5700 
3400 
3350 

2800 
2950 

2320 


Pembroke — East Pembroke 

Livonia — Ontario County Line 

Livonia — Lakeville 


Avon — Lima 


Sea Breeze — Nine Mile Point 

Bliss — Smith's Comers 


Wales Center — Wales 


Scottsville — Mumford 


Ridge — Rochester — Sea Breeze . . 
Medina — Alabama 


Pavilion — Batavia 


Parma Corners — Spencerport — 
North Chili 















EXCAVATION 



31 



Table 9. Continued 
Compiled from the Records~of the New York State 



Highway Commission. 



Plans for 19 10 



Name of Road 


Character 

of 
Country 


Maximum 

Improved 

Grade 


Width of 
Section 
between 
Ditches 


Exc. in 
Cu.Yds. 
per mi. 


Lake Part 2 & Sweden 4th Sect. 
Warsaw — Pavilion . . 


Flat 

Rolling 
Flat 

Rolling 
60% Flat ) 
40% Hilly j 

Rolling 

Flat 

Rolling 
Hilly 

a 

Flat 
(( 

Hilly 
Rolling 


3.8% 

2.6% 
5.0% 
2.2% ) 
7.0% ) 
3.1% 

One hifl [ 
5.0% J 
4-4% 
5.0% 
4.1% 
3.6% 
0.7% 
7.0% 
3.7% 
5.0% 


32' 

28'-32' 

32' 

28'-32' 

32-40' 

28'-32' 

32' 

32' 

3o'-32' 

28'-32' 

24' 

30 

28'-32' 
28'-32' 

32' 
32 


2560 
3900 
2300 
4000 
1950 

3150 

3230 

2800 

2300 
4000 
6200 
2820 
2120 
6100 
3440 
3800 


East Henrietta — Rochester 

Olean — Hinsdale 


Leroy — Caledonia^ (i.S miles) . . 
Shawnee — Cambria . . . 


Roberts Road 


Sanborn — Pekin 


Oak Orchard, Part 2 


Levant — Poland Center 

Dansville — Mt. Morris, II 

Castile Center — Perry Center . . 
Lake Shore — Lackawanna City 
Eiehteen Mile Creek 


Albion Street — Holley 

Pembroke — East Pembroke . . . 



Table 9. Continued 
Compiled from the Records of the New York State Highway 

Commission. 
Plans for 1908 and 19Q9 (Selected Roads) 



Name of Road 



Hamburg — Springville Sect. I 

u II 

Collins — Mortons Corners . . . 

Clarence Center . , .^ 

Orchard Park — Griffin's Mills 

County Line 

Geneseo — Avon 

Geneseo — Mt. Morris 

Alden — Town Line 

Pittsford — Mendon 

Pittsford — Despatch 

Clover Street Section I 

" II 

Rich's Dugway 

Left Fork — German Church . 
Goodrich Road 

Hamburg — North Collins . . . 

Lawton — Gowanda 

Chili 

Brooks Avenue 

Lyell Avenue 

Barnard's Crossing 



Character of 
Country 



Rolling 

Hilly 
(( 

Flat 
HiUy 
Flat 
Hilly 

Flat 
Hilly 



Rolling 

Hilly 

Rolling 

\ 60% Flat 

1 40% Rolling 

HiUy 

(( 

Rolling 
Flat 



Max. 

Improved 

Grade 



6.0% 

7.0% 

7.0% 

2.5% 

8.0% 

5.0% 

5.3% 

6.0% 

6.0% 

6.0% 

S.o% 

8.0% 

4.5% 

7.2% 

6.2% 

S.o% ) 

6.0% } 

9.0% 

7.5% 

5.0% 

4.6% 

2.2% 

4.4% 



Width of 
Section 

between 
Ditches 



30' 
30' 
32' 
28' 
28' 

28'-32' 

^K 
32' 

22'-28' 

32; 

24 

28' 

32' 
20'-28' 

28' 

26'-32' 

22'-32' 

32' 

28' 
24-30' 

2 6 '-30' 



Exc. in 
cu. yds. 
per mi. 



ig20 
3100 
2250 
2200 
2000 
2100 
2200 
3460 
i960 
3000 
3600 
2550 
3000 
5000 
2000 

3100 

4200 
5300 
2800 
2240 
2400 
2174 



32 



GRADES AND ALIGNMENT 



^1 



Table 9. Continued 
Compiled from the Records of the New York State Highway 

Commission. 
Plans from 1898 to 1907. (Selected Roads) 



Name of Road 



East Avenue 

Pittsford 

Fairport 

Ridge Road 

Buffalo Road 

White's Corners Plank Road 

Orchard Park 

Transit, Sections I & II . . . . 

Hudson Avenue Road 

West Henrietta , 

Scottsville, Section I .'....., 

" II 

Monroe Avenue 



Character 
of Country 


Max. 

Improved 

Grade 


Rolling 


5.0% 
5.0% 


" 


5.5% 


" 


3.3% 


Flat 


2.0% 


" 


3.5% 


" 


3.9% 


" 


4.6% 


Rolling 


3-1% 


Flat 


5.5% 


" 


4.0% 


Rolling 


5.0% 


Flat 


4.5% 



Width of 
Section 
between 
Ditches 



22 
22' 

2o'-22' 

26' 
22-25' 

22' 

20' 

22' 



2 2 '-24' 



Exc. in 

cu. yds, 
per mi. 



8160 
5840 
6580 
2150 
1700 
4600 
4200 
2100 
7100 
3400 
2000 
2100 
1850 



Table 9 

Part 3. — Compiled from the Reports of the Massachusetts 
State Highway Commission. 1896 



Name of Road 


Length in 
Miles 


Maximum 

Improved 

Grade 


Width of 
Section 
between 
Ditches 


Exc. in cu. 
yds. per mi. 


Andover 


0.6 

I.O 

\i 

0.63 

1.0 

1.49 

0.93 

1.2 

0.56 

1.0 

1-93 

1.62 

1.61 

1.05 

1.45 

0.97 

1.91 

1.48 

1. 16 

1.5 

2.0 


3.36% 
6.0 % 
5.0 % 
2.7 % 

2.6 % 
4.0 % 
2.95% 
5-S % 
1.25% 
4.25% 
4.40% 

1.7 % 
4.0 % 
6.0 % 

3.8 % 
4.0 % 
6.0 % 
5-0 % 

^•° ^^ 
4-25% 

5.16% 

S-o % 


24 
21' 
30' 

2l' 

21' 
2l'-24' 
21 
21' 
21' 
26' 
21' 
21' 
24' 
21' 
21' 
21' 
21' 
21' 
21' 
21' 
21' 


6000 
2607 
1920 
3200 
5300 
2300 
8930 
3000 
3350 
4300 
4700 
7S40 
1500 
3700 
5600 
3800 
1200 
4500 
9700 
1500 
1810 
3SOO 
3800 


Brewster . 


Dalton 


Gloucester . 


Granby 


Great Barrington 

Hadley 


Munson 


Norfolk 


North Hampton 

Pittsfield 


Tisbury 


Westport 


Wrentham 


Walpole 


Duxbury 


Fairhaven 


Fitchburg 


Gosheni 


Marion . . 


Mattapoisett 


Lee 


Leicester 





SIGHT DISTANCE 3$ 



ALIGNMENT 

High Type Pavements. — Alignment on this class of improvement 
is generally pretty well determined by existing rights-of-way. 
Changes are made for extremely unsafe conditions but otherwise 
this feature received comparatively little attention and has small 
affect on cost. 

Sharp curves on steep grades or at the foot of such grades are 
not safe; good practice calls for a minimum radius of 300 to 400 
feet for these cases. Right angle turns even on level stretches are 
inconvenient and often dangerous. New York State has adopted 
a radius of 200 feet as a minimum, wherever possible, acquiring 
new right-of-way when necessary, and it is very evident that the 
increased comfort has pleased the traveling public. 

On comparatively straight stretches the position of the center 
line should be shifted to keep on the old roadbed as much as possible 
and yet give a pleasing appearance; this is done to utilize the hard 
foundation of the present traveled way for the sub-grade of the pro- 
posed metaling. 

Sight Distances. — In designing a sidehill road, in rough country, 
the ahgnment and width of shoulder often depends upon what we 
may call '*a safe sight distance," this means that the driver of a 
machine, traveling at ordinary touring speed of 20 to 30 miles per 
hour, must be able to see far enough ahead to turn out and pass 
an approaching car without the application of brakes. In attempt- 
ing to reach a conclusion as to what is a ''safe sight distance '^ 
we have written to automobile clubs throughout the country and 
find that, in the main, they agree on from 200 to 300 feet for speeds 
of 20 to 25 miles per hour. 

Mr. George C. Diehl, Chairnian of the Good Roads Board, 
A. A. A. and County Engineer of Erie County, N. Y., gave us the 
following information for emergency stops and passing without 
slowing up: 

' ' The tests that we have conducted show that a car going at the rate of 
20 miles per hour can be stopped at 40 feet and one going at 40 miles per hour 
can be stopped at 140 feet with the emergency brake. For passing a rig 
going in an opposite direction this distance would not be necessary." 

Mr. Diehl's figures are considerably less than the distances 
given in the other answers. A minimum sight distance of 250 to 
300 feet in the practice of Division No. 5, New York State Depart- 
ment of Highways. 

In the chapter on "Office Practice,'^ tables are given showing 
the "sight distance" for different curves in "cuts.'' 

Mountain Roads. — On mountain roads, alignment is given 
careful consideration as it has a marked effect on cost and safety. 
From eastern road standpoints very few of the mountain roads 
of the west can be considered safe for traffic. Extreme safety 
is prohibitive in cost and it is out of the question to attempt to 
fulfil the sight distance requirement cited above. Much can be 
done by widening sections at sharp curves and the so-called 
dayhghting of curves shown in Figure No. 4 but a great deal must 



34 GRADES AND ALIGNMENT 

be left to the care of the driver. The main advantage of the 
method shown in Figure 4 is that even if the driver hugs the wrong 
side of the road he can see ahead. 

In alignment design the radii are made as large as possible to 
fit the mountain side without excessive grading. On steep slopes 
the grade contour must be followed closely. There is no hesita- 
tion in using radii as sharp as 80' at the head of gulleys where the 
driver can see across the curve or a radius of 100' on outside curves 
where the sight distance depends on the radius. Even these 
limits are impractical in very rough country where radii of 40' 
are considered reasonable. All outside curves with a sight distance 
of less than 100' should be posted with danger signs. 




.Bench cuf- out orfSidpe .1 

k i-Q inc rease S'lqhf D/'s-hafrce. 

J^^^^^^^^^^^^ One )^ay Crown^, 




Fig. 4. — **Daylighting" a curve. 



Effect of Alignment on Grade. — On sharp curves it is desirable 
for the driver to have first-class control on the score of safety. 
An extremely sharp curve with a large central angle also reduces 
the hauling capacity of a six horse team by from 20 to 40%. Con- 
sidering both safety and team hauling it is therefore desirable to 
reduce ruling grades on sharp curves. These considerations 
have no practical value on mountain roads for curves having 
radii greater than 100' but on sharper curves good practice recog- 
nizes this principle. Ordinary design uses radii of from 40' to 
80' on difficult . switchback turns. For a 40' radius the grade 
should^^not^^exceed 3% and_for_an_8q' radius 4% is a reasonable 
maximumr« ^^ 

Effect of Alignment on Cost.— The arbitrary limitation of mini- 
mum radius has a large effect on cost. The following example 
will illustrate this point. These revisions were made by C. H. 
Chilvers on the Rabbitt Ears Pass Road in Colorado to show the 
effect of alignment on excavation. 

^The office method of plotting a good cheap alignment are de- 
scribed in detail in Chapter XIII. 

Conclusion. — Alignment is important and worth careful study 
on new locations but becomes a minor feature where existing 
rights-of-way must be utilized. 



GRADE CROSSINGS 35 

Rabbit Ears Road, State of Colorado, Side Hill Section 



Original Design 


First Revision 


Second Revision 


Length 8.79 miles 
Width of roadway 16' 
Maximum grade 8 % 
Grades flattened on 

switchback turns 
Minimum radius 100' 
First-class alignment 

throughout 

Total amount of exc. 

91,000 cu. yd. 
First-class design but 

needlessly expensive 


Length 8.81 miles 

Width 16' 

Maximum grade 8 % 

No grade compensation 
on curves 

Minimum radius 100' 

First-class alignment but 
more curving eliminat- 
ing many expensive 
tangents 

Amount of exc. 65,000 
cu. yd. 

First-class design shows 
effect of careful intelli- 
gent alignment engi- 
neering 


Length 8.94 miles 
Width 16' 

Maximum grade 8.5 % 
No compensation on 

curves. 
Minimum radius 40' 
Poor crooked alignment 

carried to extremes 

Amount of exc. 38,000 
cu. yd. 

Illustrates extreme effect 
of alignment on cost 

From an engineering 
point of view there 
was no justification for 
this design for the to- 
pography in question 



Note. — On one switchback turn on this road a 100' radius required 
5000 cu. yd. exc. and a 40' radius 500 cu. yd. or one-tenth as much. Short 
radii are justified in isolated cases but their continuous use to save small 
amounts is poor practice. 

RAILWAY GRADE CROSSING ELIMINATIONS 

Grade crossings are being eliminated as rapidly as possible as 
they are a source of danger. The overhead clearance and width 
of roadway in subways are given in Chapter XIII. Where a grade 
crossing is necessary the alignment should be straight and if it is 
necessary to approach the track on a grade this grade should not 
exceed 5 % and the portion of the road for at least 50' and prefer- 
ably 100' on both sides of the tracks should be practically level 
to permit the perfect control of a rig as it approaches the crossing. 
Anyone owning an automobile is familiar with the dangerous 
element of driving where precautions of this kind are not observed. 
The best examples of current restrictions in regard to grade and 
alignment at railway crossings are given in Chapter XIII. 



CHAPTER II 

SECTIONS 

The date will be presented by discussion and examples of current 
practice for both High type roads in ordinary topography and for 
mountain conditions. 

High Type Road Sections. (Ordinary conditions) 

Discussion. — (Development of Standard Section.) Sections 
may be considered from the standpoints of safety, convenience and 
economy. 

For safety a rig should be able to travel on any part of the road 
from ditch to ditch without overturning; for convenience the width 
ordinarily used by traffic must have sufficient pitch to drain the 
surface to the ditches but not enough to give an uncomfortable 
tilt to a vehicle; for economy the section must be flexible in order 
to conform to local conditions. 

Th» first questions are naturally: What is a safe driving slope? 
What is a comfortable driving slope? What pitch is required to 
drain different surfaces? What are stable slopes for cut and fill 
back of the ditch line? What is the commonly used width, and 
what the maximum width of the traveled way? 

All of these points except the last two have been pretty well 
determined, and, while some engineers disagree with current 
practice the writer believes from his experience and a study of 
various State sections that the following premises can be safely 
adopted : 

That z" to i' or 4 to I isthe maximum safe driving slope. 

That i" to i' is the maximum agreeable driving slope. 

That \" to i' is the minimum slope at which an earth shoulder will shed 
water without too much maintenance. 

That y^" to i' or y^" to \' is a satisfactory crown for a single track water- 
bound macadam and that Yi" is a satisfactory crown for a double track 
waterbound macadam. 

That W or V^" to i' is a satisfactory crown for waterbound macadam 
having tar or asphalt flush coats or for bituminous macadams or mineral 
bitumen, double track roads. 

That H" or^^i'' to \' is a satisfactory crown for brick, asphalt, concrete 
or any other rigid type of pavement used on country roads. 

That stable cut and fill back slopes depend on the material and climate 
and range from H : i to 4 : i as will be discussed later. 

The width of roadway carrying the greater portion of the travel 
and the maximum width when rigs turn out to pass are not so well 
established; these two points determine the most economical width 
of hard pavement and the minimum convenient driving width no 
part of which should have a transverse slope of more than \" to i'. 



ROAD WIDTHS 



37 



Probably the most systematic record of these widths can be 
found in the reports of the Massachusetts Highway Commission 
during the years 1896 to 1900 and while the data does not exactly 
apply to present traffic conditions it indicates the general relation 
between widths of heavy and light use. Table 10 gives the results 
on a few roads showing the form used and the variation from year 
to year; the footnote for Table 10 gives a summary of the observa- 
tions on 160 roads for the years 1896 to 1899 inclusive; this brief 
was prepared by J. Y. McClintock, County Engineer, Monroe 
County, New York, and gives a better idea of the conditions than 
would be conveyed by printing the original table in full. 



Table 10. Showing Widths 


OF 


Traveled Way 










Maximum Width of 


Width of Commonly 


Town or City 


County 


Traveled Way 


Traveled Way 


:s u 






















H 


1896 


1897 


1898 


1899 


1896 


1 

M 


M 


1899 


Athol 


Worcester . 


17' 


16' 


16' 


20' 


18' 


io'-i2' 


12' 


14' 


14' 


Barre 


Worcester . 


15' 


— 


13' 


14' 


14' 


— 


g' 


7' 


8' 


Bedford 


Middlesex . 


15' 


— 


12' 


is' 


is' 


— 


8' 


10' 


9' 


Chicopee 


Hampden . 


20' 


— 


20' 


20' 


20' 


— 


12' 


12' 


13' 


Dalton 


Berkshire . 


15' 


20' 


20' 


21' 


16-21' 


20' 


16' 


18' 


I2'-l8' 


Fitchburg (W.) 


Worcester . 


is' 


is' 


14' 


18' 


18' 


10' 


10' 


15' 


14' 


Huntington . . 


Hampshire . 


^5! 


Q, 


II 


11' 


12' 


7' 


8' 


9. 


8' 


Lincoln 


Middlesex . 


15 


IS' 


is' 


is' 


IS' 


10' 


9' 


10 


10' 


Marshfield ... 


Plymouth. . 


15' 


14 


12' 


11' 


12' 


8' 


9' 


7' 


7' 


North Adams 


Berkshire . 


is' 


10-12' 


13' 


14' 


1 5 '-20' 


8'-io' 


9' 


10' 


12' 


Orange 


Franklin . . 


17' 


16' 


16' 


20' 


20' 


io'-i2' 


12' 


15' 


is' 


Taunton 


Bristol 


is' 


20' 


20' 


is' 


18' 


lo'-is' 


10' 


8' 


7'-i2' 


Width of traveled way on 160 roads in Massachusetts, measured during 


the years 1896, 1897* 1898, and 1899, and printed in the report of the 


Massachusetts Highway Commission for 1900. 


The width of stone on these roads is given as 15' wide on 130, 12' wide 


on 3, and 10' wide on 2. It should be remembered that the stone is put 


on very much thicker in the middle than at the edges. 


The maximum width of traveled way as measured was as follows: 


9 ft. wide on 2 roads 18 ft. wide on 23 roads 


10 " " " 6 " 19 " " " I 




II " '• " 2 " 20 " " " 10 




12 '■ '■ " 28 " 21 " " " 10 




13 '■ ■' " 8 " 22 " " " I 




14 " •' " 23 •' 24 " " " 2 




15 •* " " 30 " 25 " " " 4 




16 •• " " 8 " 26 " " " I 




17/' " " I " 33 " " " I " 


The width of commonly traveled way as measured was as follows: 


7 ft. wide on 12 roads 14 ft. wide on 8 roads 


8 " '♦ " 17 " 15 " " " 13 " 


9 " " " 25 " 16 " " " 2 


10 " " " 32 " 18 " " " 4 


II " '• " 10 " 20 " " " 2 


12 " •' " 30 " 22 " " " I 


13 " " " 3 " 25 " " " I " 



Crown has a marked effect on width of heavy travel. A heavy 
crown such as % to i' or i" to i' tends to concentrate the travel in 



38 SECTIONS 

the center and is a detriment on a heavy travel road. With crowns 
of y^" or less per foot there is no tendency to concentrate. For single 
track pavements where the traffic naturally stays in the middle a 
heavier crown is desirable as being easier to maintain; on double 
track roads J^" or less should be used for both the convenience of 
traffic and the distribution of wear. 

The author has measured a number of the New York State im- 
proved roads and found that the width of heavy travel checked 
the Massachusetts results but that the maximum widths were more 
averaging from i8 to 21 ft.; this probably can be explained by the 
increase in automobile traffic since 1900 which because of its higher 
speed requires more room in passing. 

Briefly stated the widths subjected to hard wear on unimportant 
roads ranged from 8' to 10'; on well traveled roads 10' to 14' and 
in unusual cases 14' to 16'. The maximum widths varied from 12' 
to 14' on side roads to 17' to 18' on the main thoroughfares and 
as mentioned above have increased to 18' to 21' in the last few years. 
From this data it seems that the best practice at present requires 

11 

I k- 10'- 20'--—^ 

Fig. s. 

a driving width of about 22' with a variable width of strong metal- 
ling determined by the traffic requirements and ranging from 10' 
to 20'. 

We have now practically developed a standard for the 22' of 
driving width; the metalling that is to carry the heavy traffic has 
a specified crown for each variety and from the edge of the metalling 
to the limits of the 22' the earth shoulder must have a slope of i" 
to i' or possibly %" to i'. The flexibility of the section depends on 
the portion outside of this 22'. The function of the extra width is 
to keep the longitudinal drainage of surface water beyond the 
portion used for driving. To do this we are limited to a minimum 
slope of \" to i' to insure transverse drainage and a maximum of 
3" to I ' on the score of safety. It is by the good judgment of the 
designer in using various slopes between these limits and various 
widths and depths of ditches, combined with the possibilities of 
different grades that the economies in earthwork are effected and 
at the same time the design is made appropriate to the local 
conditions. 

The author's experience has indicated that an open ditch does not 
have much effect on ground water; that its part in the design is to 
drain the surface water, thus preventing seepage into the roadbed 
with a resulting softening of the surface; and consequently whenever 
ground water is encountered under drains should be used. Deep 
ditches are not only useless but dangerous and the best practice calls 
for the least depth that will handle the surface water. Frequent 



GRADING WIDTHS 39 

culverts are desirable to rid the ditches of excess water. It should 
be remembered that road ditches are to protect the road and not 
to furnish farm drainage and that deep farm ditches should be kept 
away from the road section. The following section is therefore 
suitable where there is no probability of much surface water; it 
is the writer's idea of the minimum width section which will be 
satisfactory, and where it can be adopted will give the most eco- 
nomical grading design for light cuts and fills. 

^f 



;::i..J 



:/. 



0^74, 



Fig. 6. 



Effect of Grading Width on Cost. — The width of grading from 
ditch to ditch has a distinct effect on cost but no general relation 
can be established for the ordinary road improvement where an 
old road forms the basis for the new grading. Two examples are 
given to show the value of reasonable reduction in sectional widths. 

I. INDIAN FALLS— CORFU ROAD IN NEW YORK STATE 

Original Design Revised Design 

Length 1.85 miles 

NO CHANGE IN PROFILE 

No Change in Ratio of Cut to Fill 

Width of Macadam 14' Width of Macadam 14' 

" Section 30' " " Section 24' 

Depth of Ditch 18" Depth of Ditch 14" 

Original estimated Revised estimated 
excavation 7500 cu. yd. excavation 5200 cu. yd. 

This change is section alone resulted in a saving of 2300 cu. yd. 
excavation or at the rate of 1240 cu. yd. per mile, or in. money 
about $600.00 per mile. . 

2. PITTSFORD— NORTH HENRIETTA ROAD IN NEW YORK STATE 
Length 2.67 miles 

Original Design Revised Design 

Width of Section 30' Width of Section 24' 

Depth of Ditch 18" Depth of Ditch i2"-i4" 

Ratio of cut to fill 1.35% Ratio of cut to fill 1.25% 

Maximum Grade 5.0% Maximum Grade 5.0% 

Profile — Designed with straight Profile — Rolling grades and 

instead of rolling grades and reverse vertical curves used, 
tangents of 100' between 
vertical curves. 

Original estimated excavation Revised estimated excavation 

11,450 cu. yd. 6620 cu. yd. 



40 



SECTIONS 



A saving of 4820 cu. yd; 1800 cu. yd. per mile, or, in money, 
approximately $9oo.cx5 per mile. 

The revised design on this road is a good example of what can be 
saved by the use of a section that fits the conditions, a rolling grade, 
and a ratio of cut to fill that we have found from experience to be 
sufficient. 

Stable Cut and Fill Slopes Back of Ditch Line. — Economy of 
design and maintenance is affected by the selection of reasonably 
stable slopes. For the class of grading usually encountered on 
roads discussed in this portion of the chapter their ejffect on con- 
struction cost is not great and they do not generally receive much 
attention but for Mountain Roads cut and fill slopes are an impor- 
tant consideration in the design and their effect on cost are worth 
considering. 

Table 25, page 285, shows the effect in detail of various 
cut and fill slopes on yardage of the ordinary sidehill mountain 
road sections. To illustrate the point we will quote one typical 
case for say an ordinary double track section (S-14) Table 25. 



Natural Ground 

Surface Cross 

Slope 


Approximate Yardage per Mile 


Cut slope i^^ :i 
Fill iH:i 


Cut iM:i 
Fill i>^:i 


Cut 1:1 
Fill i}4:i 


5° 
10° 

15° 
20° 

< 
30 


1,100 CU. yd. 
2,200 " '' 
4,000 " '^ 
7,900 '' '[ 


950 CU. yd. 

2.000 " '' 

3.600 '' - 

7,000 " " 

12,100 " '' 


900 CU. yd. 
1,900 '' " 

3.300 " " 

6,100 '^ " 
10,200 '' '' 
19,600 '' '\ 



Occasional slides can not be avoided, but continual slipping 
shows poor design and makes both the maintenance costly and 
travel dangerous. 

Stable slopes vary for different materials and for the same mate- 
rial under different climatic conditions. A combination of mois- 
ture and frost requires the flattest slopes for ordinary soils. On 
account of the great variety of circumstances affecting the design 
no hard and fast rules can be laid down but the following table, 
based on Railroad and Highway practice, indicates the slopes that 
are generally used. In this table and throughout the text slopes 
are referred to as iK- ij etc., meaning i}4 horizontal to i vertical. 
In some of the State Standard illustrations however slopes are 
shown as i on i}i meaning i vertical on iK horizontal. It is 
unfortunate that an engineering requirement is expressed by two 
different methods in such a conflicting order and care must be taken 
to understand which expression is used. 



GRADING SLOPES 



41 













M 






M 




M 


























1. 


S 




:i: ::f:' ::s 


\(M \(N \^ 










(N Tf M 


M 


M 




M 




M 




w 






















a *-• 






















ofe 






















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(U 






















^ ^ 






















-ds 


4J 


Ti r. 


M M 


M 


M M 


M 


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1^ 


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< 


5 








C0\ rH\ 


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(N Tt MM 


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§ 


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M CO M 


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X'tH \(M V'^il 1 


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bc 
























d 
















































'-3 










'oj 














c 



































c 
























0) 












s: 




j^ 








^ 












c 
t 


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£ 
1 


^ 

^ 












1! 
> 




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(1) « 
£?5 


1 


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J^ 


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C 
PC 


^^ 


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44 



SECTIONS 



of water is expected. If for any reason it is not practicable to 
cut into the hill beyond a certain depth and more dirt is needed for 
fill than is given by the 26' section at this depth the shoulders can 
be widened, provided the tops of the slopes keep within the right- 
of-way. It is always best to use as shallow a ditch as possible as 
it simplifies the construction and maintenance of entrances to 
the abutting properties. 



^1 
\^f/ Theoretical Om cle ^ I Cr own ? 'fof ' /%/» 

, , k- /5'. --H 1 r 

k - - 22'- -^->l 

Bituminous macadam. 





Fig. 8. 



^ El. Theoretical Oracle \sCrownf:/!K':l. 

. I ■ L-lt::::::::::--/^:::::::^vl 

I _ l<— -- -26'- 28' - ----oJ , 

^ Any Width which keeps the Top ofSlopeinjidetheff.ofW,—"-'*^ 




Fig. 9. 



Concrete 
GuardRaif 




15 



Wooden 



{<- lo'-ZO 



Ouard Rail-' 



|on^/V<i, I 




"-"^ Crowniyol'-l^Ktol' '^' 

r"^ K- — i^' — - — >) " 

K ZZ'- - H 



Fig. II. 



Figure 10 gives a section showing the variations in fill. A slope 
of i" to i' beyond the 22' width is used on shallow fills. An 
embankment slope of 4 to i is used for ordinary fills up to 7' depth; 
beyond a 7' depth it is cheaper to erect and maintain guard rail 
using a I K to I embankment slope. The cost of guard rail is taken 
up under Minor Points. 

The section shown in Figure 1 1 is used for unusually heavy cuts j 
to keep the excavation as low as possible. If used on a sharp i 



TYPICAL SECTIONS 



45 



curve it should be widened, "banked" and "Daylighted" as in- 
dicated in Figures 12 and 4 to increase safety of traffic. 

Figure 12 shows a section well suited for sharp curves. The 
slope of %" to i' is not objectionable for slow traffic on macadam 
and makes easier riding for rapidly moving vehicles; it also decreases 
maintenance cost on macadam construction on sharp curves. The 
macadam should be widened on the inside of the curve as shown in 




Fig. 12. — Banked section in excavation. 




Figure 12 A. The superelevation on the curve is obtained by 
gradually raising the outside edge; the center line elevation and 
inner edge remain normal. The full superelevation is carried 
around the entire length of the curve from PC to PT and reduced 
to the normal crown at about 150 feet away from the curve ends. 
Variation in superelevation for curves of different radii is a useless 
refinement and good practice rarely adopts superelevation for 

C rown z\fo/ * 
k- I5'20'^^"--^ I 




Fig. 13. 






™-~>j 



radii greater than 800'. The maximum superelevation is generally 
used for all curves of 500' radii or less and is considered to be limited 
to i" per i' for macadams and %" per foot for rigid pavements. 
The author prefers %!' to i' and J-^" to 1' for these types. 

Figure 13 is a satisfactory village section and by the use of a 
variable width will fit conditions on most streets. ~^ 

The preceding discussion attempts to cover only the main points 
for every road presents local conditions peculiar to itself that re- 



46 SECTIONS 

quire special solutions. However, if the Engineer keeps these 
points in mind he will make an economical and appropriate design. 

^ ^evafjonjheoretical Oracle ^' ^ 

.-•'■.x^ onr J^ 



^ ., -8.0'- .,, 
1*^- -16.0'- --4: 

1 

Fig. 14. — Bituminous macadam tracks on side. 

«:. Expansion Joint \ ' '^"''''"3 '-^J""^ 

'^J '.Ifol-Cro^nA'Brick I J'^ USand Cushon^ Concref^^ 



ff 5-Z"-^CIaiiCont.Baie .SXomreteunderSramundTie Pjt-Bdp. 
"^''\, I9-0-- t ,9'0'- ^^^^ 

Village street, brick pavement. Tracks in center, "T"-rail special 
grooved brick. 

^WfchlngPost ^^^^^^^ \ 

Sidewalk .-Plain Curb ( ,, - 1^ 

ji/ j'v ' s :^' ^^ 

^-^--io'o"- r^'"%% \h 

Fig. 15. — Village section. Combined brick and macadam section 
in front of stores, where horses will be hitched close to the curb. 
Prevents pawing up the macadam. 

PLATES 

The following plates show current practice in standard hard 
surfaced road sections and serve to strengthen the points brought 
out in the discussion although they may not comply with all the 
desirable requirements. 



Plate i. — New York. 
Plate 2. — California. 
Plate 3. — Massachusetts. 
Plate 4. — Maine. 
Plate 5. — Wyoming. 
Plate 6. — Washington. 
Plate 7. — New Jersey. 
Plate 8. — W. Virginia. 
Plate 9. — Iowa. 
Plate 10. — Pennsylvania. 



TYPICAL SECTIONS 



47 



Plate i. — New York State 19 15 Standards. 

Cement Concrete 

->V^k- -«^ —ZA'-O" io 32'-6^-^"^" -^^ 



^Btv^^^' - \5ub-boftom Course if Required I 

^#^ K- -I4''0" 0rl6'-0"- -H 

^ Trans verse e xpansionjoinfj, fo b€pro\/fcfecf e very 30 ft, ^hoiN be 
composed of a creosofedj yeJ/ow p/ne or tar paper strip ^' fhickf 
conforming to the cross section of roac/wciy' Each strip may 
be composed of tv^o piecesof equa/len^th, butt Jointed and 
fastened together with approved sp/ice piece of Na 26 iron. 

A 






• Waterbound Macadam * 

•->1/^- 7» -- 24-0" to 32 '0--- - ->i/i*K- 

/ J I SCS^jil ^IL^l u. — : >*'^/g ^ of Theoreti caf Grade | | ^\^ 

K^ I 5 ub-bottom Course if Required \ ^<S~^ 

^ k- .l4'-0'-l6'-0'^ "H ^"^^ 

6 

Waterbound Steep Grades 

"^2^— - 24''0'' to32'-0- ->j/^j< — 

^^ 1 ' ^2y^jiE^£L^Lj^ ^Elevation of TheoreficaCradex \V\» 

o*J l« I >r>l I ^^^ 'bottom Course if Required \ 

k ia'-oWis-o" >• 

c 



Contracted Section 



\ks''6"-''^ 



l<-^r^^ 



e' 



•f /e V. of Theoi?et/ca/ Cn^ade ^ ^ 



-Not less than 14-0 ' 





..-H. 



Bituminous Macadonn 

•>/^}<-- —7 24'-0'' fo d2''0"' r->j/f{«- 

.;^.x j I J^^'inJP^ SfL^i^ K-^/gK of_rheoretica l_6£qde_ \_ \ »W 

'-'j^'^ \Jub -bottom Course if Required \ ^^^ 



48 



SECTIONS 



Plate i,— (Continued) 
. \\ Crown Sp^f'ff^^^ urElev. of Theoretical Grade \ \ \^^' 



'Elev. of Theoreti cal Gra o/e 

V77777777777A 



0?> 



Brick 






_.-,,., ., '6ra\/el Shoulder) "^^-f 






Expansion joints, ifof poured type shall be l" thick. For premou/ded type 
theyshall beYforl6'width,i"foriO'to24'yviclth and 4 for 32'-mdth. 
Half Section Half Section 

p. I F-2 



Top Course same asA.B orEas Specified--^ 



5ub -base as Bottom Course 

6 



^77777777? 



Top Course same as A. B or E as Specific 

"^^'^'^^^^^m ^^ ^ 'wwm 

'^'When Xelford replaces Sub -base, it is made 6" thick 
(bottom course to have the same thickness at 
tenter and edges yvhere Jub -base or Telford is used) 
Sub- base or Telford 

H 






i' 




■Asphalt 
Brick 
Sand 
-.'-Macadam 

Class Concrete 



l2">\ HS-8"'>i 

Asp halt '-^^ M ^2" ' 






^;-..-/^-''-...>l ^.^ ^"^c/dss Concrete 



TYPICAL SECTIONS 



49 





•; J J9d ,,f XIMOIJ 


1 


f^ 


ja 




^ 


^b 


"0 


M 


^S 




H 


^, 


M 


ji 






% 

»!«) 

'^i- 


no 


jappoqs 


10 


VO 




00 


i 


•;j jad ^J UAV0J3 


i 


H 

w 


's 


H 


5: 


VO 

H 


lo 


J3 




to 




^ 


•4J 

P4 

H 


^S 


%. 


*1« 
M 


to 


^ 
t^ 


ja 




% 

"* 


10 


»o 


jappoqs 


10 VO 


-M 


00 


1 
1 


•^ J Jdd ,,| UMOJ3 


2 


M 


% 


M 


% 


H 


^s 


ja 


VO 




5. 


lo 


M 


^S 


H 


% 


M 


0. 


j3 


^ 


% 

^ 






i9ppoqs 


10 


VO 


t^ 


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< 

1 
1 


•; J jad ^,f nMoi3 


1 


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^a 


M 


M 


H 


lo 

H 


J=! 




*X0 


10 


^ 




^s 


H 


CO 


10 

M 




ja 


^ 
^ 


^ ■ 

^ 


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10 


jappoiis 


10 


VO 


t^ 


00 









la 
jH .2 



^z 



1 


2^ 

c3 


•t. 


c 


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Xi 


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rt-r 


ei 


^. . 




C 








-« 




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C 


CO -^ 


.£- 


> 


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§ 


W) 




(3 
o 


«*H 

<N fO 








<u~' 






UH 


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73 


(1> 




II II 


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50 SECTIONS 

Plate 2. — California Standards. 



CuflUSfope. I2 ^heefAsphali- or AsphalHc Concrete 

J M" 3\ I ^''Concrete Base fHI'^-l 



Type A 

I2 AsphalHc Concrete. 
^%^ ill Pw ! ^. 5" Macadam Ba se. /r/// ^7 

K- - ?b- - ->l ' 

TypeB. 

^si" 3^" .'• 6"0il Macadam 

^••^■•*;;;:::!:?::;;s::::::r.':::.r"'''""T^^////fv 

• ^ 1 Slope. 

TypeC. 

CutlffShpe-^ 

4X0 n Crete Base /-f'BituminixedCu&hion 

■]■ ^^i_^. ■.■.... Ail.. /'//^•■/ 

Slope 



r "^•^' 1 

ternate S< 
Type D. 

"^ A „ >.'• \ Surfaced with Local Mater 

Cutr/SlopeSi^^ -ioL I ^ 

C^^y-ISIopel%'^^ 

^ h -^' ^ X. 



Type E. 



'^'vnrnrnmff\jf,\iu u,u Slope 

]<...^^.>j^......7.^'^.^.>l<-|. —'' -I' ..." .y^ I. 

note: I I 

T/7€ Thickness of Pavement- shown 

i&the Minimum jitso ordered bijthe y - 

///^A wm/ Enginee r it is increased. * JJ P^ ' 



TYPICAL SECTIONS 
Plate 3. — Massachusetts Standards. 



51 





is'o''., ....:, 

2i'p ."—■>■ 

25'0 — -' 

Trap : 46 tons per 100 ^^ 



91" 






Local- 41 f » 



- — - 2j'o: 

25' 

Trap : 38 tons per /OO ft. 

local- "34- » » u u 



'2i" 







-:;/" 



• /5 0"- 

" 2/'q": 

■ "25'0 -• 

Trap: 5Stor?s per/00 ft. 



Local- 50 i 










25'0" 

Trap : 4? ton s per 100 ft. 

Local: 39 » n „ ' ., 
{New5toneNo.2) 

[^ ci'n". -sJ 

I (New Stone No. T) I 

1<- - I5'0"' - ^ 

(Original Width of Macadam) 



l^tS'/ 






Section for Resurfacing 




Trap ■• 55fonsperlOO ft. \ L.J.—--- .- 

Local'- 50 *» »» » »* 



For Village Streets. 



52 



SECTIONS 



Plate 3. — {Continued) 
Note: TheBadsof Guard-Rail Posts Ivbeset 

one foot from Edge of Embankment for all Widths, 




'V- Underdrain Cobble Riled- 
Large Stone atBottom,5mall 
otoneandOravelat Top. 



i^-Halve together over Posts 



8'0" ^^r:-8'0"----^ 



|] ii ii J! 




Condition No. i. — See note below. 
.^^^^^'^'''''^—^^^^^^ouTse, No. I stone, 24 tons; screenings for binder 4 
tons. Upper course. No. 2 stone, 16 tons. * ^ 

Local Stone— Lower course. No. i stone, 22 tons; screenings for binder 4 
tons. Upper course, No. 2 stone. 14 tons. uci , 4 

Condition No. 2. — See note below. 

Trap Rock— Lower course. No. i stone. 24 tons Upper course No 2 
stone, 16 tons; screenings for binder. 7 tons. ^uurse, ino 2 

Local Stone— Lower course. No. i stone, 22 tons. Upper course No 2 
stone. 14 tons; screenings for binder. 7 tons. course, imo. 2 

Total tonnage per 100': Trap, 47; Local, 43. 
rr..^S'^A'~lu ^"l*^ penetration methods— grouting or the modified Gladwell 
method--there should be two applications of asphaltic oil, each H gal ner 
fq-/d- ^TW may be also a third appHcation of ^i gal. per sq. yd.* for 
surface finish. For surface treatment there should be one application of 

l^iSi/su'fc^f^^^^^^^^^ ^^ ^^ ^^'' -^^ ^- ^^- >^^- - the 



^X 



i'for 



21. 



"' U... ,.,.. I^'Q 




Condition No. i. 

Trap Rock— Lower course. No. i stone, 19 tons; screenings for binder, -x 
tons. Upper course, No. 2 stone, 17 tons. iJ"iuer, 3 

+^H°'^Ht^*°''^~~^^^^\?°''''^^' ^"^^ ^ ^*^^®» ^7 tons; screenings for binder, 3 
tons. Upper course. No. 2 stone, 15 tons. 

Total tonnage per 100': Trap, 39; Local, 35. 

Condition No. 2. 

Trap Rock — Lower course. No. i stone. 19 tons, 
stone, 17 tons; screenings for binder, 6 tons. 

Local Stone — Lower course, No. i stone, 17 tons, 
stone, IS tons; screenings for binder, 6 tons. 

Total tonnage per 100': Trap, 42; Local, 38. 

Note.— Condition No. i: Bituminous Treatment— Penetration— lower 
course bound with stone screenings or sand. 

Condition No. 2: Bituminous Treatment— Surface Spraying— screenings 
ot sand binder m upper course. 



Upper course, 
Upper course, 



No. 
No. 



TYPICAL SECTIONS 
Plate 4. — Maine Standard Sections. 



53 



Ledge Slope '^- 1 



Ledge 




Bi+uminous Macadam.. 



; ^ y ^^^ 



m^^^'^'^'^'^^mrr^r^^^^^ 



<.-k%-2'0'^>^ -^'0- 




d'dravel Shoulder 
for 6rades over 6 ^. 




.-.-/^-^ 



TTfmfjTmfnfj^^ 



(pvarcL.Baii' 




54 



SECTIONS 

Plate 4. — {Continued) 




Finished Orade 



-16' -■ — ><-3'6"-> 



W^ 



e"-'' I Concrete 

5+andarol Section, 
Narro w decHon to 
>^ be used when Ordered | Ledge 




Narrow Section fo ^ 
be used when Ordered 




L^■^^^^^^ ^■'^^':;; r^ii:^^^ i^^^-^IMv^^*;.;: VQAi-^ 



^-Z-d^A Rock Sec-Mon 




Surface:"'^ 



Extra Rock Cut 




dravif 5-t-oneV' Drain. 
Area i6.ae>q.F^-. 



Outfall Ditch 




6ravel V Drain Area 17.05 
SqF+. 



TYPICAL SECTIONS 
Plate 5. — Wyoming Sections. 



5S 



CL 
k /2 -— ->K — /^ 







Section fK 



Station 



Asphaltic Gravel 
to station- 







Section B 



Bitulifhic Pavement. 



Station 



to Station. 



CL. 
Kr~.s fOfc 12 ->k 10 fo 12 

U- 8-0"' — y<- S'O"- — -~A 

r 1 1 \ Rise fo Crown J-l. ' 




Section C 



<brGV'z\ Track . 



m.A. 



station 



to Station . 



|<- 12-0"' 



CL 



->1<- -/2'0 ^>j 

-8-0- — -M^ a-'c?"— --— J I 

<f^ Rise to C rown l^ iol'' 




Stati on to station. 

j I RisefoCrown Tfol, 

Section E Earth. 





Station 



testation. 



k /O' = — ->k /O' ---; 

I I RisefoCroYvn l"tL 



Variable 




Section F 



StotiorT 



Earth (Machine Work) 
to Station 



56 SECTIONS 

Plate 6. — State of Washington Typical Sections. 



-.15 — 




— 12'- 



— -X //' -i 



'"iT^/z^Wmw^ 



Ear+h £>ec+ion 





k- J5'—. 



I Min. 
Prof/ /A Gra^e., 



^lope on Macadam 



3fol' 



12' H 



/V/>7. 



^mnmm 



"^fiimi^. 



-14- 



15" 



©ravel Sec+ion 6rade. 

(One Course.) 

/5- _>L z^*^ 




A-->| Macadam ai- ' 
C.L is 2"above 



'■'-^-3- 

^1. 



-I 



<--5-j9^->t<--3 -^- 7' ->|<- 7' -4<-J-4^5?-> 

' Slope 2"' I 



im^mi^mmmmmmm 



Top Course 3 "Ed^e ' 
a/7c/ 3"Cenfer 






Slope on Macadam 
ffot' 



travel Sec+ion 
(Two Course^ 



/ Macadam erf- CL 
/ is 2"above Profile 
I Grade. 

**••• Base 3" Edge and 
5"Cenfer 



TYPICAL SECTIONS 
Plate 6. — (Continued) 



57 



Cu.F't of Concrete per I in. ft of 
Roadwaij 16 'Wide = 3. 3093. 




< /5' ^^ . jq' 



/' [<-2 ->|<-^f>j<- 6' >k 

I I Pavement „ \Jt'-yS- _ .>I 



3"x6"WoocfCurb 
to rzmain in 
place. 



'le Grade' ^^ ^ 1--2- 3 Concrete 



I /V-of/A 




i& Fooi- Roadway. 



Profile drade^ 
'inside £dge on 
Curves witfi 
Superele vat ion.) 




3x6" Wood Curb 
to remain in 
place. 



32 
Profile Grade 



1-2 -3 Concrete. 



Cu.Ft.of Concrete per Lin. Ft of Roadway 
13' Wide =d. 865. 



>L./d:-.£iJ<-^^J<-..., 




15 . Foot- Roadway. 



Profile Orade 
(Inside Edge on 
Curves with 
Superelevation^ 



-f ->|<-^^->l<-- -- 10' ->1<- IP' 

^ \ Pavement l'^'^-C- J 

'"••'2 1 , • ^ '^^ >"^ ^ i.'i'/3g 



.>U/^--> 



hi?' 



3x6" Wood Curb 
to remain Jn 
place. 



• IS-' 

'32 



Profile 6mde^^' ' '/^'^« 

% 1:2:3 Concrete 

■: , 20'—- ■ 



^smms^^^ 



Cu. Ft of Concrete per Lin. Ft. of Profile Orade 
Roadyvaij 20 ' Wide = 11.539. (Inside Fdge on 

Curves with 
Superelevation) 
20 Foo-i* Roadway. 



58 



SECTIONS 




TYPICAL SECTIONS 
Plate 7. — {Continued) 



59 




1 All Roads shown here are 20 CfoC. ofOfiches: - ->|5 

h g-'^'- 

>! /' k- Concrete 0''af Sides, fat Cerihr. 






f/e/ (7f Theoretical 6rade . 



Typ 



e I Plain. 



->1 1' K- 




, J OnSteepOrades . 



■3 

Concrete 6 atSides, 7c f Center. ^ / ' U- 



ffein forcing Metal. 
Type 2. Reinfprced. 




f 



--?-6-'->l<-- 

Concrete dht 



Side^eiatCentpr. ""^ ^ ' f^" 







Slope I "per Foo /; jT 
Types Plain. "^^ ' 




-6' >k-.-3'-><.— ^^> 



Concre+e 6 qt Sides, ezot^enten 



' Slope I" p( 



Subgrad^ Flat except at Shoulders. 

Type 4 Plain 



Slope I" per Foot'' 




-H/'H- 



Plate 8. — New Jersey Standard Section. 




This Sect/on is the Arc of a Circle drawn through ifte hurts 
a.bic 
Crown for Waterbound Macadam Vtof! 
n » dituminous tt i'tot 



6o SECTIONS 

Plate 9. — Iowa Typical Sections. 



i J ^"BnckSurfbce 




H? \<t-6'- 



-^—-/o'i-->Y'-"'-io'- — >(<- -e'-'A K- - 

4"Concreh Base k -2^ '■ 



\0^ d"eravel: 

Half Fill Section Half Cut Section 

MONOMTHIC BRICK- Type ONE 



4" Brick }^"=-.zz^ Surfaced Roadway^Zl^- - ->j l''5and-cemeni Bed ^ 



.U^ 



2' Wearing 
Sur-foce -'' 



->1 2'U-7'-e'-^-----/0^--\->\<'----/0'-j'->k-'6-'^2'k--6-'}i 

d"6rvvel. 4toncreh' h"7r«">v---:f4--.- ->] 

tee. 4 onckburtace 

Half Fill Section. Half Cut Section. 

BITUMINU5 FILLED BRICK-TYPE TWa 

.-f^^T Surfaced Roadway 32'-""->\ 





"'■\d"6n7ye/ [^'eXoncrefeSase ^pp*^^ 

K 



Half Fill Section i ^cilf Cut Section 
^9" -)\24)<j.ap ^ u p * ^ Edge o f Pavement 






—32'" 



..-.I 



U-^^-.l 



"X" 



^ 






- Edge of Pavement 



Equal 
Courses. 



All Bars f "°fo be placed in Plan View of Paving Showing Reinforcing 
C^nUr of Section. Two course concrete-type twk^^.{nameda5typebin 

Qravelfo^eLa,d-"'-ll^^^^^^2^^''' - '''"'"'"'^'^ 
''''''''''' ,ot^^f^^^^^^f\ n,sSeciionfobe 

>^X •>12»<-"-//--H<- V/'-->Jpk ^-^usedbefYfeen 

^ TWO COURSE 6RAVEL-TYPE \ Sfaiions36'45 

eFt-.Oravel f<- Surfaced Roadwaif 32'- y^/'Sravel ^ 

Shoulder shown , ^i» k- — Pavinq20— ->\ ^i" /\Sfgi» ,c,\oJ. 

and A TO he 
Laiddoyrn^ 
in Twoy 



Courses.(alsoType^) ^^^^ p.„ 3^^^,.^^ ^^,^ ^^^ 3^^^.^^ 

ONE COURSE CONCRETE-TYPE'W 
(Reinforcing same as -for Two Course) 




TYPICAL SECTIONS 6 1 

Plate io. — State of Pennsylvania Typical Sections. 



Header l:?:3 Concrete. if fur face Course. HeaderCurbing 

^^ /RiseioCrownr:§per/'/ ^^'"^''^'"'-'^ /'^'3 Concrete. 
_■■ .. - iij ^ ..^i^...: .yj, .,^,rdJ^eM:/ 

6^ u 7~e'- J< '7-6" -J t<-^" \%t-y 

■5'—4<- 




F:: 



_.[ .^. .__^ 



Header Curbing Bi+uminous Speci-Pica+ion Class ^ Header Curbing 

■■■n'f'""" * '■"■I" '• -' •'v . :; . m T i 1 1 i fi I - III ■ i ini'r i ' i n I 11 ^ ^ i fli i i iii.it T i - " ^ ■• ' i ~l rTi i< i l|i>m ■■ *• 






-5--->|< 1— /6' ->|< — -5-— -> 



Bi+uminous Specif ica+Ion Class B,djb" .^ 

^ f^adius}'^ jn y Radius^ 

^^^ ^, ^/'V \ . /FeinforcingMefal } ffise foCrorrnr'l' / <;/n^„'. 

1 ^ /■?--3toncref-e \ 5' ^ 

<„...^..„.>(< — 8- >K 6'—- ->(< ^'-— > 



Reinforced 

One Course Cemen+ Concre+e. 
Radius i' 



\ .Reinforcing Me fa/ '^'2' Surface Course Mi^ZJIixfure. 



k- 5'- 

< '- 



I'^TSConcr^^ » [Radius ^" ] 

Q' ^ Q> ... 

Reinforcing 



%V/5.y', 



. plain 



Two Course Por + Iand Cemenf Concreto 




,5" Broken Stone 



,r I 



^"Macadam 



<^ Shpeli'l' 



/ Rise fo Crown l"'\"peri' / .S" Telford 



-8'- 



ase. 



-8'--' 



5 — 



-^^y 



Broken S+one Bas^. Telford Base 
.2e'- ^ 

Water Bound Macadam. 

p'BrokenSfone ^ I .3" Macadam 

1 Rise fo Crown iHier/' / 3'.' Telford 



'■ J 



'Pe/^1/' 




g/._ ^ g'. .yU _5i 

Broken Sfone Base. Telford Base. ' 
— - 26'— - >\ 

Bituminous Macadam" PenetncJ+ion 
Method . 



62 



SECTIONS 



Plate lo. — (Continued) 



Header Curbing 



zCemenf Sand 1-4 



TAr""? i'ExpcnsionJoinfmfh Sand Bed only. „*T ,'^.7 ., 
l-?-S Concrete ■ ^f^CrmniH' mfrifiedBlvk M'"""p'"'i^"^- 




6-H 

'<'—5-0'"~'^ — 



^H zei-o'-" A 




^ HeaderCurbing ^'Cemeni Sand Bed M Mixture 
•^^^ '•^'^^m''^^^\ j Rise fo Crown jl I \ 



I CemeniSandBed 
Mi- Mixfure orl4 "Sand Bed 






/wood BLocK Stone DlocK. ^i'foS^\Sione 

I ' ''Block. 

I V "'i^' Expansion Join is .Raj/mi^ Rail Channel Filler h? Mixture^ 

Expansion Joints f^^^ f^ Crown ^V'^ \\ , Xihified orWood Blocks. 

m 




4 Cement Sand Bed '' 
1-4 Mixture or f Sand Bed ^ 



5"^ X- 5"ConcVeteh3--6 >^ '^5' Vitrified Block Gutter 
rifled Block Bituminous 

Construction for Single Car Track Roads 



I "fo i" Expansion Joints 
Expansion Joihi- f^„,f,Cromf:l /l 



.Railway Rail ChannerTiTler I:2l1ixturii 
.-Vitrified or Wood Blocks 




5->| K" B'Concrete 5'^ k- 
I'Cement Sand Bed l'^'-^ 
!'4 Mixture or ^"Sand Bed Vitrified Block Bituminous 

Construction for Double Car Track Road& 



, Concrete Gutter 



Table Showing Distance beiowCenter , 
for each !^"Wid+hPointforanyCrown2iD8' 



Curb. 


?" 


3" 


4" 


5" 


6" 


7' 


8" 


'/sW/dfh 


l'/3 


l%- 


2'/4 


d'/* 


3fi 


3'/8 


4ii' 


'^ « 


'/i 


^' 


1" 


ly* 


I'/i 


lH' 


2"' 


% V 


'/e- 


n,- 


'/* 


'/* 


%- 


'/e- 


'/i" 


Cinfer. 


0" 


0' 


0' 


0" 


Q- 


Q- 


0~ 



Table Showinq Additional Widths of Surfacing on 
Curves of Drfterent R( ?dii.Qnd Superelevation per F h Width 



Note' 

! All Proportions for Concrete as 
shown on Cross-Sections are 
Subject to such Variations as 
are Stated in the Specifications. 



Radius of 
CtrLine,Ff 


Additional 
Width 


30 


8.0 


4-0 


70 


60 


6.0 


60 


50 


100 


4.5 


180 


40 


140 


40 


160 


3.5 


180 


35 


200 


30 


220 


30 


240 


25 


260 


25 


280 


25 


300 


^0 



Kind of Surface 
Vitrified Block . 



Rise per Ft 
of Width. 



Bifuminous Surface ^ 



Concrete Surface. 



Waferbound Macadam ''^'J-Q '/* 



Note: 
fin Widening and Superelevation 
I Curves, carry fhe MeqularOrade 
I through ontheCenferLineofihe 
I Roadway, arrdmalte alt Widening 
I on Inside of Curves 



MOUNTAIN ROADS 



63 



Mountain Road Sections. 

Discussion. — The desirable requirements for mountain road 
sections are the same as for the roads previously discussed but on 
steep sidehill work the width of grading used for ordinary topog- 
raphy would be prohibitive in cost. As most of these roads are 
natural soil roads the crown is the only element of the section not 
covered in the previous discussion. For the gravel or stony 
material usually encountered %" to i' is generally satisfactory. 
For sand or heavy soils i" to i' is better practice. The old idea 
that crown should be increased on steep grades has been abandoned 
for while that expedient undoubtedly helped the drainage it caused 
more inconvenience to traffic than it was worth. In many cases 
present practice decreases the crown on steep grades to give better 
vehicle control. Crowns on mountain roads are also affected 
by the absence of guard rail or other safety provisions. The ordi- 
nary symmetrical crown is used where wall or guard rail protects 




Symme+riCQ.l Crown 
with Ouard Rail. 



One Way Crown No 
Ouard- Raji. 



Fig. 16. 



the dangerous outside slope but on many roads so much rail would 
be needed that it is prohibitive in cost and where it can not be used 
the road is tipped one way in a continuous slant toward the hill 
so that if a machine skids it will slide in against the cut slope. 
This kind of a section is not as comfortable to ride as the ordinary 
crown but if the surface is at all greasy the element of increased 
safety outweighs any minor inconvenience of side tilt. 

The width of section has more effect on cost than any other part 
of the design. On a new side hill location the relation of width to 
cost can be roughly established. It will of course vary for different 
side slopes of the hill and different cut slopes of the excavation but 
the relation will be approximately as follows, for balanced sections 
(Table 25, page 285). 

Assumed 25° sidehill slope i : i slope in cut 
1 3^ : I slope in fill 



(S- 8) 10' width (ditch to outside of shoulder) 4,300 cu. 

(S-io) 12' " ' " '' 6,100 " 

(S-14) 16' " ' " •* 10,200 " 

(S-16) 18' " •• ♦• *♦ '♦ *• 12,800 •• 

CS-J8) 20' ;♦ :: [[ !• :* *[ is,4oo " 



yd. per mile. 



64 



SECTIONS 



We may say that in general a 20' width requires about sH 
times as much excavation as a 10' width. The relative cost of 
different widths is also affected by the amount of rock excavation 
which is generally much greater for the wider widths. This 
depends on the depth of soil overlying the rock. This element 
affects the cost so much that in certain cases it has been found 
cheaper to build two separate single track roads for short dis- 
tances rather than one double track highway. 




Pig. 17. 




CASE NO. I. 
All"ln Solid*' 



Mountain roads are classed roughly as double track or single 
track, meaning the same as for railroad work, a double line of 
traffic or a single Hne with turnouts to allow passing. As each 
foot of extra width is costly it is important to determine the mini- 
mum width of grading that will serve the purpose for these two 
classifications. 

Minimum Width Sidehill Section. — If the roadbed is benched 
out of solid rock a narrower width will serve as the entire width is 



SIDE HILL SECTIONS 



6S 



firm and stable. If the section is a balanced section part in cut 
and part in fill it must be wider as embankments on steep slopes 
are liable to settle, slide or washout and it is not safe to drive as 
closely to the edge as in the first case. The amount of the road "in 
solid" is therefore the prime requisite and " — ft. in solid'' is often 
used as the specification for contract road jobs where engineering 
design is not used. Present practice favors a minimum single track, 
total grading width of lo' in rock or where the outer embankment is 
sustained by a retaining wall and a total width of 1 2' for the ordinary 
balanced section in earth. Balanced sections are generally used up 
to 30° side slopes and beyond that toe walls or retaining walls are 
necessary for earth sections. For a 30° side slope a total grading 
width of 12' results in approx. 7' to 8' in solid cut. A double track 




Quard Rail 



ff- '^ "—A 

* 5fa.659*22 ' 

El. 5344.5 
Double Track Road 



Single Track Road 



Fig. 18 



section requires a minimum total grading width of 14' in rock or wall 
sections and 16' in balanced earth section which gives approx. 10' 
in solid. These same limiting widths apply to turnout sections 
on single track roads. Where guard rail is used i ft. should be added 
to these widths. 



TURNOUTS 

On single track roads turnouts are constructed at sufiiciently 
frequent intervals so that drivers can see between them and there 
will be no danger of meeting at impassable spots. This generally 
requires from 5 to 10 to the mile. The minimum satisfactory length 
of turnout is about 60 ft. ajid the grade should be as easy as possible 
at these points. 



66 SECTIONS 

Fill Sections.— -Through fill sections must be constructed wider 
than sidehill sections as the sides are bound to slough off under 
weather action and all the elements of wear tend to decrease the 
width; 14' is considered the minimum width for a single track 
road and 20' the minimum for a double track. A symmetrical 
crown is advisable on fills even on curves. Where guard rail is 
used increase these widths 2'. These sections occur on only a small 
per cent, of the length of mountain roads. 

Through Cut Sections. — These sections are rare in occurrence; 
the minimum width, ditch to ditch, for single track roads can be 
considered as 12' and for double track 18'. The use of minimum 
widths for either through cut or fill sections on mountain roads 
has small effect on cost and for that reason more liberality in their 
widths is allowable. 

Turnpike Sections. — Where the natural ground cross slope is less 
than 5° turnpiking is the usual construction and the difference 
in cost of a single or double track is so small that it is not worth 
considering. For this class of section a minimum of 22' between 
ditches will apply to any road and a width of 24' is generally used. 

Selection of Section. — Plate No. 11 illustrates typical mountain 
road sections. 

The turnpike section is used up to side slopes of 5° for continuous 
balanced work. 

The sidehill sections are used above 5° for continuous balanced 
work. The one way crown is used on all single track sidehill sec- 
tions where guard rail is lacking. The one way crown is used on 
unprotected double track roads where the side slope is greater 
than 15°. The symmetrical crown is used on protected double 
track roads and on unprotected sections where the side slope is less 
than 15°. 

Through cut and fill sections are used where required by the 
profile. 

Superelevation is used on curves in cut but rarely on high 
through hills. The ditch on the upper side of a superelevated 
through cut section can be omitted if the cut is short. 

Cut and fill slopes depend on the natural material and climate 
and were discussed on page 40. There is too much tendency 
to use steep slopes to save on construction cost although excessively 
flat slopes are not necessary or advised it being cheaper to take care 
of minor slides by maintenance. (For eft'ect of cut slopes see Table 
25, page 285.) 

Wall Sections. — These sections are used where the natural hill 
slope is practically as steep or steeper than the stable embankment 
slope. Toe or retaining walls are necessary for earth embankments 
where the natural slopes exceeds approx. 30° and for rock fills where 
the natural slope exceeds approx. 40°. Wall details are described in 
Chapters VIII and X. Surcharged breast walls are to be avoided 
if possible. 

Intercepting Ditches. — Where considerable water runs down the 
uphill slope intercepting ditches are used to protect the cut slope 
and relieve the road ditch of excess water. These ditches discharge 



INTERCEPTING DITCHES 67 

to the nearest cross culvert and are an important part of the 
design. 




Infercepfin^ 
Di+ch 



Bench Sections. — Bench sections are used in rock ledge work. 
(See Sections S-io, Plate 11, and Table No. 25, page 294.) 

Summary of Sections. — The entire problem of sections may be 
summed up as the determination of the minimum widths of 
grading and hard surface that will serve traffic and drainage require- 
ments. As a general rule current practice handles this part of the 
design well with the exception of ditches which are often needlessly 
deep and dangerous and generally fail to regulate ground water 
which is the only excuse for their use. The use of road ditches for 
farm drainage is poor policy. Any system of special farm drainage 
should be separated from the road design except in the matter of 
culvert elevation. 



68 



SECTIONS 



Plate ii. — Mountain Roads. 



Typical Su per- E I evafed Sections on Curves. 

Never use a Supers Elevaied Sect ion where the Inside 

of the Curve is on a Dangerous Down ward Si ope. 

Use Super-ElevaHons onitj on Curves liavinqa Radius 

Lessfhan BOOH: Use file same Super-Elevation on dOO-Fh 

Radius Curves as on 100' Radius Curves. 

Thz Center Line Elevation and Portion of the Section 

on the Inside of the Curve remains Normal} the Poriion 

of the Section on the Outside of the Curve is changed 

as indicated belOY/. 



C.L. 



<-- 



C L. Croy/n 



An Lf Width 



> 



Uniform Slope i- h ' 

IT ^ 



C.L. Profile 
Orade - 




Typical Super-EI-eva+ion 
In Fill. 



<-2^< 



C.L. 



AnyYiidth 



-><f> 




'Standard Depth 



Typical Super-Eleva+ion 
In Cut. 



TURNPIKE SECTIONS 
Plate ii. — {Continued) 



69 



%■ Typical Turnpike Section© 
Designated T-aection. 



Crown Elevafionl 16" X.4? 



f2'. ^— j'.->| 

I 

\C.LPro-F/)^e Orade 



Section T-12 
Crown|-"tor 



-<:— 5--><- 



Crown 
BlevaHort 



—16' ■ 



;— 5'— »| 



C.LPro\fileOrac/i 



Section T-JS 
Crownxtol' 




Section T-20 
Crown^"to j' 



No-f-et 



I Where Side Slopee lie between 5 De^. and 15 Deo 
use a Combination of 5 and F Sections, usinq 
^5 Sections in the Cut Side and ^ F Sections 
onthe Fill Sider- 



Note: 



Use Turnpike Sections on Stapes up to 5Dea. 



70 



SECTIONS 

Plate ii. — {Continued) 



Typical Through fill Seotions ' 

Designa+ed FSec+ion&. 

Nofei Fill Slopes I'l Rock Fills. 

I^'l OrdinarLf Earth, 
li'l Special Cases. 

Utilise Wasfe Excavafion bfj Flaften/n^ 
Slopes in Fills. 






C.L. of Crown 
Elevafjon , ^„ 



-16 » 



C, Pro-FileOrade- 




Crown ElevaHon 






C.L Q-f Crown 







£L.Profl/e 



Oracle 



Section F-24 
Crown |i Vol' 




SIDE HILL SECTIONS 

Plate ii. — (Continued) 



7T 



Typical Side HillSec+ions 
/iofe: Designa+ed S Se ct i on s.. 

IUse these Sections onl^ where Side Slope 
is greater than l5Deg. 
On Side Slopes between SDeg. and iSDeq. vse 
Two-Wau Crown, except in Section S-Yo. 



Frequent Turn out- Widenin^s must be 
used with this Section. 
Section 5-8 is the Mini mum in Rock. 
Section S-IO is the MinimuminEarfh. 



C,L. of Crown 
, Elevation. 



'T 




C.LProtile 

! 6rade\ 

n 2r- 



n S-IO 
One-way Crown |.+o-| 




Seo+ion S-14- 
One-Way Crown^to l' 




CLofCroy/n \ 
Elevation. 



'oti leLOrac/e 
"15" 



CL of Crown 
Elevation ^ 
' 7" \ 



One-Way Crown |-tol 




Section 3~1& „ 
One-Way Crown^tdl 
Wherever Short Pad/ us Curves are necessarij around a Spur anditis 
Impossible to see ahead well, use this Section. 



72 



SECTIONS 

Plate ii. — {Continued) 



Typical Throu9h Cu+ Sec+ion&. 
Designated C Section©. 

Note' 'Cu-h Slopes^: I in Rock 
f Jj'l all Ordinaru Earfh 

2' I Dtsm+egrafed Rock. y^- ; / Special Soils 

ni Boulders ondEarih / . / oneSfeep Side Hills where the Use 

|.-/ Lar^e Sandstone Slabs ^ ,i .7 Uuldmake unreasonable 

andEarlh. Long Slope. 

\^ 

Elevafion-^^^^^ \\l2' 







C.LProHle 
^ urade\ 




Section C-IO. 
Crownl'tol' 



I5\,4 ^ 



Section C-IS. 
Crown ^"toT 





■Profile Grade 






'.6rade 



Section C-14. 

Crown |-"tor 
4 




'.CL.ofCror^s 
Elevaf/on 



Section C-I& 
Crown ^"tol' 

4" 



WALL SECTIONS 
Plate i i . — (Co7ttinued) 



n 



Typical Wall 6ec+ion. 
Double Track Road. 
Minimum Wid+h. 



otion Wi2. 



I.5'io2.0' 




^^; 



NOTE. 

' tfallq^neralludry 
j rubble masonrij. 
c ffsubjecffo creek 
I wash, mor-tar rubble 
I or concrete. 

Face baiter 
3 






4- 



ro-f-DrLj Rubble '-'\o.5'hW' 
'to I'. . ^ 



Typical Wall Sec+iori. 

Single Track R.oad. 

Minimum Wid-^h. 

Sec-i-iom W-6. 



Wall Sec+ions. Designated W. Sections. 



CHAPTER III 

DRAINAGE 

(i) General Discussion. (2) Culverts. (3) Small 
Bridges and Fords. (4) Underdrains. 

General Discussion. — There are three classes of drainage prob- 
lems in road work; cross drainage; longitudinal drainage and sub- 
surface drainage. Cross drainage includes culverts, bridges and 
in rare cases fords. Longitudinal drainage includes surface ditches, 
ditch protections and in unusual cases storm sewers on long hills; 
and sub-surface structures for collecting ground water cover blind 
and open throat porous drains. 

This chapter deals with the smaller structures only. For the 
theory and practice of reinforced concrete, masonry or steel long 
span bridges the reader is referred to the standard works on those 
subjects. The conditions for transverse drainage to the ditches 
were given in Chapter II and minimum ditch grades were referred 
to on page 29. Ditch protection on steep grades, storm sewers, 
and the flow of water in ditches will be covered in Chapter VIII. 

Any complete drainage scheme protects the road from wash and 
seepage, which requires culverts or bridges at all points where there 
is a natural cross drainage of accumulated water such as streams, 
swales, established drainage or irrigation ditches, etc.; at all sags 
in the road profile and on long grades at frequent intervals to re- 
lieve the road ditches of excess water and prevent washouts. 
The spacing between these ditch relief culverts on sidehill locations 
depends on the grade, soil, ditch lining and width of section. A 
narrow 10' mountain road requires more relief than a 20' road in 
the same location as even a small washout will put the narrow 
road out of commission while a moderately bad ditch scour will 
not stop traffic in the second case. No set rules on spacing can 
be given but current practice favors ditch relief culverts on 8% 
grades at intervals not exceeding 300 feet and on 5% grades not 
exceeding 500 feet unless cobble gutter or concrete ditch lining is 
used when the distance can be materially increased. On long cut 
and fill hills drop inlets into storm sewers are sometimes necessary. 

Design. — Culvert and Bridge design considers the size of opening 
required for the maximum flow, the strength necessary to carry 
traffic or to hold deep fills; the width of roadway and the type 
of structure most suitable to the requirements of topography, 
foundations and available funds. If the funds are limited the 
cheaper types may be used but all necessary structures must be 
built not only to protect the road but to establish a reasonable 

74 



WATERWAY 75 

drainage scheme which as the country develops is recognized and 
becomes fixed by usage; it is very diflScult to change surface drain- 
age in well settled districts without annoying and expensive 
lawsuits. 

Size of Opening. — The size of opening is usually determined by 
noting the size of the old structure or, if none exists, the size of 
other structures over the same stream and by inquiries of neighbor- 
ing residents or the road commissioner as to how the existing 
structure has handled the water in the past. As a general rule the 
size of opening or span should not be reduced below that of the 
present structure but in the case of steel bridges that have been 
sold to town boards by enterprising bridge companies it is often 
found that the span is needlessly long. The evidence of existing 
structures is the most reliable basis of design but the conclusions 
should be checked theoretically and for small drainage areas in 
villages and all drainage areas affecting new locations in sparsely 
settled districts either the physical evidence of high water or some 
maximum run off formula must be used. Run off formulae are 
based on the rate of rainfall, area of the watershed, topography 
and soil. The rate of rainfall varies for different geographical 
locations and the length of the storm. Reliable information for 
any locality can be obtained from the weather bureau. Short 
storms develop the greatest intensity and produce the largest 
runoff for small watersheds. The rates reached jy these storms 
should be considered in designing ditch relief culverts or cross 
culverts with small drainage areas. A liberal basis for these 
cases is the 5 or 10 minute duration rate of Table 13, page 78. 
Table 14, page 79, illustrates the method. Most culvert design 
is based on a 24 hour precipitation as illustrated in Table 16, 
page 82, and applies to watersheds of say 0.5 sq. mi. and up. 
Streams requiring structures of over 10' span generally produce 
physical evidence of highwater which can be safely used. 

Table 15, page 80, gives the size of opening used by the Santa 
Fe Railroad; Table 17, page 83, gives the size of opening for small 
culverts used by the New York Central. Table 18, page 83, gives 
the size of culvert used by the Iowa Highway Commission. These 
tables serve to illustrate the application of this principle of design. 

Weather bureau records show maximum 24 hour precipitations 
of 7.66 inches at Portland, Oregon, 5.12 inches at Los Angeles, 
California, 2.06 inches at El Paso, Texas, 7.03 inches at Kansas 
City, Missouri, 9.40 inches at New York City and 8.57 inches at 
Savannah, Georgia. These rates are rarely used for runoff com- 
putations as they represent extreme cases of rare occurrence. 
Good practice uses a 24 hour rate of from 4 to 6 inches. Openings 
based on these rates where the culvert will handle the water with- 
out quite running full will take care of unusual cases by the forced 
discharge due to the formation of a shallow pond on the up stream 
side of the road. Table No. 19, page 84, gives the normal discharge 
of small culverts laid at different rates of grade. To illustrate the 
use of tables 13 to 19 three examples will be given. Suppose water 
from 2 sq. mi. of flat farming country in the North Atlantic 



76 DRAINAGE 

States is to pass through a culvert having a natural slope of 0.5' 
to the hundred. 

Table 16 is figured for a 4'' rainfall in 24 hours which is reasonable 
for this section. This table shows a runoff of 334 second ft. for 
flat farm land. For a slope of 0.5 ft. per 100 table 19 shows that a 
5' X 5' culvert will carry the water. 

Suppose we have steep rocky ground of say 200 acres or }i 
sq. mile in Oklahoma and a culvert slope of 2' per 100. The 
best data is the Santa Fe table No. 15 which gives an opening of 
51 sq. ft. at 10 ft. per second or a run off of 510 second feet. 
Table 19 shows that a 5' X 4' culvert on a 2% grade will carry 
this but that the velocity is high and the culvert must have a solid 
bottom and riprap protection at both ends. Where pipes or solid 
bottom culverts are used high velocity is not objectionable but 
where the bridge type is used a sufficiently large opening to keep 
the velocity down to 10 ft. per second or less is advisable. 

Suppose a ditch relief culvert drains 2 acres in the cloudburst 
region and can be laid on a slope of 3 ft. in a hundred. Use last 
column Table 14 which gives 12 second feet which from Table 
19 gives a 16'' pipe. 

Strength. — Dead loads are readily determined but reasonable 
live loads are a matter of judgment. Many of the states limit a 
vehicle load to 1 5 tons on improved roads without special permission 
but loads in excess of this occur now and then. The old culverts 
and bridges on our roads are practically without exception too 
light for modern traffic. Permanent culverts should be designed 
to carry the dead load plus a 20 ton vehicle load with 25% impact. 
Standard culverts shown in Plate No. 15, page 92, seem needlessly 
strong but small concrete culverts are generally backfilled and used 
during construction before they develop their full strength and 
practical considerations require the excess material. A design 
load of a 20 ton vehicle with 30% impact is desirable for small 
permanent solid floor bridges of 10' to 50' span and this loading 
is often used for even timber bridges in States similar to Wyoming 
where oil development, etc., requires the movement of heavy ma- 
chinery, although usually where timber is used a 10 ton live load 
with 50% impact is considered good practice and for mountain 
roads 6 tons will usually be acceptable. For long span solid 
floor steel or masonry structures a live load of 150 pounds per 
square foot plus a 20 ton vehicle with 30% impact is first class 
modern practice. This value is higher than generally used. 

These loadings are safe for military purposes as the following 
statement of Major General W. M. Black, Chief of Engineers 
191 7 will show. 

"Our existing ordinance liable to accompany a field army will have its 
heaviest representative in a 12-inch howitzer weighing about 27,000 lb., 
18,600 lb. of which are on the front wheels. The base or distance between 
the front and rear axles is 18 ft.; width of track 7 ft. 4 in. width of tire 8 
inches; width of tire shoes 12 inches. This howitzer is drawn by a 75 H. P. 
caterpillar tractor weighing 25,000 lb. Comparison with the largest present : 
day commercial trucks shows that a road or bridge substantial enough for 
such will suffice for the ordinance load." 



TYPE OF STRUCTURES 77 

Table No. 51, page 561, gives the safe load for steel I-beams. 

Table No. 52, page 563, gives the safe load for timber beams. 

Table No. 53, page 564, gives the safe load for concrete slabs. 

Table No. 53 A, page 565, gives the effect of depth of fill on con- 
crete slabs. 

Table No. 54, page 566, gives the safe load for concrete beams. 

Table No. 55, page 567, gives the safe load for timber columns. 

Width of Bridges. — Culverts are made long enough to accommo- 
date the normal road section. There is nothing more unsightly or 
dangerous than the narrowing of the normal section at a culvert. 
First-class design widens the section at culvert locations and even 
with minimum head room uses an out-to-out dimension of not less 
than 30 feet. This same rule applies to short span permanent 
bridges up to about 25' span which on high type road improvements 
should have a clear width of 22' between parapets. Above 25' 
spans the roadway width depends largely on the location of the 
structure and probable traffic but for most main roads a 20' clear 
roadway is satisfactory for permanent structures and a 16' roadway 
for temporary timber structures. Plates No. 20 to No. 30, page 100 
to 124, illustrate current practice. 

Type of Structure. — For small drainage areas some form of pipe 
culvert is generally used which will be discussed in more detail 
under Culverts. 

From 2' to 5' spans the box culvert type is' popular. 

From 5' to 20' spans the slab or stringer form of construction is 
reasonable except under deep fills where the semicircular arch is 
better practice; from 20' to 50' spans Pony Truss or Parapet girder 
types are available for most conditions or arches where the founda- 
tion is suitable. Pony Trusses are desirable up to about 80' 
span and beyond that the through Truss type. 

The following list illustrates the practice of the Iowa Highway 
Commission. 

1. Box culverts and slab bridges 2' to 20' span. Not economical over 20' 
span. 

2. Reinforced concrete arches 8' to 100' span. Foundation must be 
excellent. 

3. Pony truss steel bridges with solid concrete floor 30' to 80' spans. 

4. Reinforced concrete girders 20' to 50' span. Very economical but 
j require careful design and construction. Not economical over 50' span. 

In the matter of type the author desires to emphasize the desira- 

■ bility of simple design particularly for small structures. Mass 

I concrete for sides and bottoms is preferable to thin reinforced 

sections (see New York Standards, page 92). It may not be as 

scientific or theoretically as cheap but better results are obtained 

with the usual inspectors. Road commissioners often do not under- 

\ stand the object of the reinforcement and either leave it out alto- 

\ gether or get it in the wrong place. For large structures where a 

I competent inspector can be employed this objection does not hold 

but even for such structure mass concrete for abutments, retaining 

! wall, etc., is to be preferred. 



78 



DRAINAGE 



Table No. 13.— Rates of Rainfall. Short Storms 
Short storms of the greatest intensity occur as cloud-bursts 
in the mountain and arid regions between the Sierras and the 
foothills of the Rockies. The intensities of these storms are not 
well recorded but partial records indicate as high a fall as 11 
inches in one hour. For these regions culverts for small drainage 
areas should be made at least twice as large as for eastern or 
southern conditions. (See last column, table No. 14.) 

Maximum intensity of Rainfall for different periods taken from 
the U. S. Weather Bureau Records. Intensity at rate of inches 
per hour. 


Location 


5 Minute 
Duration 


10 Minute 
Duration 


One Hour 
Duration 


Atlanta, Georgia 

Boston, Mass 

Chicago, 111 

Cleveland, Ohio 

Denver, Colo 

Detroit, Mich 

Duluth, Minn 

Galveston, Tex 

Jacksonville, Fla 

Milwaukee, Wis 

Memphis, Tenn 

New Orleans, La 

Norfolk, Va 

Omaha, Neb 


5 . 5 in. 

6.7 in. 

6 . 6 in. 
5 . 6 in. 
3.6 in. 
7 . 2 in. 
3.6 in. 

6.5 in. 
7.4 in. 

7 . 8 in. 

6 . 6 in. 
8 . 2 in. 
5.8 in. 
6.0 in. 

5.4 in. 
6.6 in. 
4.8 in. 

7.5 in. 


5 
5 
5 
3 
3 
6 
2 
5 
7 
4 
4 
4 
5 
4 
4 
6 

3 

5 


5 in. 
in. 
9 in. 

7 in. 

3 in. 

m. 

4 in. 

6 in. 

1 in. 

2 in. 

8 in. 

9 in. 

5 in. 
8 in. 
in. 

in. 
8 in. 

1 in. 


1 . 5 in. 

1.7 in. 

1 . 6 in. 

1.1 in. 

1 . 2 in. 
2.2 in. 

1 .4 in. 
2.6 in. 

2.2 in. 

1 . 3 in. 
1.9 in. 
2.2 in. 
1 . 6 in. 
1 . 6 in. 

1 . 5 in. 

2.2 in. 

2 . 3 in. 

1.8 in. 


Philadelphia, Penn 

Savanah, Geo 

St. Louis, Mo 

Washington, D. C 



RUNOFF 



79 



Table 14. — Maximum Runoff. Small Watersheds 
Burkle-Ziegler, Sewer Formula 



Cubic 
















feet per f Av. cu. ft. rainfall 1 4 


/Av. slope of ground in 


second 


per acre = C X -j per second per acre \ X A 
g culvert. [ during heaviest fall. J ' 


/ feet per 1000 


reachin 


^ No. of 


acres drained 




C = 0.75 for paved streets and built up 


business blocks. 




C = 0.625 for ordinary city streets. 








C = 0.30 for villages with lawns and macadam streets. 


Assumed C = 0.25 for farming country. Note.— 


-This value is high from 




the standpoint of sewer design but culverts 


are short and 




might better be liberal in size. 






One inch of rainfall per hour equals i cu. ft. per seconc 


per acre. 




Discharge in Cubic Feet per Second 






Rate of Rainfall 4" per Hour 




* *Assumed 


Area 






Runoff Steep 
Stony Moun- 










in 


Fall 5' in 1000 


Fall 20' in 1000 


Fall 50' 


in 1000 


tain Slopes 


Acres 












C = o.30 


C = o.25 


C = 0.30 


C = o.25 


C = o.30 


C = o.25 


Rainfall 8'' 
per Hour 


I 


1.8 


1-5 


2.5 


2. 1 


3-1 


2-7 


6 


2 


3.0 


2.5 


4.2 


3-5 


5.4 


4.5 


12 


3 


4.1 


3.4 


5-7 


4.8 


7.2 


6.0 


18 


4 


5.0 


4.2 


7.2 


6.0 


9.0 


7-5 


23 


5 


6.0 


5.0 


8.5 


7-1 


10.7 


8.9 


28 


6 


6.8 


5.7 


9.7 


8.1 


12.2 


10.2 


33 


7 


7-7 


6.4 


10.9 


9.1 


13-7 


II. 4 


38 


8 


8.5 


71 


12.0 


10. 


15. 1 


12.6 


42 


9 


9.3 


7.8 


13.2 


II .0 


16.5 


13-8 


46 


10 


lO.I 


8.4 


14.3 


XI . 9 


18.0 


15.0 


50 


20 


16.9 


14. 1 


24.0 


20.0 


30.2 


25.2 


90 


30 


23.0 


19.2 


32.5 


27.1 


40.7 


33-9 


120 


40 


28.5 


23.8 


40.3 


33.6 


50.9 


42-4 


150 


50 


33-6 


28.0 


47-7 


39.8 


60.0 


50.0 


180 


60 


38.6 


32.2 


54-6 


45. 5 


68.7 


57-3 


200 


70 


43-3 


36.1 


61 .4 


51-2 


77-3 


64.4 


225 


80 


48.0 


40.0 


679 


56.6 


85.2 


71.0 


250 


90 


52.4 


43-7 


73-9 


61.6 


93.1 


77.6 


275 


100 


56.7 


47-3 


80.2 


66.8 


100.8 


84.0 


300 


200 


95-4 


79-5 


134-6 


112. 2 


169.7 


141. 4 


550 


300 


129-0 


107.7 


182.9 


152.4 


229.7 


191. 4 


750 


400 


160.0 


133-6 


227.0 


189.2 


285.6 


238.0 


880 


500 


190.0 


158.0 


268.0 


223.5 


336.6 


280.5 


980 


600 


216.0 


180.0 


307.0 


256.0 


387-0 


322.8 


1,050 


640 


230.0 


*I92.0 


323.0 


269.0 


406.3 


338.6 


1,100 




* 200 second feet by Table 16. 








** Based on Santa Fe Table 15. 







8o 



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82 



DRAINAGE 



Table i6. — Maximum Runoff, Dickens Formula 
D = C-x/M^ Runoff expressed in second feet. 



The following tabulation is for a 24 hour precipitation of 4" 


rain and for topography similar to the farming sections of the 


Eastern Atlantic States. For 6" in 24 hours correct the quanti- 


ties in proportion to C as follows. 


4'' Rainfall 6" Rainfall 


Flat Country Flat C = 200 Country C = 300 


Rolling Country C = 250 Rolling Country C = 325 


Hilly Country C = 300 Hilly Country C = 350 


For steep stony watersheds and a ()" rainfall use the Oklahoma 


Column of Table 15. 


Area in Square Miles 


Flat Country 
C 200 


Rolling Country 
C 250 


Hilly Country 
C 300 


O.I =64 acres 


36 


45 


54 


0.2 


60 


75 


90 


0.3 


81 


lOI 


121 


0.4 


100 


125 


150 


o-S 


119 


149 


180 


0.6 


136 


170 


204 


0.7 


-^^Z 


191 


229 


0.8 


169 


211 


253 


0.9 


i8s 


231 


■ 277 


I.O 


200 


250 


300 


2.0 


334 


417 


501 


3.0 


456 


570 


684 


4.0 


564 


705 


846 


5-0 


668 


^2>S 


1002 


6.0 


764 


955 


1 146 


7.0 


860 


1075 


1290 


8.0 


950 


1 188 


1426 


9.0 


1038 


1297 


1556 


lO.O 


1122 


1402 


1682 


20.0 


1890 


2362 


2834 , 


30.0 


2560 


3200 


3840 


40.0 


3180 


3975 


4770 


50.0 


3760 


4700 


5640 


60.0 


4310 


5400 


6480 


70.0 


4840 


6050 


7260 


80.0 


5360 


6700 


8040 


90.0 


5840 


7300 


8760 


lOO.O 


6320 


7900 


9480 



For areas under o.i square mile, see Table 14. 



CULVERTS 



83 



Table 17.- 


-New York Central and . 


Hudson River R. R. 


CULVERTS FOR SmALL DrAINAGE ArEAS. 


Steep, Rocky 

Ground. 

Acres 


Flat Cultivation, 

Long Valley. 

Acres 


Size. Diameter 
in Inches 


Equivalent Capacity. 
Pipes 


5 


10 


10'' 




10 


20 


12" 




20 


40 


16" 




25 


50 


18" 


two 16" pipes 


30 


60 


20'' 


two 16 ^ pipes 


45 


90 


24" 


two 18" pipes 


70 


140 


K 


two 24" pipes 


no 


220 


K 


two 30 " pipes 


150 


300 


A2" 


two 30'' pipes 


180 


360 


48" 


two 36" pipes 


280 


560 


60'' 




Note. — To be used only in the absence of more reliable infor- 


mation, particularly existing culverts over the same stream. 



Table 18. Culvert Design. Iowa State Highway 
Commission 1 



Size of Culvert 
Opening 


Maximum Acres . 


Minimum Acres 


2'X 2' 

4'X A' 

6'X 6' 

8' X 8' 

10' X 10' 


70 

_ 376 

1300 

2700 

5000 


28 

140 

520 

1120 

2000 



CULVERTS 

Engineers do not differ much in the design of these structures. 

For high type roads they should be permanent; should be large 
enough to take the flood flow; should if possible be self -cleaning; 
must admit of being cleaned easily and as previously stated must be 
long enough to accommodate the normal width of road section. 

For low typ^ roads the requirements are the same except that 
temporary or semi-permanent culverts may be used if the funds 
are limited. The different kinds are as follows: 

Concrete or masonry culverts Permanent 

Cast iron pipe culverts " 

Double strength vitrified clay pipe Semi-permanent 

Ordinary concrete pipe culverts *' " 

Corrugated metal pipe culverts " " 

Dry rubber masonry culverts " " 

Timber and log culverts Temporary 



84 



DRAINAGE 



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OBSTRUCTIONS TO CULVERTS 85 

Cast iron pipe or concrete box culverts are generally used on 
high class improvements. Corrugated metal, concrete or vitrified 
pipe and dry masonry on low class improvements and timber or 
log culverts in mountain road work. 

For moderate sized drainage areas the culvert opening is pro- 
portioned to the runoff but for small areas the size is determined 
by the convenience of cleaning rather than by the discharge capacity. 
Where sufficient fall can be obtained to make the culvert self- 
cleaning, a 12'' pipe is feasible under shallow fills but where the flow 
is sluggish, nothing less than a 16" or 18'' pipe will serve satisfacto- 
rily. Long culverts under deep fills should never be smaller than 
2' wide and 3' high to permit cleaning by hand if necessary. 

The self-cleansing velocity of flow for sand and earth particles 
is about one foot per second; for coarse gravel about three feet 
per second (Ogden's Sewer Design, page 134). A pipe laid on a 
slope that gives a velocity of five feet per second when flowing one 
quarter full should keep clean. This requires a fall of approx. two 
feet per hundred for a 12'' pipe and is the minimum grade at which 
the 12" size should be used. 

It is our opinion that a culvert should have the same slope as the 
stream bed. If given a greater slope the outlet end tends to clog 
and if a lesser the inlet end will plug. It is unusual for culverts to 
fill badly except when placed at the foot of a steep hillside where 
the stream velocity is naturally reduced. At such points an extra 
large structure should be designed with the idea of providing suffi- 
cient waterway even after the contraction caused by this settlement 
has occurred. Such a culvert should be cleaned after each freshet. 
The use of paved dips in the roadway at such points in place of 
culverts is not advised as they are dangerous and cause accidents 
unless very gradual. A man not familiar with the road often 
loses control of his car. Ditch relief culverts on grades should be 
laid at an angle of about 45° with the center line in order not to 
retard the water at the inlet end. 

More trouble is experienced from culverts becoming filled with 
ice due to alternate freezing and thawing weather. This is par- 
ticularly true of small culverts draining springs. Culverts as 
large as 2 X 2 have frozen solid in this manner and if 
this condition is anticipated the size should be regu- 
lated accordingly or trouble will be experienced dur- 
ing the spring break up. The following ingenious 
expedient has been successfully used on roads where 
the culverts fill with ice and snow during the winter. 
A small pipe is suspended inside of the normal cul- 
vert. In the fall this small pipe is plugged and in the 
spring just as the snow begins to melt the plugs are removed and 
the first water flowing through the small pipe melts the ice and snow 
rapidly for the entire length of the culvert so that it is generally 
completely free to handle the main spring runoff. 

Where pipe culverts are laid on steep slopes special buttresses 
well imbedded in the hard slope should be provided to prevent 




86 



DRAINAGE 



crawl or slip. Well built headwalls should hold up to 
slope and beyond that extra anchors should be provided. 



say 12 




Fig. 20. 

In designing culverts under side roads, the length must be great 
enough to provide an easy turn for traffic; many times a saving 

Main Road 



Macadam 



Side Cuk in Ditch Line •"-^ 

"1 \^ 

5icle Culvert Set 
Back on Side Road\ 




Fig. 21. 

in length can be made by placing the culvert a short distance down 
the side road as shown in Figure 21. 



Sidewalk 




Fig. 22. 



Figure No. 22 shows a form of culvert often used in village 
streets where deep ditches at the culvert site would be objectionable. 

While vitrified pipe or concrete pipe are not recommended for 
cross culverts in high-class improvements they are the most suitable 



RELATIVE COST 



87 



construction for ditch drainage under driveways etc., the wooden 
boxes built by some departments are not economical which is 
shown in the following estimate of relative cost of small unimportant 
' culverts given by A. R. Hirsch in Wisconsin Road Pamphlet No. 4. 



Kind 


Size of 
Opening 


Length 


First Cost and 

Maintenance for 

100 Years 


3" Hemlock box 

Concrete box 


15 in. sq. 
15 in. sq. 
18 in. 
18 in. 
18 in. 
18 in. 
18 in. 


20 
20' 

28' 

26' 


$252.00 
40.00 
35-00 
41.00 
42.00 
166.00 
196.00 


Concrete oioe 


Single strength V. T. P. . 
Double strength V. T. P. . 
Cast-iron Dioe 


Corrugated steel 



Relative Cost of Culverts. — The relative cost depends largely on 
the location, material available and length of haul. The following 
costs are approximately correct for the northeastern states during 
the years 1912-1914. 

Table 21 gives comparative costs for permanent culverts and 
shows that cast iron is generally not economical over 18" in diam- 
eter. Pipe is to be preferred where the headroom is small. 

The following list shows the approximate cost per ft. of vitrified 
and corrugated metal pipe culverts. 





12" 


15" 18'' 24" 


36" 


48" 


Vitrified pipe culverts 
Corrugated metal cul- 
verts 


$0.60 
I 25 


$0.90 
I 50 


$1.10 

1.80 


$2.00 

2.75 


4.00 


$6.50 



Corrugated metal is to be preferred to vitrified tile if the head- 
room is small as it is not as hkely to fail under heavy loads. 
Small log culverts cost approx. as follows : 



Size of Opening 
12" X 18" 
12" X 24" 
14" X 36" 
24" X 36" 



Approx. Cost per Foot 

$1.30 
1.40 
1 .60 
1 . 70 



The difference in cost between corrugated metal and log culverts 
is not enough to warrant the use of small lot structures except in 
unusual cases. 



88 



DRAINAGE 



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«» "' 



SMALL SPAN BRIDGES 



89 



Plates 12, 13 and 14 show standard pipe culverts. 

Plate 15 shows first-class simple massive box culvert design. 
This is as satisfactory a type as there is in use. 

Plates 16 and 17 show good examples of semicircular and circular 
culvert practice. 

Plate 18 shows the combined masonry and concrete type which 
is suitable where stone is plentiful and concrete costly. 

Plate 19 shows log culverts used on mountain roads. 

The shape of opening for small concrete culverts should permit 
the use of collapsible forms. 



Plate 12. — Cast Iron "Pipe Culvert. New York State 
Standard. 



p I a 




K- ;; -Z4-4''ioZ6-4-- V 

I \„ 2f Mof Lessfhan. J , 




■'•■9" '''6",NofLessfhart.' 6'; Hoi Less than'.' 

Longi'+udinal Section. 



SMALL SPAN BRIDGES 

The area of opening, width, live loading and economical type 
were discussed in the first of. the chapter. Most ordinary soils 
afford satisfactory foundations for small span bridges but piles 
must be used for muck or quicksand and are advisable if much 
scour is anticipated which can not be prevented by rip rap protec- 
tion. Pile foundations are required for all large structures where 
rock foundations are not available and are desirable for any con- 
crete structure over 30' span. 

The safe foundation load on various soils recommended by the 
"New York Building Code" and ''Baker's Foundations" are as 
follows : 

New York Building Code 

Soft clay I ton per square foot 

Ordinary sand and clay in layers, wet and 

springy 2 tons " " " 

Loam, clay or fine sand, firm and dry. . . 3 " " " " 
Dry firm coarse sand, stiff gravel or hard 

clay 4 " " 

{Continued on page 98.) 



go 



DRAINAGE 



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:gVi 







METAL CULVERTS 



91 



Plate 14. — Corrugated Metal Culverts. 
Hampshire. 

^ It 



State of New 




Longi+udinal Sec+ion 




End Elevcation. 
TABLE OF PROPERTIES. 



Diame+er 


%f.^ 


Capaci+LjjCu. 
Ff.perSec. 


Concrete 
Cu.Yd&. 


10" 


0.048 


1.64 


1.75 


12" 


0.033 


2.36 


2.0 


14" 


0.025 


3.21 


2.3 


16" 


0.020 


4.20 


2.6 


IB" 


0.0/6 


5.31 


2.9 


20" 


a 012 


6.54 


3.2 


24" 


0.010 


9.42 


3.8 


30" 


0.007 


/4.73 


4.9 


36" 


0.005 


21.21 


6.1 


VeJocltu:r3.0 Fi.perSec. **n*''^ 0.027 \ 



Quantifies Figured -from Minimum 
Dimensions, 



92 



DRAINAGE 



Plate 



New York State Small Box Culverts. 





Alternative 

Cross Section for 

Collapsible Forms. 



«■'' 



Longitudinal Section. 




Culverh to be Bui It with 
End Walls.) 



End Wall. 




c 
a 

«/3 


■7^-5 


c 1 

Pi 

\- < 


Is? 


Z'O" 


e" 


12" 


0.6 


3'0" 


6'- 


12" 


1.2 


4'0" 


6" 


12" 


1.2 


5'0" 


6" 


12" 


I.Z 



Table of Dimensions. 






r~~""~~*'~r5r. 






•^ 



m^^^ 



-DoYveh 0.25°' 
NetArea 
rO"lon0}l2C.toC. 



</5-H 



Longitydlinal Section. 



Part 
Cross Section. 



CONCRETE CULVERTS 



93 



Plate i6. — Massachusetts Standard for Concrete Arch 
Culverts. 






r/O'i 



One End a88cu.ycls. 



0.064- cu.ydsi. 
perfr. 



(<._-. 5V-- 



r;^w^ 



1 



H/^^ 



^/5; 






H~23'>l 



One End I.Hcu.yds. 



K— - 6'6" 



\J3iZ 






Si 



«/5i 



One End I39cu.yds. 



^2^^^V^ 



n 



<-/^v 



0.089 cu.yds* 
per ft-. 

K- g^'-X 

O.M4cu.yd^ 
perfr. 




r- 



One End K61 cu.yds. 




0.123 cu.yds. 
per-ft-. 



I</2>1 




One End 1.91 cu. yds. 



K- 56 "H 



0.18 cu. yds, 
per ft-. 



94 



DRAINAGE 




o 

CO 






fir- 



to ^ 



^ g ^ I ^ I ^ -5 



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1^ 



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■<7J/r> 



>| j9]^''-"-lj2- '^^'"'•Y^joJ^'^^ctBjOd gjg 







CULVERTS 



95 




OQ ^ -^ ti: o 

. O 4- ^ H- O y 



I 



.....f.f,.;.>L...f.^^..,>| ^ 

"^J — A\^ 



h 



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o 

+ 

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k 



96 



DRAINAGE 



Plate i8. — Typical Masonry Culvert. State of New 
Hampshire. 




Plan 



3— 






[<-3-'-->)<- 9'-3"- 







-^^^1^1 




Part Longi+udinal Sec+ion 



m m 



\c:^\P^ 



c^l.:^^ 









Half Section 
B-B 



Half End 
Elevation. 




Depth 
Fill 


Length 


Bar&A'/2"Sq. 


Masonry 
Cu.Yd& 


Concrete 
CaYds 


Paving 


Spacing 


Number 


Length 


/ 


21-0' 


7 " 


40 


5''9" 


24.3 


3.0 


10.2 


2 


2/'-6' 


6'/2" 


43 


99 


24.6 


3.0 


10.4 


3 


24-6" 


1V2" 


43 


99 


26.6 


3.4 


If.d 


4 


27^6" 


7 " 


51 


99 


2d. 6 


3.8 


13.1 


5 


30^6" 


1 " 


56 


99 


30.6 


4.2 


14.4 


6 


33'''6" 


QVz'^ 


66 


♦ » 


32.6 


4.6 


I5.S 


d 


39-6" 


6 " 


33 


«« 


36.6 


5.4 


10.4 



TABLE OF.QUANTITiES 4x4-'CULVERT 



LOG CULVERTS 



97 







O CL 
-J iO 



98 DRAINAGE 

Baker's Foundations 

Rock (poor) 5 tons per square foot 

" (solid & first quality) 25 " " 

Dry clay 4 '' " 

Medium dry clay 2 ] " " 

Soft clay I ton " 

Cemented gravel 8 tons " 

Compact sand 4 " '' 

Clean dry sand 2 " " 

Quick sand and alluvial soil }4 ton " 

Where piles are used for types of construction where slight 
settlement is not objectionable a loading of from 10 to 15 tons for a 
sound well driven pile is conservative practice. 

The safe load for a timber pile driven with a gravity hammer can 
be figured from the following simple formula. (Iowa Bridge 
Specifications.) 

Safe load in lb. = — ; — 
s + I 
W = weight of hammer in lb. 
H = fall in feet 

S = average penetration in inches per blow for the 
last three blows. 

Scour. — Scour is produced in different soils at approximately 
the following stream velocities. 

Sand 2 to 3 ft. per second 

Loam 2 tosK " " " 

Firm gravel 5 to 6 " '' " 

Riprap protection reduces scour. According to Trautwine a 
velocity of 8 miles per hour or 12' per second will not derange 
quarry rubber stones exceeding J^ cu. ft. deposited around piers 
or abutments. If the natural stream velocity is not over 10 ft. 
per second the span is usually regulated so that the velocity under 
the bridge during freshets will not exceed 10' per second. If the 
natural stream velocity of flow at the bridge site is not known it 
can be approximated roughly for small streams by the formula. 

V = cVrs 

Where V — Velocity of flow in feet per second 
C = Constant assumed value 60 
_, ^-. , ,. ,. Cross sectional area of flow 

K — Hydraulic radms :prr~r. — \ = :: 

Wetted perimeter 

S = Slope of stream 

Example,— To approximate the freshet velocity of the stream 
shown having a fall of i.o' per 100' or 53 feet per mile. 



FORDS 



99 




^ Water Arlcn 100 °Lrl 

^'' hefted P^/7We^'"'2S ft. 



V = c Vrs 

C = 60 
100 

4 



R 

s = 



25 

I 



F = 60 V4 X o.oi = 60 -\/o.o4 = 60 X 0.2 = 12 ft. per second. 

Where much ice occurs piers in small streams should be avoided. 
They can be used to advantage to reduce cost however if there is 
no danger of ice or debris jams particularly if the flow is sluggish 
and in the latter case for wide shallow streams the trestle design is 
economical. 

Paved Fords. — For wide shallow arroyos of the arid regions 
of the west paved fords are in general use. These channels 
only carry water during sudden severe storms and it would be 
practically prohibitive in cost to provide large enough structures 




0§^s^ Marking Posts. 



Fig. 23. — Paved ford. 



to carry the sudden large infrequent flows. The road across an 
arroyo is kept slightly below the natural elevation of the wash and 
is paved with concrete, cobblestone or timber (see sketch). The 
alignment is straight and the location of the pavement is shown 
during flood by 4 marking posts 2 at each end which also indicate 
the depth of water so that it can be used even if covered with water 
unless the depth is too great for safety which can be determined 
by the gauges on the range posts. As the concrete is below the bot- 
tom of the stream no scour occurs and generally a thin layer of 
sand is deposited on the concrete which can be easily cleaned off 
with a road machine. 



lOO 



DRAINAGE 



Plate 20. — Light Wooden Bridges. vState of Wyoming. 



^ 4x6 Curl?. J :^ 




\i-Max.6-8'--^\ 



^^^^^^^ ^^^^^^^ 



Cut Washer. 



§x9 Bo If, 
Cui Washer 




Pile AbiMf-ment CnbAbufment 

' ^ ' fhandLo^s. 

Side Eleva-Mon. 

{men Piles are drive rr 
for Head or Win^ Walls, 
use 4 Piles in End denf. 



(Painf Rails and Posfs 
HOT£ \ wifh Two Coafs ofWhiie 
[Lead. 

+ Roadway 
16-—-" 
,.''-?x6"Bloch,2'CfoC. 

'~ T'Steel Wire Spihes, 

2perJoisfs. 



fxaydolf:. 
12x12x24' _ 

fOriffP/nJ^ 
Z'Long. 




fxddolf , 
f| ilxlO'lagScrews/ctoC. 
y^4\6"Curb. 



Half Section Pile Abutment. Half Section Crib Abutment. 



TIMBER BRIDGES 



lOI 









wd 


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% fc % Vf+3 

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TIMBER BRIDGES 



107 






U0I4099 



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PILE TRESTLES 



109 




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DRAINAGE 



Plate 24. — (Continued) 

Dimensions and Quantities for Superstructure 

Capacity is-Ton Truck 







Intermediate Panel 




Panel 






















Length 
(L) 


Size 

of 

Joists 


Joists 


Floor 
Railing 
Details 


Total 
Lumber 


Bolts, 

Washers, 

Spikes, 

Nails 


Feet 


Inches 


Ft. B. M. 


Ft. B. M. 


Ft. B. M. 


Pounds 


ID 


6X12 


590 


800 


1390 


80 




4X14 


460 


840 


1300 




II 


6X12 


650 


870 


1520 


90 




4X14 


500 


920 


1420 




12 


6X12 


700 


940 


1640 


90 




4X16 


620 


990 


1610 






8X12 


lOIO 


. 1020 


3030 




13 


6X14 


880 


1020 


1900 


90 




4X16 


670 


1070 


1740 






8X12 


1080 


1090 


2170 




14 


6X14 


950 


1090 


2040 


90 




4X16 


720 


1 140 


i860 




15 


8X12 


1150 


1170 


2320 


100 




6X14 


lOIO 


1170 


2180 




16 


10X12 


1530 


1240 


2770 






6X14 


1070 


1240 


2310 


100 




6X16 


1230 


1240 


2470 




17 


10X12 


1620 


1340 


2960 






8X14 


iSio 


1340 


2850 


120 




6X16 


1300 


1340 


2640 




18 


10X12 


1710 


1410 


3120 






8X14 


1600 


1410 


3010 


130 




6X16 


1370 


1410 


2780 




19 


10X12 


1800 


1490 


3290 






8X14 


1680 


1490 


3170 


130 




6X16 


1440 


1490 


2930 




20 


8X14 


1760 


1560 


3320 


130 




8X16 


2020 


1560 


3580 




21 


loX 14 


2310 


1640 


3950 


140 




8X16 


2110 


1640 


3750 




22 


loX 14 


2410 


1710 


4120 


150 




8X16 


2210 


1710 


3920 





PILE TRESTLES 



III 



Plate 24. — {Continued) 
Capacity io-Ton Truck 



Panel 


Size 




Intermediate Panel 










Bolts, 


Length 
(L) 


of 
Joists 


Joists 


Floor 
Railing 
Details 


Total 
Lumber 


Washers, 
Spikes, 
Nails 


Feet 


Inches 


Ft. B. M. 


Ft. B. M. 


Ft. B. M. 


Pounds 


10 


4X12 


400 


640 


1040 


70 




3X14 


350 


680 


1030 




II 


4X12 


430 


700 


1130 


80 




3X14 


380 


740 


II 20 




12 


6X12 


700 


760 


1460 


80 




3X14 


410 


800 


1210 




13 


6X12 


760 


810 


1570 


80 




4X14 


590 


860 


1450 




14 


6X12 


810 


870 


1680 






4X14 


630 


910 


1540 


90 




4X16 


720 


910 


1630 




15 


6X12 


860 


930 


1790 






4X14 


670 


970 


1640 


90 




4X16 


770 


970 


1740 




16 


6X12 


920 


990 


1910 






6X14 


1070 


990 


2060 


100 




4X16 


820 


1030 


1850 




17 


6X12 


970 


1070 


2040 






6X14 


1130 


1070 


2200 


no 




4X 16 


870 


mo 


1980 




18 


8X 12 


1370 


1130 


2500 






6X14 


1200 


1130 


2330 


120 




4X 16 


910 


1 1 70 


2080 




19 


8X12 


1440 


1 1 80 


2620 






6X14 


1260 


1 1 80 


2440 


120 




4X16 


960 


1220 


2180 




20 


8X12 


15 10 


1240 


2750 






6X14 


1320 


1240 


2560 


120 




6X16 


1510 


1240 


27 50 




21 


lOX 12 


1980 


1300 


3280 






6X 14 


1390 


1300 


2690 


130 




6X 16 


1580 


1300 


2880 




22 


loX 12 


2070 


1360 


3430 






8X 14 


1930 


1360 


3290 


130 




6X16 


1660 


1360 


3020 




23 


loX 12 


2160 


1420 


3580 






8X 14 


2020 


1420 


3440 


130 




6X16 


1730 


1420 


3150 




24 


loX 12 


2250 


1470 


3720 






8X 14 


2100 


1470 


3570 


130 




6X16 


1800 


1470 


3270 




25 


loX 14 


2730 


1560 


4290 






8X 14 


2180 


1560 


3740 


150 




6X16 


1870 


1560 


3430 




26 


loX 14 


2840 


1610 


4450 


160 




8X 16 


2600 


1610 


4210 




27 


loX 14 


2940 


1670 


4610 


160 




8X16 


2690 


1670 


4360 




28 


loX 14 


3050 


1730 


4780 


160 




8X16 


2780 


1730 


4510 




29 


loX 14 


3150 


1790 


4940 


160 




8X16 


2880 


1790 


4670 





Washers to be ogee type cast iron ; 
or steel plate washers for j^^" bolts. 



' and %" bolts, and cut wrought iron 



112 



DRAINAGE 



Plate 24. — {Continued) 
Dimensions and Quantities— Substructure 



Grade to 
Ground 



Feet 



10-12 
12-15 
15-18 
18-23 
23-26 
One cap io"X I2"X i7'-o" 



Sway Bracing — Intermediate Bent 



Sets 



No. Reqd. 



Length 



Feet 



18 
20 



5 & 20 
20 



Lumber 



Ft. B. M. 



90 
100 
no 
190 
200 
170 



Bolts 



Pounds 



35 
35 
35 
60 
60 



Grade to Ground 


Bulkhead— End Bent 


LumjDer 


Spikes 


Feet 


Ft. B. M. 


Pounds 


4 

6 
7 
8 


27P 

360 

460 
550 
640 


5 

5 

10 

10 

10 



FRAMED TRESTLES 



113 



Plate 25. — Typical Framed Trestle. Illinois Central 
Railroad. 






> ^.,^»„ . e'x /4"5frmgers. 

^ 2x4- Bracing. ^ ; 



flooring 3x12x16' 
Planks.; 



vo ^x H-Sf ringers 



^ ^ 2x4''' Bracing. I 
2'^/0) ! 3 xl4^f ringer. \ J 




Plan 



"3x14 Stringer 




,, %/**• Slope /fof 
'^-^''*- Slopeljfol 



Sfcfe E'eva+ion. 



(\j CO ^ oj cvj 



.lt:|:?|:l*;^Sf| 



2-io^'^y\'^'W2^icP 
fz'xizxid'J:\^-'fP-4'-^^^ e'xe'xS'Post. 

\ p^-'^ \%^^^''xl5'Bol-hs. 

\^3^'x22'Dr!H-bolf. 



I 



^"x22"Dnff'bo/ts% \ 
3^xld"Dri-ffl?o/-fs/ •» 



-12K.!2xl6Cap. 
"^ 3'J(5x20'Brace. 
"^ 3x8 X 16 'Co /far Brace. 
-'3x8x20' Brace. 
"^t^l2^xld'5ili 
--8x12x3' t2'xl2"x24'Po5h 
Mudsills. 




dxIZ'xd'Muc/Siils.V 

3(S5^8-h'0' 



Bent© 2 ond B. 
Showing Road way for Single 
Track Crossing 



3x8 Brace 
2x4" Bridging 

":;^ 3"x8 Collar Brace 

'•\j4^l8"Bol-t5. 

•.^ ^4x2\" Balis, 

■./ <f| *^ ^'^''-Siongifudina I Braces 
bolted to Post '2-^x18" 
Bolts, 

X^x22"DriH-bolts. 

\^^'xl8"DriftboIt3. 
l2x/2'x20'Sill. 



Ben+s 3 and 4- 
Showing Roadway for Double 
Track Cross inq 



114 



DRAINAGE 




CONCRETE TRESTLES 



*»5 









w 








1 




o o o o o^^^^^^ 

t^ t>00 POO <D 0) <U o D OJ 








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C/3 




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O 


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n 


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t-t-oo roo a C C C C C 




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M M M M «^000000 


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'd'd^'d^'d 


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< 


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a 


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s 


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MHMCSNt^Qt^lj^f^iy, 


11 


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d cede C M ^ '^ 


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hJ 






cS (3 


d) O O 0) <U 0) 


Ui 


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Tfvo ooofNcieccaa 






M M M 0, NqQQQQQ 


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I— 1 




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jfl C « 














CO 03 (U 








CO P^ pq 



jQ 



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JO O >< 

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rt:i:l o 

^i\ bo 
Qi ^ d 

O g c« 



la 

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o o 



2^a 
Q.a« 



ii6 



DRAINAGE 



Plate 27. 




f k-W 
'\N^rt(0x2") 



End §)evatioh. 
General Dimensions Semi-Circular Arch Culverts 



s 

span 


Thickness at Springing 
Line 


Thickness of Ring 


Height of Haunch 


T 


K 


C 


R 


J 


V 




Concrete 


Masonry 


Concrete 


Masonry 


Concrete 


Masonry 


6 


2'-6" 


2'-6" 


xo" 


10" 


i'-9" 


2'-o" 


8 


2'-6" 


2'-6'' 


11" 


12" 


2'-6" 


2'-6" 


10 


a'-o" 


3'-o" 


12'' 


12" 


a'-o" 


3'-o" 


12 


a'-e" 


s'-e" 


14" 


15'' 


s'-e" 


3'-9" 


14 


s'-Q" 


3'-9" 


IS" 


15" 


4'-o'' 


4'-6" 


16 


4'-o'' 


4'-o- 


16" 


15" 


4'-8" 


S'-o" 


18 


4'-6" 


4'-6'' 


18" 


18" 


S'-o" 


s'-e" 


20 


,'-o" 


Sl-o" .. 


18" 


18" 


K'-6" 


e'-o" 



SLAB BRIDGES 



117 



Plate 28. — New York State Slab Bridges. 

Note 

All rods to have a deformed 
cross-section. All rib metal to be 
of medium steel. 

2d class concrete in all slabs 
and parapets. 3d class concrete 
in wings invert and abutments. 
Wing walls on the outlet end of 
all square culverts with concrete 
floors to be built parallel to the 
center line of the culvert. Round 
all exposed edges to i^ inch 
radius. 



ffocfs 0.25°"NetArea., 
Spaced IZ"C.toC. 
W^iSpansS'todS!) 
Plan. 




DowehO.iS 
IZ"Cfrs. 
Pile Foundations to be 
UsedinLiqhtandShiir- ^.^ 
ing Soils. Pave when Wc 
Ordered by Div. Engineer 



.'Pods in Slab to be Exfen- 
\ ded 24 Diams. beyond 
\ ^ Neat Lines of , 
\ " Abutment 



Elevation. 



BottomWidihofthe 
Abutments not less than 
^ of Total Height from Bottom 
of Abutment toTop of Slab. 




Section on CenterLine 



For Typical 
Section "F" 

Where culvert covers 
become a part of con- 
crete base for brick 
pavement, transverse 
reinforcement should be 
extended 12" beyond 
back of abutment into 
concrete base. 




IS%r45''Skew\J 
ZdhrmrlS'A i 
\ 
\ 

\ 



Rods in Slab to be 
Extended 24 Diams. 
beyond Neat Lines 
7-\ of the Abutments. 



':Rod5 0.25'' 
NetArea; ^ 
Spaced IZ 
^ CrtoC. 



Dimensions of slabs on page 



ii8 



DRAINAGE 
Plate 28. — (Continued) 



Span 


Thickness of 
Slab* 


Net Area 

of 
• Rods 


Rod 

Spacing 

C-C 


Length 
Dowels 


5 


8" 


0.25sq/' 


4¥ 


12" 


6 


9"^ 


<( 


4" 


n 


7 


10" 


o.39sq-" 


Si" 


u 


8 


10" 


n 


Si" 


{( 


9 


11" 


it 


S" 


u 


10 


12" 


li 


4-1" 


« 


II 


12" 


o.s6sq." 


6i" 


iC 


12 


13" 


<< 


6" 


18" 


13 


13" 


it 


Si" 


u 


14 


14" 


U 


sr 


<( 


IS 


14" 


« 


s" 


u 


16 


IS" 


(( 


4f" 


(( 


17 


IS" 


(< 


41" 


« 


18 


16" 


{( 


4l" 


(( 


19 


17" 


a 


4i" 


« 


20 


18" 


o.77sq/' 


si" 


(( 


21 


18" 


a 


Si" 


iC 


22 


19" 


u 


5" 


24" 


23 


19" 


(1 


S" 


(( 


24 


20" 


« 


4f" 


« 


25 


21" 


i.oosq." 


Si" 


« 



For Spans 5' to 19' W = 18'' For Clear Height 10' or less 
" " 5' to 19' W = 24" " " " 11' to 15' 

" " 20' to 25' W = 24" " " " 15' or less 

For Clear Height 7' or less E = 3'- o" 
8' to 10' E = 4'- o" 
" above 10' E = s'-o'' 
* Note. — The thickness of slab given is for shallow fills. For 
the effect of deep fills see Table 53A, page 565. 



STRINGER BRIDGES 



119 



Plate 29. — New York State I-beam Bridges. 



fxpanded Metal Embedded in 
b "Concrete (Z^CIass)^ 

Length of Culvert 




'\<^/'e 



Exp.Metal- 
Steel Barj'--'^. 




Cross Section of Parapef 
Showing Reinforclncj. 



^ 



Paintall Beams 
1^2 Coats Lead 
and OiL 



\^j^i^^^{^mf^^m^mw^WMM^^'' 




Round all Expoied 
Edqe5to2^'Rad. 
Exp. Metal to be , 
J'e"ord'>tlZ"Mesh\ 
v/eiqhinq not less 
than I2lbs. 
persq.it 



Longitudinal Section. 



Part End Elevation. 



^5teell-Beam 



W^' 




I- Beams Spaced as Shown 

on Table I. 
Expanded Metal 
Ernbedded In 6" 
2S Class Concrete. . 



()'tolZ'high,x-'Z4't(Hx2{') 
Spansl8to30Feet. 




|<--x-->i 
e 'tolZ'high, x= l8^(Hx2^') 
IZ'to.20'" ,x^l8t(Hx3") 

Spans 6 ton Feet. 




^- Length of Culvert 
^ ^Z enqth of Culvert is taken as the 
.,,„ ^Distance from Outs.foOutside ofPara- 
.^Vpetsorfrom 0,to0.of6uarclRailandMeaS' 
vuredonaiineatFlghtAnglestoCLofRoad. 
^ Span is Taken as tfie Distance bet Abutm'ts 
yy. ^i^easured on a Line parallel to the C.L.ofRoad. 
^at Top of I- Beams. Angle of Skew is the Angle 
bet the C.L. of Culvert and a Line at if. Angles to C.L.ofRoad. 
ti=Total Height of Abutment ^ ^ 
A and B = Deflection of Wings in Degrees. 
L and M^Lenath of Wings. , , ^ ^_. 

P = Length of Abutment i^leasured along Face of Top^ 

Skew Culv&rt. 



I20 



DRAINAGE 



lI^H9djji-ynn 



VOOO O N tvooo O N tvooo O N rfvOOO O N rj-vo oo O n ■* 






Ut'J 



<N <N <N w N cOfOfOcOfO^^^^fTj-voiO lO io uovo O vO vO S 



saijidg spunojj 



M <N M fOfOcOfOc0^t^TtrflO«0 1^ io^x5 VO VO VO O R t>. 









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uStJ 

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00 Ov O M Cj fo '^ >OvO t^OO Ov O M (M fo lovo f^OO Ov O c^ fO ? 



Mcjc^cscswc^focofoeo 



0000060666666666666666666 



lOqvOVO <N00 -^H l>.tOM00 OvlOlOH t^TtO t^foioMOO^ 

tj- xo lovo t^ t>»oc5 ovovOMt 



CO X 



mSUa'J 00 Ov O H M fO •^ tovo t>.00 0» M N ro -^ tovo t^OO 0> O H N fO 



;ooj Sz 



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M OvvO "ti- N vovo ^00 M u-> t^ 



00 VO O M N Tt O t^OO Ov o> O 
^, ^.^ -r^OvMroioOPJOOMTj-i^M 

M W cs f0f0r0r0i0»0 lov© t^OO 0> Ov 0» O 



^^^-5«^,„'' * ^ * 5„5*-.**'L*.5^5^ *-.*_* * * 



nh«n|-«nHnhfni'4iH«t-|'« 



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O f0i00vi0f^0vt~«.0 rOVO OvMD OvO t 
MMHHNWMCO"^10»0 lovO VO Ov C 



O O M H W VO t^ t>.00 



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"' •-' •^' ^' v' v' J v' v' v' v' v' O v' v' v' v' v' v' v' ^' ^' 



saqouj 
q:jdaa 



M9^g 






M9^S 



*0 f* 1^00 OOOvO O c^ « w M NV)ioiiOxoio 



VO tooooooooo 



rt- vjvovo ^^00 OvOvO^ ,,, w-,^>^ 

N o»vo ^9 Q r^ -^ H ovvq foq ^■^►^oq locj qvv6 "ro 6 oo io ci' 
Tt ^ ir>vO t^ t^oo 0*0^6 H cJ c5 co-^rj- irjvo vd lAoo 6> 0\ 6 m 

HHMHHHMHHHHHHHWC* 



O VO fj OvvO fO OvvO N OvvO W OvvO N OvtOWOO »/^N00 tOMOO 

oj q ov t«.vo »^ po N H 0*00 *:• »^ -^ fo H o Ov t^vo «o to n h p> 
lovovo i>o6 6^ 6 t 



O VO ^0 OvvO ^^ OvO W OvtON OviOMOOvO WOO tOHOO tOMOO 
»OvO t^OO 0> O H W CO -4 tovd lAoO Ov d H w fo ■^ v>vd t^oo 00 

MHWHMHMHMHWCSC<WC*W<N N N 7« 



B 

pq 



Pt4 
.S 



Span, all Culverts 



VO t^OO Ov O w < 



STRINGER BRIDGES 



121 



o 
to 

M 
II 

w 

H 

< 

r 

o _ 

to 

H 


Cubic Yds. 
each ft. in 
length of 
Culvert 
more or less 
than 25 ft. 


iCjoosBj^ 


H t^ rt CO COVO <N Tt t-- crOvoO 00 M 

<N -^ x>- q POO 00 q "^ qs cooq fo qv 

H \-K \-< (N cs cs rOfO'^'^^iO tovO ^ 


3;3JDU03 


00 Tt■c^lOT^T;^<N OiH '^ 00 to 

0\ <N TtvO On <N to M tooq ^ ^ •"! H 
o'm h h h(N <n POrOcO-<t'«tiO tOvO 


Cubic Yards 

Third Class 

Masonry 


sSm^t 


M '^ too 00 M vq CO "^vq CO to q coo 

d to M 00 t^O H Tt OnvO t}- to I>. m 
M H c^ CS CO '^0 t^OO W '^O 0^ 

M H H H H 


s.inqv 2 


1^ t^o c^ H to Tj-vq CO tooq t^oq -^ 
c^o <N cn t^ to C006 00 Ov d M CO tood 

cs CO r}- ^ too ^^•OO O^ c^ CO -^ too 

M H M H M H 


5S- 


sSujAV ^^ 


<N00 0\cocot^ONO tOTj-l>.H00 000 

tood <N 00 -"^ M c> CO rj-od CO d 00 c. d 

w IH M CO CO too t^ O^ M cs rf t^ 

H M M Hi 


s^;nqv z 


(N "«tO CS 01 tOOO t^ H H CO <>< 

r}-O\tOH00 toC^OO too t^OO 
01 cs CO '^ •^ TjoO r».00 On w CS CO to 


f5 




« 


J>- Q coo ON M 01 toOO 01 tooO w 
-THOO tocoO t^toCN 0\i>-'rt*H On 

CO to i>.o6 d oi rj- to !>. d* d "N tJ-vo" t^- 
MHMHHM0401CS0101 


A 


M\o oio 01 t^oioo cooo H 00 rt- 0^ rh 

tOOO H t^CSOO COtOTj-H tOMO 01 

CO too CO O^'H. oi Tt-tot^ONd oi coto 
HHMMHHO1010101 


CO 

II 
« 

o 
O 
CO 

11 

< 

O 


Cubic Yds. 
each ft. in 
length of 
Culvert 
more or less 
than 25 ft. 


Xjuosispi 


i>- H 00 to too ON O^ On Ht tJ- On t^O t^ 
H ^0 On oi 1000 •^OO CO *>• H M NO 
HMHHoioioicocOTt-Ttto toNO 


3;3Jouo3 


•^ t^OO COOO ^^ M ^^ to too to CO 

Q\ H covq 00 M -"^ q CO i>- H ^ q "^^ On 

d H H M w oi oi cocOco-^-^tototo 


Cubic Yards 

Third Class 

Masonry 

• 


S3UTA\ ^^ 


toON-^t^-Oi H H coioO rj- t->-vo *^ "^ 
vd d 0' oi d On On tJ-CO* 4 m d ci ^ »-^ 

M H OJ 00 CO -^O t^ ON M CO lA t^ 
H M ^ H OJ 


s,;nqv 2 


tOCOtOCO»OCOtOt^01 01 iocOcoi>-io 
00 ^ t^Tt-c^ d '^"'^"^Tf too i>. On 
01 CO •-•}■ rl- too i>»00 On H 01 co "^ to 


-ggcS 


s3niM^ 


tooioq "^"^"^w ^^"^01 ONThw to 

tOON^ONtocOOl toOO O1O0 to-^O dN 
H H 'N CO "^ tovo 00 On H CO to i>. 

\^ ^ \-K ¥^ 


s,;nqv z 


CO CO q q "^ cooq ^^qqi-^. oot^q 

cooo rf d CO d oi H H M H M oi "4 

01 0> CO rt" Tj- too t^OO On H 01 CO Tf 




2. 


% 


t^ COO On M On 01 toOO OI toOO H 
00 COO t^tooi ONt^rJ-H 0^\0 CO H 
cotot^ONd oi ^tot^ONH oi -"^vd 00 

MMHHHH01O1OI0101 


^ 


1^ COO ON 01 ON 01 tOOO OI tOOO H 
CO NO COO t^tOOl ONt^TfM OnO CO M 

C0tOl>.dN0 01 riftot^ONM CS ■^000 

MMMHMMOIOJOIOIOJ 


:iu9m;nqy 
JO :^qSi3H 


K . 


t^OO ON H 01 CO "d- too i>.00 On 

HMMlHMMMMMMOl 



122 




DRAINAGE 






°0 

II 

W 

o' 

II 
< 

o 


Cubic Yds. 

each ft. in 
length of 
Culvert 

more or less 

than 25 ft. 


XiuosEp\[ 








9;ajDuo2 


rt CO vo 0\0 ""^vO vO vO H t^vO OO W On 

fovq <^ ^. ^ q "^ ci t^ fooc Tf o t^ CO 

HHHcJ cicOCO'^'^lO lOsd !>. I>.06 






Cubic Yards 

Third Class 

Masonry 


sSmjv^t' 


00 « woqoq q "^q^q -^ "^oq t>. t^vo 

vd M l>.COIH H H l>.COC>t^t^C>'4H 
H H « CO Tt »OVO 00 On M t^lOOO H 

H H H M (^^ 






s,;nqv 2 


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OnOO 0000 c5n6 m voONiOO' t^coc^ 

Tf rj- lONO ^>-00 O cs CO "^NO 00 On H CO 

H M H M M M M r» M 






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sSujAY ^ 


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to On tJ- t^ lO "s^j-OO H t^ fO H H Tt On 
H c^ oj co-^tot^CO O CN'^vooO 

H H H M M 






s,;nqv 2 


q ^foq Tfioo^ooo t^o Ono o 

CO O 00 t^vO lOVOtot^O tJ-OncO 0\nO 
ro ""t Ti- lO-O t-*00 O w CO f to t^OO O 

MMMIHMMI-4M 




'g 


1 


If 


)^ 


ThvO On M ^0 lO t^ <N TfvO 00 O <N Tj- 

tN CO tJ-OO t^OO Os \-< c< vo -^ lO t^OO On 

'ii-VO 00 CS tJ-vO O^ >-^ cotot^O^H CO 

HHHHHCSC<<N(NCSCOCO 




1 

U 


^ 


vq Mvq HvO HVO y-wO hvO hvO hvO 
CO too 00 Onh c^ Tftot^ONQ H CO'^ 

HHHHHHCSCSCSCS 




1. 


o 
H 
II 

pq 



< 

M 
% 

CO 


Cubic Yds. 

each ft. in 

length of 

Culverts 

more or less 

than 25 ft. 


Araos-Bj^ 


lO CO TfvO O to rf CO O^ ^^00 O "^ M O 
conO OnC^vO OncoO T^0^"^0 toH t^ 
HHH<NCSCSCO'^'^Ti- tOvO VO f^ t^ 






9:iajDU03 


On CO On t^ Xr^OO <N00 ONCOONt^t>.0 rf" 

q CO tooq H rj-oq -"^-oo co t>- m t^ cooo 

HMHMCSC^CSrOCOTt-Tj-tO lOVO NO 




< 


Cubic Yards 

Third Class 

Masonry 


s2m/^Y ^ 


00 CO q 00 t^ On Tf tooq lO CO M i>. Th (N 

VO H f^COM O »-< f^C^ ONl>.t^ONTj-H 

H H cs CO "^ too 00 On M CO tOOO H 






s,:>nqv z 


co<NO t^O Oncom t^ rfO q to O 
coO r^toTCSM OnQ c^ •^^^0 ^oo 
CO -^ "^ too t^OO Cn M CS CO •«:f O t^OO 




■ 




s2m^ t' 


ooq TT^ q^^>.i>-co"^Ti-qN^^ h loio 

tood Tf O* O "^ cooo* M O* CS M M cooo* 

H CI CS CO '^ to t^OO O CS Tj-O OO 

IH M H M H 






s,:inqv c 


o oq to CO t^NO q^^qqo^^qoo 

t^ CS* OnO- CO w d ^O t>od ON CS rf 00 
CS CO CO ''t too 1:^00 On w CS Tt loO 








ll 


1^ 


TfO O^'r* CO to r^ <N "^O OO O CS rf 

Tf too 00 o^ q M CO Tj- loo ^ On q M 

■4o 00* 6 CS* to i>. dv H* CO to !>. dN CS* rf 

HHMHHCSCJCSC) M CO CO 






h5 


Tj-qN-^ON-^qNTtONrtONTt-qN'^qNT}- 

CO ri"0 !>. d» d <N CO too 00 On H CN t}- 
MMMMH HMCSCSM 






:jn3ra:|nqv 
JO ;qSi3H 


K 


O t^OO On O M cq CO "«t too t^OO O O 

HMHMMMMHMHCS 





STRINGER BRIDGES 
Plate 29. — {Continued) 



123 



Tahle No. 6 


Nun 
For Con 








- 


iber I-Besims 
Crete Covers only 








p = Jl^^ncrf ti rkf ATMifmAntc 1 


Length of Culvert 


Spacing 




"&»<" "» *».i^« 


















2'-^" 


2'. 9/. 


3'-o* 


15° Skew 


30" Skew 


45' Skew 


18 


5 


5 


4 


18.64 


20.79 


25.46 


19 


5 


5 


5 


19.67 


21.94 


26.97 


20 


6 


5 


5 


20.71 


23.09 


28.28 


21 


6 


6 


5 


21.74 


24.25 


29.70 


22 


6 


6 


5 


22.78 


25-40 


3I-II 


23 


7 


6 


6 


23.81 


26.66 


32.53 


24 


7 


6 


6 


24.85 


27.71 


33-94 


25 


7 


7 


6 


25.88 


28.87 


35.36 


26 


8 


8 


7 


26.92 


30.02 


36.77 


27 


8 


8 


7 


27-95 


31.18 


38.18 


28 


9 


8 


7 


28.99 


32.33 


59.60 


29 


9 


8 


8 


. 30.02 


33-49 


41.01 


30 


9 


9 


8 


31.06 


34-64 


42-43 


31 


10 


9 


9 


32.09 


35.80 


43-84 


32 


10 


9 


9 


33-13 


36.95 


45.26 


33 


II 


10 


9 


34.16 


38.10 


46.67 



Application of Tables 

Quantities for a 30** Skew Concrete Culvert, concrete top, length 
30 feet, opening 13 feet high and 12 feet wide. From Table i, an 
opening 12.12 ft. wide 30° Skew is a 14-ft. span requiring (see 30-ft. 
length, Table 6) 9 1-Beams spaced 2'-9*' c. to c. (9 X 400) = 3600 lbs. 
I-Beams; 218 lbs. Bars; 400 + (5X16) = 48osq. ft. Ex'p'd Metal; 
9.78 + (5 X 30) = 11.28 cu. yds. 2d class Concrete .32 lin. ft. Pipe 
Rail. An opening 13 ft. high will require Abutments, 16 ft. high 
(13' + 2' in ground + 10" I-Beam = 15'- 10''). From Table 4, 
Abutments^ ii8.ocu. yds., Wings = 102.9 cu. yds. (5X4.79 = 23.95 
cu. yds. 5 ft. extra length of Culvert) 118.0 + 102.9 + 23.95 ~ 
244.85 cu. yds. 3d Class Concrete. 

For Spans of more than 17 feet, use Masonry Tables for Con* 
Crete Abutments and Wings. 



124 



DRAINAGE 



Plate 30. — Typical Method of Reinforcing a Concrete 
. Parapet Girder Bridge. 



3-i-3e^ 






\mMm 



ira:tiauiJijj;iji;Lj^ 



2-/'-33' 

Same Spadm -fbrSirrups. 






STEEL UST. 



Beam Section B-B Showing Spacing ofxrf Stirrups and 
. Bending of Beam B<:jrs.. 



Z-f-2Z'e^- 




26'—- - ■ 

/?-|-r5' 43-^41-26-3' 






^::25:_^ — _^ — jj 
I 



MO 


».^,«i*.™H 


8 




?5^4" 


««r.-7 


hOR. 


C^ 


-yTT 


^?>8 






n 


/" 


/6'-0' 






?4 








VfffT. 


?o 




II'- 0' 


>V>(iZ.S 




/? 




taf-cf 




Hl)H. 


« V 


25i0> 




» 




7V 




vfffr 




V.-l^ir'o'a.Aelw*! 




»V|2*ifl' 


" 










BEAM 








33^£^ » 




^ 




-7^ 


" 


v£«r. 


fOOTISS 





«Arr 9'0' 4-3' 



ALL BARS-Sq. WISTED-HILD STEEL 

41"-//' 
^•1-23-6" 



%"-l2'' 
Section- A- A 



Planfor 4x4 Piling 
if Necessary 




yJioadSurface. 



Camber Formsfo prevent Sag. 
deiel Strips to be Used on all Exposed Corners 
All Steel iobe Placed before Concrete Is Started. 
Concrete to be I'M Mixture. 



Elevation 



„ t'^ raceOldmilniih Concreie.l2"thick. 
Depth Dmaube increased if a Firm Footinq can 
be Found wfhin a Short Distance: if not4x^'s/Kil/- 
be Driven to Solid Bearing 



Design used by Monroe County, New York State. 



UNDERDRAINS 



I2S 



Underdrainage 

The purpose of under drains on hard surfaced roads is to intercept 
the ground water before it reaches and softens the sub-grade. On 
a sidehill road the drain is usually placed under the ditch on the 
uphill side (see Figure No. 24, position No. i) where the greatest 




Position No. I 



Direction 
of Seepage 



Fig. 24. 

depth can be obtained with the least excavation and where the 
water is caught as it flows out of the hill. 

Some engineers place the drain in position No. 2 (Figure 24) 
but this requires more excavation for the same depth and for side 

fa 



? T/jroat^^ 
Position N0.2 I Position No. I Position No. 2 

Pig. 25. 

seepage is not as effective. The usual depth for drains is three 
feet below the surface. 

Where the road is on a descending grade, the water will flow out 
of the hill directly under the stone and the drain is placed as in 

Y--2.0'--^^ }<-- 2.0'-^^ 

Baclifili^^^^;^i^^^m^^^<^f^^lf 



No. 4 Stone-: 

No. 2 Stone orOnuveii 
ParmTile } Joints 



— ^ — V^r'Open Tfiroat 



WrappeoHnBuriap^'O'^ ^'l-O^ 

Fig. 26. 

Figure 25, position _i, or two drains are built in position No. 2. 

Position I is the usual practice, being cheaper and more effective. 

The argument for the two side drains is, that in case the throat 

becomes clogged, a side drain can be taken up without disturbing 



126 DRAINAGE 

the macadam. This rarely occurs in a center drain, as it is better 
protected than those in position 2 and in case the center drain does 
clog, side drains can be constructed at any time. 

There are two kinds of drain in general use: 

No. I is built entirely of stone with an open throat roughly 
laid as shown; it is satisfactory in a water-bearing strata of gravely 







M 




'>"""i>n>>\"">l{f Trrrrf — - 

a! 

Fig. 27. 

loam or clan, but does not work so well in quicksand, which is 
liable to fill it up. It is generally cheaper, however, than No. 2. 
No. 2 is built of porous farm tile or vitrified tile of a suitable 
size (usually 3" to h") with open joints, wrapped with a double 
or triple layer of burlap; the pipe is surrounded and covered with 
clean gravel or %^" crushed stone to a depth of 6", the remaining 
depth of the trench being filled with large stone. If this drain has 
a good fall and the outlet is kept free, it will rarely clog even in 
bad quicksand. 



SUMMARY 127 

The author has successfully used the following method to pre- 
vent the outlet from clogging; after being brought out from under 
the macadam, the drain is continued under and across the ditch 
line, then keeping outside the ditch line, and using a slightly smaller 
gradient than that of the open ditch, the tile is continued down the 
hill until it reaches a point eight or nine inches above the ditch 
grade. Here it is turned into the open ditch through a small 
concrete head-wall and w^hat little material it tends to deposit is 
washed down the ditch by the surface water (see Figure 27). 

Summary of Chapter. — The present bridge situation demands 
attention as even in the richer states it is lagging behind the im- 
provement of the roads. The separation of Bridge and Highway 
funds and the lack of central control often results in the ridiculous 
situation of a modern road limited in use by antiquated bridges. 

Road pavements can be strengthened from year to year by 
additions in thickness and the construction of better surfaces on 
top of existing improvements but structures must be rebuilt entire 
to increase their strength and for this reason more foresight in re- 
gard to future traffic must be exercised in their design. A liberal 
allowance for increased loads is desirable. Liberality in size of 
waterway for culverts is also good policy as it adds only slightly to 
the cost and materially decreases the difficulties of maintenance. 

The design of drainage must be complete and reasonable and if 
the existing scheme is not feasible it should be changed regardless 
of law-suits as whenever an improvement is made it is always 
cheaper to correct mistakes at that time than it will be at a later 
date as every year's use fix the channels more firmly. 

The selection of type offers the greatest chance for reasonable 
economy in culvert and bridge design. 



CHAPTER IV 

LOW TYPE EARTH, SAND -CLAY AND GRAVEL ROADS 

These types of construction are the initial steps in final road 
improvement and serve to gradually pull traffic ''out of the mud.'* 
They are the only types that can be reasonably built in unsettled 
communities or scattered agricultural districts without outside 
aid and if properly located, graded and drained are well worth 
very careful engineering attention. They constitute such a large 
percentage of the mileage of road work that they are probably of 
more economic importance than the higher type macadams and 
rigid pavements. 

They however are only makeshifts under adverse weather con- 
ditions (5 months in the year) as compared with the more substan- 
tial forms and must be regarded as such. They require continuous 
maintenance but not the same degree of perfection in maintenance 
as better roads nor anything like as much money in yearly upkeep 
as traffic is light and no one expects or demands that roads of this 
kind be kept in perfect condition. 

The gravel road will serve in a fairly satisfactory way up to about 
250 moderately light rigs per day. 

The following table taken from Agg's Construction of Roads 
AND Pavements gives an idea of the traffic capacity of gravel and 
macadam roads. 

This shows approximately the practical limit of these roads 
and indicates that earth, sand clay, or gravel are reasonable for a 
large mileage. 



128 



TRAFFIC LIMITS 



129 



Average Daily Traffic Limits in Massachusetts 

Table showing results of observations of traffic on different types of road 
surfaces in Massachusetts. ^ Standard road, 15 ft. in width; gravel or water- 
bound macadam, 5 or 6 in. in thickness, with adequate drainage and proper 
foundation, with 3 ft. gravel shoulder on each side. 



Type of Surface 


Light 

Teams, 

Carriages, 

Wagons 


Heavy 

Teams, 

One-horse 


Heavy 
Teams, 
two or 
more 
Horses 


Automobiles 


A good gravel road will wear 
reasonably well and be 
economical with 


50-75 


25-30 


10-15 


50 to 75 




Needs to be oiled with 


50-75 


25-30 


10-15 


Over 75 


Oiled gravel, fairly good, 
heavy cold oil, ^^ gal. to 
the sq. yd. applied annually 
with 


75-100 


30-50 


20 


500 to 700 or 
more 




Waterbound macadam will 
stand with 


175-200 


175-200 


60-80 


Not over 50 
at high speed 




Cold oil or tar will prove 
serviceable on such macad- 
am with 


175-200 


175-200 


60-80 


50-500 




Macadam will then stand, 
but the stone wears, of 
course, with 


175-200 


175-200 60-80 


500 or more 




*Waterbound macadam with 
hot asphaltic oil blanket 
will be economical with 


100-150 


50-75 


25-30 


1500 and 

more with 

fewer teams 






And stand at least 








50 trucks 










But will crumble and per- 
haps fail with over 

(On narrow tires, ice, farm 
and wood teams, etc.) 


150 


75 


30 




* Waterbound macadam with 
a good surface coating of 
tar (3'^ gal. to the sq. yd.) 
will stand with 


100-150 


50-75 


25-30 


1500 or more 


(But requires to be recoated 
annually with }i gal. of tar 
per sq. yd.) 



It Is assumed that all road surfaces are kept constantly patched, that be- 
fore applying bitumen the road surface is cleaned and patched, and the 
bitumen covered with pea stone and sand or gravel and kept covered so that 
it never picks up. 

* Author's Note. — One coat penetration bituminous macadam will 
stand any number of light autos and more steel tire or truck traffic than 
shown above, because it takes the wear more directly and has no blanket 
coat which crumbles under such traffic. 



130 



SAND-CLAY AND GRAVEL ROADS 



EARTH ROADS 

Rut Roads. — The simplest form of road is the so-called rut road 
used in the arid regions of New Mexico and the southwest. They 
are constructed, by clearing the right-of-way of brush and then 
cutting two shallow parallel ruts in the surface vegetation or soil 
crust by means of two cutting irons gaged to fit the ordinary 
wagon track. A wagon trail of this kind can be constructed for 
from $5.00 to $15.00 per mile; can be used by autos with fair com- 
fort at speeds up to 15 miles an hour and on the flat mesas of this 



mmsvjmmmmm. 



-^^i'— 



Rut road.^ 

district are more lasting and satisfactory than the ordinary turn- 
piked section as so little rain falls that an elevated fill grade does 
not consolidate and is worse than useless for traffic. On these 
rut roads any rain storms that occur wash the coarser particles of 
the soil into the ruts and gradually an armored track is formed below 
the general elevation of the mesa. No drainage structures are 
necessary where construction of this kind is adopted. 



n:-> 



Cutting rig for rut road. 



Earth Roads. — The same principles of grade, section and drainage 
apply to this class of road as to the higher types except that the 
surface ditches are generally made slightly deeper and more care 
is taken with the underdrainage; this is necessary as the earth 
road becomes more easily saturated with water than types which 
are sealed over on the surface. If the natural soil is good road ma- 
terial such as gravel, disintegrated rock, hardpan or sandy loam 
this type of construction carefully graded, drained and shaped 
by blader finish and maintained by dragging makes a satisfactory 
road for light traffic. Their cost depends on the amount of grading 
required and the methods that can be used. The cost of drainage 
culverts, incidentals, etc., will vary but will run about $600 per mile 
for good work. 

Simple blade machine turnpiking, where the dirt from the ditches 



SAND-CLAY ROADS 131 

makes the center fillcost (in districts similar to Wyoming in 1914- 
191 5) about $150 per mile. The same work at present (1918) 
is bid off for about $200 per mile. A fair relative price for first- 
class work of this kind including drainage and incidentals can be 
placed at $600 to $800 per mile. 

In rolling country requiring grade reductions by cut and fill and 
wagon haul a fair relative price including drainage and incidentals 
is approximately $1500 to $3000, where no rock is encountered. 

In mountain road work where the excavation runs anywhere 
from 1000 cu. yd. to 30,000 cu. yd. per mile with a large percentage 
of rock the cost will run anywhere from $1000 per mile to $25,000 
per' mile. A fair average for such conditions is $3000 to $6000 per 
mile. 

As previously stated it is entirely a matter of required grading. 
The approximate cost of different classes of grading are taken up 
in more detail in Chapter X on "Preliminary Investigations." 

Current practice in earth road sections is shown in the following 
plates. 

Mountain Roads, Plate No 11, page 68 

Wyoming Standards " " 5, " ^55 

Iowa Standards " " 31, " 132 

Pennsylvania Standards, " "32, " 132 

Current practice in grading and finishing are given in typical 
specifications, page 139. 

Earth road maintenance is discussed in Chapter VII. 

Where the soil is not a good road material the surface is improved 
by artificial mixtures of selected soil or by surfacing with gravel, 
chert, disintegrated granite, slag, shell cinders, etc., in fact any local 
material that gives body to the surface and prevents softening. 

Sand- Clay Treatments 

Where the natural soil is clay the resisting power of the surface 
during wet weather can be increased by the addition of sand. 
Where the natural soil is deep sand the surface can be made firm and 
resilient by the addition of clay. The so-called sand-clay treatment 
aims to provide a surface layer of mixed sand and clay about 10" 
to 12" deep (see Plate No 33, Alabama Standards) in which the 
sand forms the body and the clay just fills the voids in the sand and 
acts as a binder. It can be readily seem that different materials will 
require different proportioning of the sand and clay; the only sure 
way to get the best results is by experiment on the road during 
construction but to give an idea of the approximate proportioning 
the following list of recommended mixes is taken from the Good 
Roads Year Book of the American Highway Association, 191 7. 

Sand- Clay Roads 

The grains of which sand is composed are usually hard and tough and 
able to resist abrasion if held securely in place. In an asphalt pavement 
they are held by the asphalt and a wearing surface of great resistance to 



132 



SAND-CLAY AND GRAVEL ROADS 



Plate 31. — Iowa Typical Section Earth Roads. 

X ^^V^' L- ll'tQ. ^ Jlp. .; 





L-_ n TQ >u Ji.w. .>J 

I /3' ; 13' 1 

[--"■■ — H-->b^lk- — -^ 




Boftom of Difches' 
fo be Rounded. 









Plate 32. — Pennsylvania Standard Earth and Gravel 

Roads. 

Rise fo Crow n^: I 

Ordina -y Soil. 
2'^ /5'_._.___.->i< IS'.. 

^Risefo Crown /f V ' 

TTTTTTTTrmrmmTTTTTTTrmmmr^^ . 

^30'- — >| 

Gravel not fo exceed I in Di'a 
Rise fo CroY/n^ -7 ' 4"eravef / or 10%0-fClaj and Free from 

^ allLumpSi 





Oravel Roadwau. Xlean Ban kdravelfo Pass ^2 

„. , ^ ,1,1 ^ Screen, retained bua^ Screen. 

Rise fo Crown I' I . ' ^^J jru,, • l^ 

i nfwimiJr}i\}nw)in)nm 77TTTmf7m^^ ^^<^c?fnfe/^/r7^ 

fo be Pebbles. 



Id' .^- 



I 



30' 

Sandtj Loam . 






SAND-CLAY ROADS 133 

abrasion results. In a sand-clay road they are bound together by clay in a 
less firm manner but one giving excellent results on well drained roads carry- 
ing light traffic. The aim of the builder of such a road is to employ just 
enough of the stickiest clay at his command to fill the pores of the sand and 
to mix these materials together so thoroughly that there are neither lumps 
of clay nor pockets of loose sand left in the surfacing. This gives the maxi- 
mum amount of hard sand to carry the traffic and the minimum amount of 
clay to bind it. More sand makes a less durable road and more clay makes 
one which becomes soft more rapidly when wet. 

There is a great difference in the value of different clays for such work. 
Some of them become dough-like when mixed with a certain amount of water 
and can be molded into objects which retain their shape after drying. If 
these molded objects are immersed in water they will retain their form for a 
long time. These varieties are called "plastic clays "_ and the most plastic 
are called "ball clays." There are other varieties which fall to pieces more 
or less quickly when wet, as quicklime does, and they are therefore called 
''slaking clays." They are more easily mixed with sand than the plastic 
clays but they have much less binding power and a road built with them is less 
durable when dry and more easily rutted when wet. The amount of clay 
to be used can be determined by a simple field test described as follows by 
Andrew P. Anderson: 

From typical samples of each of the available clays, test mixtures, varying 
by one-half part, are made with the sand so that each clay is represented by 
a set of mixtures ranging by successive steps from one part sand and three 
parts clay to four parts sand and one part clay. These are worked up with 
water into a putty-like mass and from each mix two equals quantities are 
taken and rolled between the palms of the hands into reasonably true spheres, 
labeled and placed in the sun to dry. When thoroughly baked, a set of 
spheres representing any one clay is placed in a flat pan or dish and enough 
water poured gently into the pan to cover them, care being taken not to 
pour the water directly on the samples. Some samples will begin to disinte- 
grate immediately. Those breaking down most slowly contain most nearly 
the proper proportion of sand and clay for the particular materials. The 
relative binding power of the various clays may then be determined by 
comparing the hardness and resistance to abrasion of the various dry 
samples having the correct proportion of sand and clay, as determined 
by the water tests. 

In February, 1917. representatives of 21 state highway departments and 
of the U. S. Office of Public Roads recommended the following mixtures for 
hard, medium and soft classes of sand-clay roads. 

Hard Class. — Clay, 9 to 15 %; silt, 5 to 15 %; total sand, 65 to 80%; sand 
retained on a 6o-mesh sieve, 45 to 60%. 

Medium Class. — Clay, 15 to 25%; silt, 10 to 20%; total sand, 60 to 70%; 
sand retained on a 6o-mesh sieve, 30 to 45 %. 

Soft Class. — Clay, 10 to 25 %; silt, 10 to 20%; total sand, 55 to 80%; sand 
retained on a 60-mesh sieve, 15 to 30%. 

By clay is meant material separated by subsidence through water and 
possessing plastic or adhesive properties; it is generally below q.oi mm. in 
diameter. ^ By silt is meant the fine material other than clay which passes a 
200-mesh sieve and is generally from 0.07 to o.oi mrn. in diameter. ^ By sand 
is meant the hard material which passes a lo-mesh sieve and is retained on a 
200-mesh sieve, and is generally from 1.85 to 0.07 mm. in diameter. 

The larger part of the following explanation of the construction of 
sand-clay roads was prepared by W. S. Keller, State engineer of 
Alabama, where many miles of sand-clay roads have been built 
and are giving good satisfaction. 

Every farmer who lives in a section of country where both sand and clay 
are prevalent, is more than likely traveling over a section of natural sand- 
clay road but is ignorant of the fact. He can call to mind some particular 
spot on the road he travels though it may not be more than 100 feet in 
length, that is always good and rarely requires the attention of the road 
hands. Good drainage will be noticed at this place and if he takes the trouble 
.to investigate, he will find that a good mixture of sand and clay forms the 
wearing surface. If this 100 feet of road is always good then the entire 
road can be made like it provided man will take advantage of the lesson 



134 



SAND-CLAY AND GRAVEL ROADS 




SAND-CLAY ROADS 



135 




136 



SAND-CLAY AND GRAVEL ROADS 



taught by nature and grade the road so that the drainage will be good and 
surface the balance of the road with the same material. If it is not possible 
to find this ready mixed surfacing material convenient to the read it may 
be possible to find the two ingredients in close proximity. In case the road 
after grading shows an excess of sand, clay should be added, or in case clay 
predominates, sand should be added to produce good results. There are 
four general ways in which sand-clay roads may be built. 

1. Ready mixed sand and clay placed on clay, sand or ordinary foundation. 

2. Sand and clay placed on soil foundation and mixed. 

3. Clay hauled on a sand foundation and mixed with the sand. 

4. Sand hauled on a clay foundation and mixed with the clay. 
Taking up the various methods in order. 

1. A natural mixture of sand and clay can often be found where the two 
materials are found separate. The most important point is to know the 
natural mixture when seen. The very best guide to this is to find a natural 
piece of good road. A sample from the best of this good section will, fby 
comparison, indicate what is required, close to the road to be surfaced. This 
natural mixture of sand and clay can be noticed where red clay and sand 
crop out, usually well up in the hills, having ditches and cuts the appearance 
of red sandstone. A good stratum of well mixed sand and clay will stand 
perpendicular in cuts and ditches, resisting erosion almost as well as sand- 
stone. A test of the best natural sand-clay mixtures will show the sand 
forms about 70% of the whole. The test is very simple. Take an ordinary 
medicine glass, measures 2 ounces of the mixture into the glass and wash 
out the clay. Dry the remaining sand and measure again on the medicine 
glass. The loss will be the amount of clay originally contained in the mass. 

Before placing any sand-clay on the road, the road should be graded to 
the desired width. The surface of the graded road should be flat or slightly 
convex. The sand-clay should be put on from 8 to 12 inches in thickness, 
depending on the character of the sub-grade or foundation. With a hard 
clay for foundation, 8 inches of sand-clay will suffice. If the sub-grade is 
sand it is well to put on as much as 12 inches of the surfacing material. 
After a few hundred feet of surfacing material has been placed, a grading 
machine should be run over it to smooth and crown the road surface before 
the top becomes hard and resists the cutting of the blade. It is a good plan 
to turn the blade of the machine so as to trim the edges of the surface part, 
discharging the excess sand and clay onto the earth shoulders. After one 
round trip with the blade turned out, the remaining dress work with the 
machine should be with the blade turned in, with the exception of one trip 
down the center of road with the blade at right angles to the axis of the road 
for the purpose of distributing any excess of material left in the center. 

After the machine work, it is well to follow with a drag, which smooths 
any rough places left by the machine and leaves the road with a smooth, 
even surface. A sand-clay road, unlike other roads, can not be finished in a 
short space of time. It can be left in an apparently finished condition with 
a hard smooth surface, but it will be found on close examination that the 
hard surface is in reality only a crust, below which there are several inches 
of loose material. After the first hard rain the crust softens, the road be- 
comes- bad and the work appears to be a failure. This, however, is just 
what is needed to make it eventually good. After the surface has dried 
until the mass is in a plastic state, it should be dragged until the surface is 
once more smooth, with proper crown, and should be kept this way by drag- 
ging at least once a day until the sun has baked it hard and firm. The mis- 
take of keeping traffic off during this process of resetting should not be made. 
The continuous tamping of the wlieels of wagons and hoofs of horses is just 
what is needed to compact the sand-clay into a homogeneous mass. The 
ordinary roller is not very effective in this work, but corrugated rollers have 
given excellent results. One type which is widely used has 18 cast iron 
wheels weighing 300 pounds each, which compress the bottom of the mixture 
first. As the material becomes more and more compact the wheels ride 
higher and higher and finally the surface is so hard that the roller does not 
sink into it at all. A drag is an indispensable machine in the construction 
of any kind of sand-clay road. 

2. Sand and clay placed on a soil foundation and mixed. This is neces- 
saiy where the old road has neither a sand nor clay foundation and it is 
impossible to find the two ingredients ready mixed, but possible to get both 
in separate state near at hand. The clay should first be placed on the road 
to a depth of 4 inches and the required width. It is not wise to place more 



GRAVEL ROADS 137 

than a few hundred lineal feet of clay before the sand is hauled, as the clay 
rapidly hardens and makes the mixing process difficult. After, say, 400 
feet of clay have been placed, the clay should be broken by means of a plow 
and harrow, if it has become hard, and sand to a depth of 6 inches placed on 
it. This should be plowed and harrowed in thoroughly. This is best done 
immediately following a rain, as the two can be more satisfactorily mixed. 
The traffic aids the mixing and should be encouraged on the road. After 
the mass appears to be well mixed, the road should be properly shaped, as 
previously explained. The road should be given watchful attention and 
should sand or mud holes appear, a second plowing and mixing should be 
given it. 

3. Clay hauled on a sand foundation and mixed with the sand. The 
mixing process is similar to that described under second head. It is only 
necessary to add that as the foundation is sand, a little more clay will be 
necessary than where the foundation is of clay or soil. 

4. Sand hauled on a clay foundation and mixed with clay. The clay 
foundation should be plowed to a depth of 4 inches and harrowed with a 
disk or tooth harrow until the lumps are thoroughly broken or pulverized. 
Sand should then be added to a depth of 6 inches and mixed as before 
described. 

Sand and clay can be mixed best when wet, but as most road construction 
is done in the summer months, it is necessary to do most of the mixing dry 
and keep the road in shape after the first two or three rains, while the pass- 
ing wagons and vehicles give the road a final wet mixing. A sand-clay road 
is the cheapest road to maintain, for the reason that it can be repaired with 
its own material. With a drag or grading machine ruts can be filled with 
material scraped from the edges, whereas on gravel or macadam roads, this 
is not possible. The repairing of these roads can be^ done almost exclusively 
with the drag, only enough hand work being required to keep the gutters 
open and the growth of weeds cut on the shoulders. Holes are repaired by 
adding more sand-clay, and when many of them appear fresh sand-clay 
should be spread over the surface of the road. If the road gets into really 
bad condition, the roadbed should be plowed up, reshaped and fresh sand- 
clay added. This is unnecessary where the road is maintained properly and 
the travel is not too heavy for the type of construction. 

The maintenance of sand-clay is discussed in Chapter VII. 
Specifications for sand-clay are covered in Part III. 

Sand-clay roads can not be considered as finished until traffic has 
used them for a year or two and all the small areas showing improper 
mix have been remedied by maintenance. 

The cost of surfacing with sand-clay varies as any form of con- 
struction with labor, length of haul, cost of materials, etc., but 
generally adds from 15c. to 35c. per square yard to the cost of an 
earth road. A fair comparative figure would add $1000 to $2000 
per mile for a 16' width of sand-clay to the cost of an ordinary dirt 
road in the same location. 

Sand-clay construction is not advised if good road gravel or other 
coarse local materials are available. 

GRAVEL ROADS 

A coarse well graded gravel is the most satisfactory material for 
a cheap road. It giv^es body to the traveled track, binds well, 
rides easily and with a consolidated depth of 8" to 20" holds all 
ordinary loads after it is well consolidated. For wheel pressures 
and depths of metaling see Chapter V, page 152. 

At the present time 50% of the mileage of surfaced roads in the 
U. S. are gravel roads. 

They are however hard to consolidate quickly and need carefully 
continuous attention to prevent the formation of ruts, holes, or 



138 SAND-CLAY AND GRAVEL ROADS 

humps. Gravel roads can not be built by merely dumping loose 
gravel on the road and then hoping that traffic will put it in shape. 
A large mileage has been built on this principle and the results 
are shameful. A successful gravel road requires careful select ion 
of the gravel, careful spreading, careful consolidation and constant 
maintenance. The best practice is shown in typical specifications 
Part III but the essential features will be summarized at this 
point. 

Size of Gravel 

Gravels suitable for road work are widely distributed over the 
country. They occur in bank deposits and in stream beds. The 
prime requisite of a gravel for foundation courses is that it contains 
a large percentage of coarse pebbles to give body and distribute 
the wheel loads. The prime requisite for a surfacing gravel is hard- 
ness of the stone and well graded coarse and fine particles which 
will take the wear evenly and bond well. Pit run gravel varies 
greatly as to size and composition even in a single pit and for this 
reason no definite limits can be well set for the proportion of 
sizing. In general it can be said that for foundation courses any 
coarse gravel, which when screened through a ^i^" mesh contains 
less material passing the screen than retained on it, can be success- 
fully manipulated without screening to remove the excess sand. 
In some localities this limit is not feasible on account of excessive 
fine material and the limit of fine material passing a }yi" mesh is 
placed at 60 % but in reality a gravel of this fineness does not produce 
satisfactory results and a road on which it is used becomes more 
nearly a sand-clay construction than a gravel type. For a top 
course the large stone above i J'^" in size should be screened out and 
if pit run is used the sand passing the J^" mesh should not exceed 
40% of the volume. The most satisfactory top is a screened gravel 
but this adds materially to the cost. Where screened gravel is 
used '^'2" to 3" is satisfactory size for the bottom course and J^" 
to !%" for the top course. 

The following specification has been recommended by the com- 
mittee on Materials of the American Society of Civil Engineers. 

Two mixtures of gravel, sand and clay shall be used, hereinafter desig- 
nated in these specifications as No. i product (for top course) and No. 2 
product (for middle and bottom courses). 

No. I product shall consist of a mixture of gravel, sand and clay, with the 
proportions of the various sizes as follows: All to pass a I'^i" screen and to 
have at least 60 and not more than 75 % retained on a ^^ inch screen; 
at least 25 and not more than 75 % of the total coarse aggregate (material 
over 3'i inch in size) to be retained on a ^^ inch screen; at least 65 and not 
more than 85 % of the total fine aggregate (material under 3^ inch in size) 
to be retained on a 200-mesh sieve. 

No. 2 product shall consist of a mixture of gravel, sand and clay, with the 
proportions of the various sizes as follows: All to pass a 2^ inch screen and 
to have at least 60 and not more than 75 % of the total coarse aggregate to be 
retained on a i inch screen, at least 65 and not more than 85 % of the total 
fine aggregate to be retained on a 200-mesh sieve. 

Bonding Properties. — Clean gravel will not bond well. A small 
percentage of clay, loam or lime dust is desirable and necessary. This 



GRAVEL ROADS 139 

per cent, ranges from 10% to 20%. For bottom course, pit run 
a gravel which contains over 20% of clay or loam should not be 
used; from 10% to 15% gives the best results. For top course 
10% is about the maximum clay or loam allowable. Many so- 
called cementitious gravels of lime rock contain or produce under 
trafl&c a first-class rock dust binder of the highest grade. Clay 
or loam can be added to a clean gravel by mixing at the pit or by 
placing a thin layer of such material over the gravel as spread on 
the road and mixing it with the course during consolidation. 

Spreading. — Gravel must be uniformly spread; there are two 
general methods; the trench spread (Plate No. 34) and the feather 
edge spread (Plates 35 and 36). The feather edge spread is probably 
the better method. In either case the depth should be uniform 
and the surface properly crowned. Gravel should not be dumped 
in piles; it should be spread along in windrows and the spreading 
finished by shoveling, raking or by road machine blade scrapers. 
If pit run gravel is used the course should be harrowed to distribute 
the sizes uniformly. The ratio of compacted to loose depth is 
approximately 1.2 or 1.25. That is a loose depth of 8" will compact 
to about 6J^". If screened gravel is used the filler should be 
added before the course is rolled. 

Consolidation. — Consolidation is the hardest feature of pit 
run gravel construction. Detail methods are described under 
gravel' foundations, Chapter V, page 156. A combination of traflSc 
and roller consolidation while the gravel is moist gives the best and 
quickest consolidation although traffic alone will put it down 
firmly if given time and the shape is kept intact by constant drag- 
ging with a hone or road machine. The following Minnesota 
Specification shows the methods employed where a road roller is 
not used. 

MINNESOTA SPECIFICATIONS 

Graveling 

Description. — Graveling shall be construed to mean all surfacing with 
pit run gravel, screened gravel or crushed rock, or crushed rock screenings 
built in two or more successive courses. 

Material. — All materials shall be of a quality approved by the engineer 
and shall be the best obtainable from the specified pit or quarry. Materials 
for the first course shall contain no stone which would be retained on a screen 
having 2}^^ inch openings. Materials for the second course shall contain 
no stone which would be retained on a screen having i inch openings. If 
available material contains an excess of sand, such excess shall be handled as 
provided by special specification for each job or project. 

Sub-grade. — The cross-section of the sub-grade shall be as shown on the 
standard cross-section # accompanying the plans. Graveling upon a wet 
pauddy roadbed will not be permitted. If the graveling is not done in con- 
junction with the grading as a part of the same contract, the sub-grade for 
the full length of job embraced in the graveUng contract, shall, before being 
graveled, be dressed by the County to the cross-section above mentioned. 
Thereafter, the contractor shall keep it dressed to the specified cross-section 
and free from ruts, waves and undulations, as part of the graveling contract. 
If the grading and graveling are performed under the same contract, the 
preparation of the sub-grade shall be performed as part of the grading item 
and no additional charge will be allowed therefor under the graveling. 

Loading and Hauling. — Loading from pits shall be performed in such a 
manner and by such methods that a uniform grade of materials will be 
delivered upon the road. Stone exceeding the sizes specified, shall not be 



I40 



SAND-CLAY AND GRAVEL ROADS 



Plate 34. — Iowa Typical Gravel Roads. 




J 's" . 

'^ Shoulder Drain. 

/Requires 2450 Cu. Yds. oi 6rave! per Mile. \Maximum'Z'6" 

"half Section m Fill, Half Section m Cut. 
CUA5S"A" DOUBLE TRACK ©RAVEL ROAD. 



CLASS A SINGLE TRACK 6RAVEL ROAD. 




Requires I&&5 Cu.Yds. of6ravelperMife. 
Hal-f Section in Fill . Half Section in Cut. 



(Mi'nimum'l'6\ 
\Maximum'Z-6' 



It to lO'fo 



4/^^-~.-J 



--M — e- 




Requires 680 Cu. Yds. of Gravel per Mile. 

Half Section in Fill Half Section in Cut, 

CLASS "b" 10 FT. SRAVEL ROAD. 

ITTrc f^frol Sq&few -for Maintenance Is recommended -for all gravel Roads. 
The Class's^ Section is approved only wifh the understanding that a suitable 
Patrol System for Maintenance will be adopted. Wider Cross-sections 
using the same Thickness ofQwvei mil be approved on application, 



GRAVEL ROADS 



141 




142 



SAND-CLAY AND GRAVEL ROADS 



Plate 36. — Minnesota Gravel Road Section. 



{'Sub-grade 5hapeda& shown 
^F^rsf- Course'' "^'"^ ©ravel Surf «acl n q -for Li9h+ Tra-ff i Qo 
|<_- /g' ^ 12' 



ZZLo.3' 



Dep+h la^Course O.OO' O.OO' 
Depfh2<l!*Cour&e 0.00' 0.00' 
To+al DeptH O.OO' O.OO' 



at ^^ 

0.18' 0.21* 0.23' 0.25* 0.23* 0.2l" 0.18' 0.00' 0.00' 550 CaYd.perMi. 

0.00' O.IO' 0.15' 0.15' 0.15' 0.10 000 O.OO" O.OO' 250 v » » » 

0.16' 0.31' 0.38' 0.40* 0.38 0.3l' 0.18 0.00 O.OO' 500 »♦ *f " *r 
Gravel Surfacinq -for Medium Traffic. 



-12' - 



12' - 



Depth l?tCourse 0.00 0.17 
■Depi-h22^Course0.00 OOO' 
TolBlDep+h 0.00 0.17 



I 



0.21' 025' 0.29 0.32* 0.29 0.25* 0.2:1 ' 0.17' 
0.09 0.15' 0.18' 0.18' 0.18 Oj5' 0t09' O.OO' 
030* 0.40' 0.47 0.50' 0.47 0.40' 0.30* 0.17" 
S+andard 6ravel Surfacinq Secfion. 
'f2' >]<- 12' -^- 



0,00 SOOCaYd.perMi. 
O.OO' 400 »» »» »f *> 
0.00' 1200 »' '» •» »» 



-H 

^ ! 



*5fCour&€ O.OO' 

i^Course O.OO ^OO' 0.10' 

ToialDepfhO.OO 0.17* 0.30' 



£.17' 0.20' 

t5oo' 



,0.23 0.27' 0.30' 0.30* 0.30' 0.27 0.23' 0.20' 
0.17' 0.20 0.20' 0.20" 0.20' 0.20' 0.17' O.IO' 
0.40' 047 0.50' 0.50' 0.50' 0.4V' 0.40' 0.30" 



0.17* 0.00'IOOOCaYd.perMi. 
0.00* 0.00* 600 " '» »' " 
.0.17' 0.00'l600"»» » *' 



^n Excavation 

U---* minr ->Kr 2 '->K— 
WadeLine\ j 



Genera 1 Grading Section InEmbankment- 

C.L. , 
-12' >t<- -12 H „^> 



0,2' Finished Line 



Irt Excavation. 



16rade fo Cross-section shown bu Heavy Line) 
Ciaij or of her good Bearing Material being 
placed in Top to Cover poorer Soil.- diaded 
and Planed Finishing to produce Crown indicated 
by Dotted Line. 

Grading Section in Sand InFmbankment 

.....yp ' ^- /2' ->, 

ir 

0.2' 



tnDeep Soundings. 



Grading Section in Swamp 



In Firm Swamp, 



GRAVEL ROADS 143 

loaded. No earth, sod or any foreign or vegetable matter, nor an excess 
of sand or clay, will be allowed in the gravel, and care must be taken that 
strippings be not mixed with the gravel. Any loads taken to the work 
containing such objectionable materials will be rejected. 

Dumping and Spreading First Course. — The first course material shall be 
deposited in a uniform ridge on the center line of the road and shall be 
spread immediately upon the sub-grade to a uniform section. This work 
shall be started at a point on the road nearest the pit or loading place and 
shall proceed therefrom until the extreme haul in that direction is reached. 

Shaping and Compacting. — The surfacing material shall be shaped, while 
being compacted under travel by the use of a blade grader, tooth harrow, 
planer or other suitable means. Ruts formed by the hauling or by travel 
shall be dragged full at least once each day and more frequently if necessary, 
to prevent cutting through the surfacing material into the sub-grade. Holes, 
waves and undulations, which develop and are not filled by dragging shall 
be filled by adding more material according to the direction of the engineer. 
The shaping of the material shall be performed according to the direction 
of the engineer and shall be continued until the material is well compacted, 
free from ruts, waves and undulations and is made to conform to the cross- 
section indicated on the standard above mentioned. 

If the material is not sufficiently compacted by the above methods within 
twenty days after placing, the engineer shall direct the character, amount 
and method of applying the binding material necessary to produce a com- 
pacted surface, and the contractor shall provide the necessary labor and 
equipment to perform such additional work at the unit prices submitted 
for the application of the regular surfacing material. The County shall 
furnish this binding material in the same manner as provided for the regular 
first and second course material. 

Second Course. — When the first course is compacted and shaped as speci- 
fied, to the satisfaction of the engineer, he shall authorize the application 
of the second course materials. It shall then be applied, shaped and com- 
pacted by the methods specified for the first course. _ The work of shaping 
and compacting shall be continued until the material is well compacted 
with the surface free from ruts, waves and undulations and conforming to 
the specified cross-section. 

Maintenance. — Maintenance is discussed in Chapter VII. 

Oiling. — Oiling with a light cold asphaltic oil or cold tar is re- 
sorted to under a moderately heavy automobile traffic. No 
gravel road should be oiled till at least a year old so that it is com- 
pletely consolidated and firmly bound. The surface must be 
well cleaned of excess fine dust and the oil applied in two or three 
successive light coats of approx. J^ gallon per square yard at inter- 
vals of two or three months. It takes more than one application to 
give even moderately good results as the clay and loam in the road 
tends to prevent the formation of a good bond between the oil 
and gravel but if persistent treatment is adopted this method in- 
creases the power of gravel roads to withstand touring car traffic 
but of course does not increase their structural strength or make 
them suitable for heavy unit freight hauling. 

Cost. — Pit run gravel varies in cost from 50c. to $1.50 per con- 
solidated cubic yard in place. Screened gravel from $1.00 to 
$2.00 per consolidated cubic yard. 

Gravel surfacing adds approximately $1000 to $3000 per mile 
to the cost of an earth road in the same location and a fair compara- 
tive price for this type including drainage and incidentals ranges 
from $2000 to $5000 per mile. 

Other Coarse Materials. — The same principles apply to the 
use of any available local material such as slag, chert, caliche, 
disintegrated granite, cinders, shell, etc., each one of which can be 
used to advantage in special localities. 



r44 SAND-CLAY AND GRAVEL ROADS 

Miscellaneous Special Cases. — Alaskan Climatic and soil re- 
quirements afford special problems; the following quotation from 
Engineering and Contracting of March 6, 191 8, indicates an inter- 
esting condition as described in the report of the Alaskan Highway 
Commission. 

"The most unusual and troublesome feature encountered in construction 
is the permanently frozen ground which covers a large portion of the entire 
interior, and which is protected from thawing during the summer by a thick 
layer of moss, turf, or decayed vegetable matter. The character of this 
frozen material varies largely in different sections of the territory, and even 
in the same section. It may be gravel, clay, silt, peat, or clear ice, or a com- 
bination of two or more of these elements. 

When gravel is encountered the problem presents no special difficulties; 
the moss or turf is stripped off, and the road graded in the usual manner. 
When the material is clay, experience has shown that the same procedure 
can usually be followed, but the grading is a slow and rather expensive 
process. After the protective covering of vegetable matter is removed, it 
is necessary to allow the soil to thaw and dry out somewhat before it can be 
worked, and unless a considerable period is allowed to elapse between the 
stripping and the grading, it will be found that the thawing has not extended 
to sufficient depth to permit of completing, the grading in one operation. 
When the necessity for the road is not pressing, an appreciable saving can 
be effected by stripping the road bed and digging drainage ditches during 
one season, completing the construction the next year. 

In those localities, however, where the frozen material is silt or peat, the 
stripping of the roadbed quickly results in the formation of a quagmire 
through which a man or horse, even without a load, can pass only with the 
greatest difficulty. Such soil has sufficient bearing value only as long as it 
remains frozen, which makes it desirable that the moss or turf over-lying 
it be kept intact. This layer of vegetable matter is not of itself able to 
sustain traffic, necessitating the addition of a protective covering — usually 
pole or brush corduroy when timber is available. Fortunately the growth 
of scrub spruce timber which covers a large part of interior Alaska, except 
the Seward Peninsula, affords excellent material for this corduroy. 

Where the trees are large enough pole corduroy is constructed by grubbing 
all stumps and roots from the roadbed, leveling it, and laying perpendicu- 
larly to the axis of the road a single layer of poles from which the largest 
and stiffest branches have been trimmed. Ditches are then dug at a dis- 
tance of 3 to 5 ft. from the ends of the poles, and the material therefrom, 
after rejecting the top layer of vegetable matter, is placed on the corduroy 
for the double purpose of protecting it from wear and affording a smoother 
roadway. If the soil in the ditches is entirely unsuitable for this covering, 
other material, preferably gravel, is hauled on from the nearest available 
source. 

Where the spruce timber is of very small size, or where only small willows 
are available, as on the Seward Peninsula, brush corduroy is used. The 
method of construction is similar to that described above, except that the 
single layer of poles is replaced by mattress of untrimmed brush containing 
sufficient material to give a thickness of at least 6 inches when compressed. 

When corduroy has been properly protected, its life in most parts of 
Alaska is quite long. Poles taken out of the road after 10 years of service 
have been found to be in excellent condition. 

The 3 to 5 ft. berm which -s left between the ends of the corduroy and 
the ditches is very necessary to protect the corduroy from undermining, as 
the ditches, under the action of sun and rain, slough and cut rapidly. Ordi- 
narily, as the frozen soil thaws and cuts away the moss of the berm gradually 
assumes a gentle slope to the bottom of the ditch, effectually protecting the 
corduroy, but where the cutting is severe, it often becomes necessary to 
revet the insides of the ditches with moss or turf. Frequent outlets from 
the ditches must be provided, and when the amount of water reaching the 
ditch on the upper side of the road is large it is advisable to construct an 
additional ditch parallel to the road and about so ft. away, with sufficient 
outlets to culverts of ample size. 

Along the Pacific coast of Alaska no frozen ground is encountered, but 
the mountainous character of the country, the excessive rainfall, and the 
difficulties of clearing, have made the work, as a rule, even more expensive 



ALASKAN ROADS 145 

than in the interior. Unless the soil encountered in this region is gravel, 
it will not stand up under traffic during the heavy and continuous rains, 
and some protective covering is required. Fortunately gravel is usually 
found at no great distance; otherwise corduroy or plank roads are constructed. 

The numerous swift streams of glacial origin found in the Pacific coast 
section and throughout the Alaskan range in the interior have been the source 
of much trouble and expense. Flowing through gravel beds varying in 
width with the volume of water carried up to 2 miles or more, they rarely 
have any fixed channels. It is by no means uncommon for one of these 
streams to abandon an old channel and establish itself in a new one ^i mile 
away almost over night. When warm weather causes rapid melting of 
snow and ice in the glaciers, these streams become raging torrents of enor- 
mous destructive force, and roads paralleling them are in constant danger 
of being washed away. Numerous methods of bank protection to prevent 
damage from this cause have been tried, of which the following has proved 
to be the cheapest and most effective: A layer of loose brush of sufficient 
length to give the requisite protection is placed on the threatened bank, per- 
pendicular to the current and weighted below the center with stone enveloped 
in galvanized-wire netting, the whole being anchored in place by wires ex- 
tending to "dead-men." For emergency work when the water is too high 
to permit of placing the wire netting and rock, the brush is made into fas- 
cines inclosing sacks of earth, which are then placed against the threatened 
bank and wired to it and to each other. This form of protection is easily 
and quickly constructed and has repeatedly demonstrated its effectiveness. 

As now constructed, the width of wagon roads varies with the formation 
of the ground and the amount of traffic expected, but as a general rule roads 
graded by other means than the road grader are given a minimum width of 
20 ft. between ditches, and those on which the road grader is used a minimum 
width of 24 ft. On steep sidehills and where rock work is involved, the 
width is reduced to 10 or 12 ft. The standard width of clearing is 30 ft. 
but this is increased to 60 ft. where necessary in order to secure the beneficial 
action of wind and sun on the roadbed. 

Sled roads for winter traffic only are cleared for a width of 16 ft., with all 
stumps, hummocks and similar obstacles removed for a width of 8 ft. _ They 
are constructed where the amount of traffic is not great enough to justify 
a wagon road, where the cost of building a wagon road would be prohibitive, 
or where the communities along the route are amply served by water trans- 
portation during the open season, as is the case with the Fairbanks-Fort 
Gibbon sled road. If it seems probable that future development may de- 
mand or justify a wagon road, the location is made as for a wagon road, in 
order that work done on the sled road may be of use when the improvement 
is made. 

Trails designed for travel by dog team in winter or by pack train in sum- 
mer are given a width of 8 ft., with all stumps and underbrush cutoff as 
close to the ground as possible. 

In the past, the work of constructing and gradually improving the roads 
has been so generally intermingled with maintenance operations that a sys- 
tematic plan for maintenance has not been put into effect, nor would such 
a plan have been feasible in view of the uncompleted state of the roads. At 
the present time, however, the condition of parts of the more important 
roads, notably the Valdez- Fairbanks Road, is such as to make practicable 
their maintenance by dragging. As Alaska has only a very small agricul- 
tural population, the method adopted in many states of contracting with 
farmers adjacent to the road for the necessary dragging can not be used, 
but it is intended to place on completed sections small maintenance crews 
consisting, as a rule, of two men each, supplied with a team, wagon, drag, 
and the necessary small tools. Two such crews have been employed on 
the Valdez-Fairbanks Road during the present summer, with very satis- 
factory results. On several of the gravel-surfaced roads in southeastern 
Alaska the patrol system of maintenance has been used in connection with 
more extensive repairs. The results show the method to be very effective 
for roads of this character. 

The average costs per mile, including construction and maintenance of 
all roads and trails constructed by the board since its organization in 190S 
are as follows: Wagon road, $3,419; sled road, l379;. trail, $ii3; ^A division 
of these amounts to show the exact cost of construction proper is impossible, 
but a careful analysis of the available data indicates that the following unit 
costs of construction, including bridges, may be accepted as approximately 



146 



SAND-CLAY AND GRAVEL ROADS 



correct: Wagon roads, $2,475 per mile; sled roads, I300 per mile; trails 
$65 per mile. The average costs of maintenance during the past season 
were as tollows: Wagon roads, $250 per mile; sled roads, S14 per mile- 
trails, $8 per mile." * 

Arid Regions. — In the arid regions fills must be avoided. Ordinary 
earth roads are constructed below the general elevation of the 
ground as follows: 

Na-hura! 6round Surface -•, 



which keeps them mqjst longer; shallow ditches are used for the 
same reason. In many cases a hardpan formation underlies the 
sand surface and in these conditions the sand surface is scraped off 
and the road built on the underlying strata. 

Where fills must be used they should be made during the rainy 
season and the addition of clay to a sandy soil helps consolidate 
the traveled way. Readers are referred to the reports of the 



y^Surfaceo fSand 




UnderlLfin^ Hardpan 

State Engineers of New Mexico and Arizona for further data on 
the special treatment of roads under these conditions. 

Summary of Chapter. — Roads of the type discussed in this 
chapter form the groundwork of future high-class pavements and 
represent the greater percentage of mileage of roads in this country. 
They are entitled to more engineering supervision than they have 
received in the past. 



CHAPTER V 

GRAVEL AND STONE FOUNDATION COURSES FOR HARD 
SURFACED PAVEMENTS 

Concrete foundations are considered under "Rigid Pavements'^ 
in Chapter VI. 

The real foundation of a road is the earth sub-grade; generally, 
however, the term foundation is used in speaking of the lower 
course of stone, gravel, etc., used to help distribute the concentrated 
wheel loads. A discussion can be developed under the following 
heads. 

1. The bearing power of different soils. 

2. The concentrated wheel loads on improved roads. 

3. The distributing action of foundation courses and the depth 
required for different soils. 

4. The different kinds of foundation courses. 

5. The distribution of the stone in the foundations. 

6. Special cases. 

I. Bearing Power of Soils 

The sub-grade develops its greatest bearing power when dry. In 
the following discussion we assume that the soils are protected by a 
well designed drainage system. 

Mr. W. E. McClintock, Mem. Amer. Soc. C. E. Chairman of the 
Massachusetts Highway Commission, published in the 1901 report 
of the Commission a valuable statement of the results of their inves- 
tigations on the bearing power of soils and the distribution of wheel 
loads by the macadam. 

"The Commission has estimated that non-porous soils, drained of ground 
water, at their worst will support a load of about 4 lb. per square inch; and 
having in mind these figures the thickness of broken stone has been adjusted 
to the traffic. 

"On a road built of fragments of broken stone the downward pressure 
takes a line at an angle of 45 degrees from the horizontal and is distributed 
over an area equal to the square of twice the depth of the broken stone. 
If the division of the load in pounds at any one point by the square of twice 
the depth of the stone in inches gives a quotient of four or less, then will the 
road foundation be safe at all seasons of the year. On sand or gravel the 
pressure can be safely put at twenty pounds per square inch. 

"Acting on this theory the thickness pi the stone varies from four inches 
to sixteen inches, the lesser thickness being placed over good gravel or sand, 
the greater over heavy clay, and varying thicknesses on other soils. In 
cases where the surfacing of broken stone exceeds six inches in thickness, 
the excess in the base may be broken stone, stony gravel or ledge stone; the 
material used for the excess depending entirely upon the cost, either being 
equally effective." 

147 



148 GRAVEL AND STONE FOUNDATIONS 

It will be noted that the values of the safe bearing power of soils 
are well under those used for building foundations. The depths 
however are not enough for modern traffic as will be discussed later. 
For purposes of convenient reference traffic is classified on page 164 
and will be referred to as Classes I, II, III and IV. 

2. Concentrated Wheel Loads 

There should be some limit placed by law to the maximum 
load per lineal inch of tire for vehicle using improved roads. The 
roads can then be designed for this load with no danger of failure 
from unreasonable pressures. Road work is handicapped in this 
country by the lack of wide tire statutes and the regulation of 
traction engines using sharp lugs on the wheels. At present it is 
necessary to assume a loading that will probably not be exceeded 
by the unregulated traffic. Many engineers favor a law limiting 
the load on improved roads to 700 to 800 lb., to the lineal inch of 
tire width, which is a reasonable limit; with a six inch thread this 
would mean a load of nine tons for a four wheel wagon provided the 
load was uniformly distributed. This is beyond the limits of team 
hauling. 

Most of the mechanical trucks in present use have tires wide 
enough to reduce the pressure below this limit. Near some of the 
large cities, however, mechanical trucking has increased to propor- 
tions that amount to a regular freight line and excessive loads are 
carried; the load and speed for such trucks must be regulated, for 
no road can stand abuse of this character. In special metropolitan 
districts where truck freighting is desirable to relieve rail congestion 
or where it is economical by means of its direct loading and delivery, 
specially designed toll roads, which are self supporting financially, 
could be built to handle much heavier loading, but for free public 
use roads, maintained by the community, a gross vehical load of 12 
tons is a reasonable limit. 

The following regulations governing the control of motor trucks 
and traction-engines were prepared by the New York State High- 
way Commissioner to go into effect in 19 14. 

Regulations for State and County Highways Adopted 

BY THE Commissioner of Highways of the State of 

New York 

Section i. — No traction-engine, road-engine, hauling-engine, trailer, 
steam-roller, automobile truck, motor or other power vehicle shall be 
operated upon or over the state or county highways, the face of the wheels 
of which vehicle are fitted* with flanges, ribs, clamps, cleats, lugs or spikes. 
This regulation applies to all rings or flanges upon guiding or steering wheels 
of any such vehicle. In case of traction-engines or hauling-engines which 
are equipped or provided with flanges, ribs, clamps, cleats, rings or lugs, 
such vehicle shall be permitted to pass over said highways provided the 
cleats are fastened upon all the wheels of such vehicles, and are not less than 
2>^ in. wide and not more than i^i in. high, and so placed that not less than 
two cleats on each wheel shall touch the ground at all times, and the weight 
shall be the same on all parts of said cleats. 



MILITARY LOADS 149 

Section 2.-^No traction-engine, trailer, steam-roller, automobile truck, 
motor or other power vehicle shall be operated upon or over the state or 
county highways; nor shall any object be moved over or upon any such 
highways upon wheels, rollers or otherwise, in excess of a total weight of 
14 tons, including the vehicle, object or contrivance and load, without first 
obtafning the permission of the State Commission of Highways as here- 
inafter provided. No weight in excess of 8 tons shall be carried on any one 
axle of any such vehicle. 

Section 3. — The tire of each wheel of a traction-engine, road-engine, 
hauling-engine, trailer, steam-roller, automobile truck, motor or other power 
vehicle (except traction-engines, road-engines, and hauling-engines) shall 
be smooth, and the weight of such vehicle, including load, shall not exceed 
800 lb. upon an inch in width of the tire, wheel, roller or other object, and 
any weight in excess of 800 lb. upon an inch of tire is prohibited unless 
permission is obtained from the State Commissioner of Highways as here- 
inafter provided. 

Section 4. — No motor or other power vehicle operated upon any state 
or county highway shall be of a greater width than 90 in., except traction- 
engines which may have a width of no in. 

Section 5. — No traction-engine, road-engine, hauling-engine, trailer, 
steam-roller, automobile truck, motor or other power vehicle, carrying a 
weight in excess of 4 tons, including the vehicle, shall be operated upon any 
state or county highway at a speed greater than 15 mi. per hour; andno 
such vehicle carrying a weight in excess of 6 tons, including the vehicle 
shall be operated upon any such highway at a speed greater than 6 mi. 
per hour when such vehicle is equipped with iron or steel tires, nor, a speed 
greater than 12 mi. per hour when the vehicle is equipped with tires of hard 
rubber or other similar substance. 

Section 6. — The State Commissioner of Highways, upon proper applica- 
tion in writing, may grant permission for the moving of heavy vehicles, 
loads, objects, or structures in excess of a total weight of 14 tons over state 
and county highways, upon proper application in writing being made there- 
for, and under such restrictions as the Commissioner may prescribe. 

Section 7. — The owner, driver, operator or mover of any vehicle over 
any state or county highway shall be responsible for all damages which 
said highway may sustain as a result of a violation of any of the provisions 
oi the foregoing Rules and Regulations, and the amount thereof may be 
recovered in an action of tort by the State Commissioner of Highways or 
by any County Superintendent of Highways of any county or by any Town 
Superintendent of Highways of any town in which said violation occurs. 

I. Section 8. — These regulationstake effect October 20, 1913. 

"Section 24 of Chapter 25 of the Consolidated Laws entitled 'The High- 
way Law ' provided that any disobedience of any of the foregoing rules and 
regulations shall be punishable by a fine of not less than |io and not more 
than Si 00 to be prosecuted by the Town, County or District Superintendent, 
and paid to the County Treasurer to the credit of the fund for the mainte- 
nance of such highways in the town where such fine is collected." 

Under these regulations properly enforced any of the ordinary 
foundation courses can be successfully used provided the depth is 
varied to meet the soil condition. 

Military Loads. — Major General W. M. Black, Chief of 
Engineers, gives the following information on the loads military 
roads must be expected to carry. 

Our existing ordinance liable to accompany a field army wilt have its 
heaviest representative in a 12-in. howitzer weighing atout 27,000 lb., 
18,600 lb. of which are on the front wheels. The i>ase or distance between 
the front and rear axles is 18 ft. ; width of track 7 ft. 4 in.; width of tire, 8 in.; 
width of tire shoes, 12 in. This howitzer is to be drawn by a 75 h.p. cater- 
pillar tractor weighing 25,000 lb. Comparison with the largest present-day 
commerical trucks shows that a road substantial enough for such will suffice 
for the ordinance load, so that in this particular, as well as in a strategic way, 
roads suitable for commercial purposes will meet the military requirements." 

Secretary of War Baker gives the following requirements for 
military roads: 



I50 ' GRAVEL AND STONE FOUNDATIONS 

*' The following requif^ments as to construction within the areas mentioned 
are recommended: (i) Road to have a smooth, hard surface of broken stone 
or a. pavement not less than 20 ft. in width and capable of supporting the 
loads hereinafter specified for bridges; (2) grades not to exceed 5 per cent., 
except for short distances (less than 50 yd.) where they shall not exceed 
10 per cent.; (3) bridges to be of iron or masonry and of type to support 
loads of a 6 in. howitzer (3000 lb. on front wheels and 6500 lb. on rear wheels, 
distance between axles 12 ft., width of wheel track 5 ft.^ or a 3 ton truck 
loaded (6000 lb. on front wheels, 8000 lb. on rear wheels, distance between 
axles about 10 ft., width between wheels, center to center, about s ft.^i- In 
hilly country, where road foundations are necessarily hardpan or rock, the 
importance of artificial surfacing is less important than the completion of a 
well drained roadbed joining the roads in the adjacent valleys; and it is 
therefore recommended that in such cases the completion of an unsurfaced 
graded road be completed before the requirement as to artificial surface is 
enforced." 

Commercial Loads. — Records of produce dealers show that heavily 
loaded farm wagons weigh about 5000 lb. of which about 0.6 is on 
the rear axle. The rear wheels carry approx. 1500 lb. on 3 to 3 J^" 
tires and allowing for 25% impact exert a pressure of approx. 
600 lb. per linear inch of tire. Large modern trucks^ loaded weigh 
about 10 tons and carry approximately three-fourths of the weight on 
the rear axle. Each rear wheel is generally equipped with two six 
inch rubber tires and exert a pressure of approximately 700 lb. per 
linear inch. The author believes that a road designed for a 5 ton 
load on a 1 2" tire or at the rate of 800 lb. per linear inch should be 
safe. 

Note. — The length of wheel bearing on a well constructed mac- 
adam road is about i". 

The use of this loading and the application of the rules for dis 
tribution of pressure given by Mr. McClintock in the preceding 
quotation results for ''Main Roads" (Class II and Class IIA 
traffic, see page 164) subjected to heavy frost action in northern 
climates, in a total consolidated depth, including top course, of 
9" on fine gravel or coarse sand and 22'' on wet heavy clay or fine 
loam of which more than 30% passes a No. loO sieve. For feeder 
roads (Class III traffic) in northern states and for Class II traffic 
in chmates free from frost these depths can be safely reduced to 
5" to 7" on gravel and 15" to 20" on clay. 

The thickness to be used in the intermediate cases must depend 
on the judgment of the engineer. The following examples are 
intended only as a guide for the more common cases for roads on 
which the traffic makes a macadam design reasonable. The 
amount for special cases often depends on trial. 

Coarse sand and gravel require from 5" to 9", New York State 
uses 7" as a minimum. Massachusetts uses the following section 
on good gravel (Fig. 28). 

Wherever the stone is less than 6" it should be laid in one course 
and classified as top stone. 

1 Pierce Arrow 5 ton trucks have the following specifications (19 18). 
Maximum body width, 7' Weight of chassis, 7800 lb. 

Wheel base, 14' to 17' Body, 2500 lb. 

Gage, 69" Net load, 10,000 lb. 

Two 6" tires on each rear wheel. 75 % of net load on rear wheels. 

Total weight of truck loaded, 20,000 lb 



DEPTH OF MACADAM 



151 



For a light clay loam an average depth of 9" to 1 2" is sufficient 
in cut; for fills over 2' deep 9'' is enough; high fills even of clay 
often having onee settled rarely give trouble with 9" of stone. 

Heavy clay requires at least 15'' in cut; if the soil is springy or 
especially poor 18" to 24" is advisable. 

For shallow fills see Figure 29. 

In shallow or "pancake" fills, clay or fine sandy loam should 
never be used where the natural surface at this point is of a better 




variety, as they are almost certain to become saturated with water 
and will either squeeze or heave out of shape; long shallow fills are 
to be avoided, which is considered in laying the grade line, but where 
unavoidable, the best available material should be obtained and the 
original surface well broken up to form a bond with the new fill. 
Where clay is used it should be treated as in cut. For clay fills 
of intermediate depth (i to 2 ft.) a stone depth of 10" to 12" is 
satisfactory. 

Oici Surface ^ 
Oood Matenah 



Fig. 29. 

To illustrate the different stone depths that may be used in a 
short distance an extract follows from the construction report on 
foundations for "Clover Street Sec. i" a road near Rochester, 
New York. This was built in 1907-1908 and has held satisfactorily 
under farm traffic (Class III). 

Clover Street Road, Section i 

The normal depth of stone on this road was 7" — 3" top, 4'' 
bottom. 



Station to Station 


Character of Sub-grade 


*rotal Depth 
of Stone 


180 183 + 25 
183 + 25 186 + 25 

186 + 25 187 

187 190 

190 191 

191 193 
193 200 


Cut in sand and gravel 

Clay fill 

Light Clay cut 

Sand, gravel and clay 

Ordinary Clay cut 

Clay loam fill 

Sand and gravel 


6" 

8" 

11" 

7" 
12" 

7" 
6" 



152 



GRAVEL AND STONE FOUNDATIONS 



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FOUNDATION COURSES 153 

Preparation of Sub -grade 

It is evident from the pressures to which a road is subjected that 
the sub-grade must be well consolidated before placing the founda- 
tion stone. This is usually effected by rolling with a 10 or 15 ton 
steam roller, exerting a pressure of 350 to 500 pounds per linear 
inch or wheel width, and is continued until the grade is firm and 
compact. 

The difficulties of consolidation in different soils and the methods 
of overcoming them will be included in Chapter XV. 

KINDS OF FOUNDATION COURSES 

The foundation courses in ordinary use are as follows: 

ki. Crushed stone. 
2. Screened gravel. 
3. Field stone sub-base. 

4. Pit gravel sub-base. 

5. Field stone sub-base bottom course. 

6. Pit gravel sub-base bottom course. 

7. Quarry stone base or Telford. 

I. Broken Stone Bottom Course. — This style of construction 
is the one in most general use. Where local stone is abundant 
and well distributed, such a course will cost^ from $2.00 to $2.50 
per cubic yard rolled in place; where imported stone is necessary, 
the cost depends largely upon the freight rate and the length of 
haul and may run as high as $5.00. Bottom of this kind is generally 
used where the total depth of stone metaling does not exceed 6" 
to 8" after rolling. Beyond these depths it is often cheaper to 
substitute sub-base or sub-base bottom course for a part or the 
whole of the broken stone course. 

The method of construction by the New York State Highway 
Commission is shown in the following extract from their 191 1 
specifications: 

Stone Macadam Bottom Course 

"After the sub-grade has been prepared and has been accepted by the 
engineer, a layer of broken stone of the approved size and quality for bottom 
course shall be spread evenly over it to such a depth that it shall have, when 
rolled, the required thickness. The depth of the loose stone shall be gaged 
by laying upon the sub-grade cubical blocks of wood of the proper size and 
spreading the stone evenly to conform to them." 

** The roller shall be run along the edge of the stone backward and forward 
several times on each side before rolling the center. Before putting on the 
filler the course shall be rolled until the stone does not creep or weave ahead 
of the roller. In no case shall the screenings or sand for filler be dumped in 
mass upon the crushed stone, but they shall be spread uniformly over the 
surface from wagons or from piles that have been placed on the shoulders. 
It shall then be swept in with rattan or steel brooms and rolled dry. This 
process shall be continued until no more will go in dry, when the surface 
shall, if required by the engineer, be sprinkled to more effectually fill the 

1 All costs are for comparative purposes and are based on 1912-1914 
conditions. 



154 GRAVEL AND STONE FOUNDATIONS 

voids. No filler shall be left on the surface, and the bottom course stone 
shall be swept clean before covering with top course. Only such teaming as 
is necessary for distributing the materials will be allowed on the bottom 
course. Any irregularities or depressions, the result of settlement, rolling or 
teaming, if slight, shall be made good with broken stone of the same size used 
in the bottom course, otherwise the stone shall be removed and the sub-grade 
regraded and rolled. Such removal and restoring of the surface shall be made 
at the expense of the contractor. Screenings shall not be used in leveling up 
irregularities or depressions." 

Massachusetts used no filler; otherwise their construction is 
substantially the same as New York. 

Where imported stone is specified or the local stone is suitable 
for both top and bottom courses, the size used for bottom course 
is known commercially as "No. 4 stone" and ranges from 2^^" 
to 3%'' in its greatest dimension; the smaller size is used for the 
top course, for concrete and for filler; where the local material is 
only fit for bottom, the course is made up of stone ranging from i" 
to 3M" in order to use up the total output of the crusher. The 
stone smaller than i'' is used for filler, on the shoulders, and some- 
times for the cheaper grades of concrete. In specifying the sized 
stone for a particular job, economy is considered. Stone sized 
from i'' to 3%" is perfectly satisfactory. The only reason for 
limiting the usual size from 2%'' to s%^' is that it leaves the i" 
to 2%" stone for the top course; a uniform grade is important for 
the top and the size mentioned gives a smooth finish. 

The ratio of loose depth to rolled depth is given on page 591. 

Where filler is not used in the construction of the bottom course 
more binder is required for the top; it is our opinion that the use 
of filler is the better construction but it must be of good quality. 

The clause concerning teaming in the quoted specifications is 
a dead letter; teaming helps to consolidate the bottom provided 
it is distributed over the full width and care is taken in watching the 
course to prevent loss of shape when the traffic is first turned on or 
after a long continued rainfall. 

2. Screened Gravel Bottom Cotirse. — Screened gravel i" to 3 J^" 
in size is used in place of crushed stone; the course is constructed in 
the same manner as described above, except that a filler containing 
some clay or clay loam is preferable to a coarse sand, and it is 
often necessary to wet the course in order to consolidate it satis- 
factorily. It is also necessary to apply the filler before the course is 
rolled. 

A gravel bottom should be made somewhat thicker than a 
crushed stone bottom as the fragments do not interlock as firmly 
as crushed stone. 

The choice between a screened gravel or crushed stone bottom 
depends entirely on the relative cost. Under favorable conditions 
a screened gravel bottom course will cost from $1.30 to $2.00 per 
cubic yard, rolled in place. A course pit run gravel is preferable to 
a screened gravel bottom. 

3. Field Stone Sub -base. — Field stone sub-base is constructed, 
as shown in the cut, of field boulders roughly placed and filled with 
gravel, waste No 2 stone or stone chips; no attempt is made to 



SUB-BASE COURSES 155 

finish the top of the course exactly to line and grade, as any small 
inequalities can be filled with bottom stone. The depth varies 
from 5" to 2q" depending on the soil encountered and the size of 
the available field stone. In designing a bottom course of this kind, 
care must be taken to have accurate data as to the average size of 
stone available. If the demands of a foundation were fully sat- 
isfied by a 5'' sub-base course, it might still be more economical to 
use a f course if the stone averaged seven inches, because the 
extra work of sorting and sledging to a 5''. size would result in a 
higher cost per square yard than for a "j" depth. 

The amount of stone and filler required per cubic yard in place 
is given on page 591. 




'^-Sub'Base 



Fjg. 30. 

Under favorable conditions this sub-base can be constructed 
for $1.00 to $1.50 per cubic yard. 

4. Pit Gravel or Creek Gravel Sub -base. — Stony gravel is a sat- 
isfactory material for sub-base; it can be readily constructed for 
any depth from 2 " to 24 " if required, and where a pit or creek bar 
is near, the cost of such a course should run from $0.80 to $1.25 
per cubic yard. 

The ratio of loose to consolidated gravel for such a course is given 
on page 591. 

5. Field Stone Sub-base Bottom Course. — Sub-base bottom 
course is essentially the same construction as sub-base, except that, 
as the top course is placed directly upon it, the stone must be more 
carefully assorted as to size, more carefully placed as to line and 
grade, and a better grade of filler must be used. 

Crushed stone (crusher run) or coarse gravel make a satisfactory 
filler. 



gmuiiUM 



.'Top Course 



'^Sub-Base Bottom Course 
Fig. 31. 

The course can be of any depth from 5" up, depending, as for 
sub-base, on the soil and average size of stone; it is practically 
impossible to make a large stone bottom of this kind conform 
exactly to line and grade; a variation of \" either above or below 
grade is usually allowed and the inequalities taken out with the 
top stone; this requires that the top course must be at least 3" 
deep after .rolling. 



156 GRAVEL AND STONE FOUNDATIONS 

Sub-base bottom is especially applicable for long stretches of 
road requiring a depth of ^" to 20"; it usually costs from $1.30 
to $1.70 per cubic yard in place where fence stone is available, 
and by its use the item of higher priced bottom stone is reduced. 
However, on a hard foundation it is generally better to use 4" 
to 5" of ordinary broken stone bottom course instead of the sub- 
base bottom course even if more expensive, because the small 
stone construction is more uniform in its resistance to heavy loads 
and the top course will we,ar more evenly and longer. 

An extract from the 191 5 New York State Specifications is given 
below: 

Sub-base Bottom Course 

When field or quarry stone is used for constructing the founda- . 
tion course it shall be of a hard, sound and durable quality, accep- 
table to the engineer; the stone shall be placed by hand so as to 
bring them in as close contact as possible. When quarry stones 
are used they shall be placed on edge. The depth of the stone shall 
in no case be greater than the depth specified for the course, the 
width shall not be greater than the depth, nor more than 6 inches, 
and the length shall not be greater than one and one-half times 
the depth, nor more than 12 inches. The distribution of the 
stone shall be of a uniformity satisfactory to the engineer. The 
long dimension shall always be placed crosswise the road. After 
laying, this course shall be thoroughly rolled with an approved 
roller weighing not less than 10 'tons, and shall then be filled with 
stone or coarse gravel as directed and again rolled until the stones 
are bound together and thoroughly compacted; but no gravel 
shall be used for filling except under written permission of the 
engineer. All holes or depressions found in rolling shall be filled 
with material of the same quality and the surface shall be rerolled 
until it conforms to the lines and grades shown on the plans. When 
field stone is used approved tailings may be used for filling. In 
all cases a sufficient amount of fine material shall be used to fill 
all voids. In limited areas where the use of a roller is impracticable 
heavy tampers may be used to consolidate the material. 

6. Pit Gravel Bottom or Sub -base Bottom. — A stony gravel 
containing not over 15% of loam makes a satisfactory course; the 
depths vary from 4" to 18''; pit or creek gravel even when unusually 
coarse has from 40 to 60% of fine material; a suitable gravel for 
pit run bottom should not contain more fine material passing a H" 
screen than coarse material retained on a 3^'' screen. If there is a 
large excess of fine the gravel should be screened and remixed at the 
bin in proper proportions. 

The great difficulty in this construction is to get proper consolida- 
tion without too much delay. It is advisable to lay a course of 
this kind at least two weeks ahead of the top stone in order to give 
traffic and rains a chance to help consolidate the course. The 
addition of 10% of loam to clean gravel will quicken the consolida- 
tion. This can be done either at the pit by leaving a thin layer 



TELFORD BASE 157 

of loam when stripping which runs down with the gravel in loading 
or by placing from J^" to 1" of loam on top of the gravel as spread 
on the road; the author has succeeded in getting rapid consolida- 
tion by snatching loaded teams over the loose course with the road 
roller; the roller continually smooths out the gravel and eases the 
haul for the teams; the horses' hoofs and wagon wheels punch into 
the gravel and pack it down rapidly. Sprinkling helps. A gravel 
bottom consolidates unevenly and it is always necessary to reshape 
it somewhat after consolidation; about $0.05 per cubic yard should 
be allowed for this reshaping of crown and elimination of humps 
and hollows. A properly consolidated gravel bottom will permit 
a 4 ton load on 33^'' tires passing over it without making a wheel 
mark over y^" deep; this is a simple available construction test. 
We have gone into some detail covering this construction as it is 
the most economical type of bottom in a large number of cases but 
is not generally favored because it is harder to consolidate than the 
other types of bottom. With a 3'' or preferably a 4'' macadam top 
it has proved perfectly satisfactory on all but the heaviest traffic 
roads. 

The cost of a gravel bottom ranges from $0.80 to $1.50 per cubic 
yard in place provided the hauls are short. 

The depths of gravel is gaged by blocks or lines and the ratio 
of loose to rolled depth is approx. 1.2 (see page 591). 

7. Telford Base. — Telford base is rapidly going out of use in the 
United States because of the difficulty of maintaining a top course 
laid upon it. It seems to be too rigid and is more expensive than 
sub-base or sub-base bottom course, costing about $1.80 to $2.00 
per cubic yard under favorable conditions. 

A good description of a telford construction is given by Mr. 
William Pierson Judson in "Roads and Pavements.'' The fol- 
lowing quotation is an extract from his book. 

"On this sub-grade are then placed by hand the stones forming the telford 
foundation, which may vary in size as shown below; each stone must be set 
vertically upon its broadest edge, lengthwise across the road and forming 
courses and breaking joints with the next course, so as to form a close and 
firm pavement. The stones are then bound by inserting and driving stones 
of proper size and shape to wedge the stones in their proper position. All 
projecting points are then broken with a sledge or hammer so that no pro- 
jections shall be within four inches of the finished grade line. 

"The telford foundation is then rolled with a steam roller of ten or more 
tons weight, until all stones are firmly bedded and none move under the 
roller. All depressions are then filled with stone chips not larger than two 
and one-half inches, and the whole left true and even and four inches below 
the line of finished grade and cross-section. 

"A good workman will average about twenty minutes in setting a square 
yard of this telford foundation, which may be formed of any kind of quarried 
rock which is most available. 

"The practice in 1901 in the states named is here shown." 



IS8 GRAVEL AND STONE FOUNDATIONS 

Table 21 a. — Sizes of Stone for Telford Foundation, in Inches 





Depth as 
Set on 


Width as 
Set 


Length 
Set Across 




State 


Edge 


Road 


Remarks 


Max. Min. 


Max. Min. 


Max. Min. 


New Jersey . . 


8 8 


4 — 


10 — 


Alternate end 
stones double 
length. 


Mass 


6 5 


10 4 


15 6 


Two inches gravel 
rolled on sub- 
grade as base. 


Conn 


8 8 


10 6 


18 8 


Macadam covering 
formed in one 
layer. 


New York . . 


8 6 


10 4 


15 6 


Used only on un- 
stable ground as 
foundation for 
macadam. 



bistribution of Stone in Foundations. — In the discussion of sec- 
tions, Table 10, page 37, shows that most of the traffic normally 
keeps to the middle 10' to 12'. It would therefore appear logical 
to make the central portion of the road thicker than the sides. 
This applies without doubt to roads of moderate traffic where the 
teams generally travel in the center of the macadam and only oc- 




casionally turn out to pass but for heavy traffic double track roads 
this idea is wrong. On such roads the greatest wear and heaviest 
wheel load occur about i ft. from the edge of the hard pavement and 
many of these roads develop the shape shown in the above 
sketch. It therefore seems advisable to keep the full depth of 
metaling for the full width on Class I and Class II traffic roads. 

For Class III traffic the varying thickness indicated in Figures 
32 and $^ is applicable. 

Figure 32 is an example of such a foundation course for ordinary 
soils as used by the New York State Highway Commission in 1910. 

Figure 33 is an example of an economical sub-base, for a light 
traffic road as used by the Illinois Highway Commission in 1910. 

Special Cases. — ^Long stretches of comparatively level ledge rock, 
muck and vegetable loam may be placed under this head. 

Where a road is on the surface of ledge rock for any distance, the 
usual cross-section of part cut and part fill can not be used because of 



SPECIAL CASES 



159 



the high cost of shallow rock excavation for ditches; the grade 
should be lifted to make the normal section fill and the best available 
material (not clay) used in its construction. Where conditions of 
this kind prevail, dirt is usually hard to obtain and often a stone 
fill is cheaper and also more satisfactory. 

The construction shown (Fig. 34) was used for a stretch of two and 
one-half miles on theLeroy-Calendonia State Highway in New York, 
where ledge rock was encountered as described. 




The price for the stone fill was $1.23 per cubic yard in place 
constructed as shown; the road was built in 19 10 and has given sat- 
isfaction; the minimum thickness of top for such a fill is 3'' as it is im- 
possible to construct it exactly to line and grade; it was found that 
by allowing a variation of \" either above or below the grade eleva- 
tion, the fill could be readily constructed, and these small inequali- 
ties were taken out with the top stone. A top course having such 
a variable thickness should be paid for by weight and not by volume 
in place (see page 586, ''Cost Data"). 




Fig. 33. 



Peat, Muck, Vegetable Loam, or Silt.— Where the material is 
semifluid the only solution is a pile and grillage foundation. 

Swamps, as ordinarily encountered, can be treated successfully 
by using a corduroy or mattress foundation covered with a deep 
fill of gravel or large stone. In some cases where the muck is com- 
paratively stiff, a gravel or boulder fill alone mil give a satisfactory 
foundation. 

Where swamps are crossed by improved roads, the location 
usually follows the old road which has often been corduroyed in 
the past; in such cases the old foundation should not be disturbed; 
a sufficient additional depth of stone can be added to keep the 
shape of the section intact. 



i6o 



GRAVEL AND STONE FOUNDATIONS 



As an example, the Scottsville-Mumford New Yofk State im- 
provement crossed a looo ft. stretch of muck on the old road loca- 
tion; it was found that the original cedar corduroy was in good 
shape; an i8'' depth of large boulders was placed on the old founda- 



I 

k ^IB'\0"-"- 

Screened Gravel or \ r' Bitum mous\ Top 

Broken 5/(g/7g-— ^l^ kJ^^ i ' ^a 




V 



'Method "A'' 



? '1^ Gravel Broken '-"^IJ^^ Ledqe Rock 
Stone, Fence or / -^ 

Quarry Stone Ffll./ 



,,x Crusher- Run above |" 

' ^'' .'Best Available 

Mate rial, not 
Xlay 



\, 



'Method "B'! 



Fill can be made of fence stone, gravel, quarry spalls, stone 
chips, or run of crusher stone over %" in size. 

Method A . — Boulders up to 2 cu. ft. can be used, placing the 
largest in the bottom of the fill; the top layer must be fairly uni- 
form and not over 8'' in size and must be roughly placed by hand 
to reduce the voids as much as possible, provided this layer of 
large stone is within 4'' of the bottom of the top course. The top 
8" to be filled with stone chips or gravel and a cushion of at least 
2" of screened gravel, stone chips or crusher run of broken stone 
over %^" in size to be placed on top to bring the fill to the correct 
grade and crown for the top course. 

Method B. — Same materials and manipulation as Method A, 
except that provided the top of the boulder fill is more than 4" 
from the bottom of the top course the top layer of the boulder fill 
need not be placed by hand (see sketch, Method B). 



Fig. 34. 

tion and surfaced with 6" of broken stone macadam. This stretch 
of road has kept its shape and has not settled, it affords a good 
example of the statement made on page 150 that in many special 
cases the depth of the stone is determined by trial; the boulders 




Swdrnp 



"^Old Corduroy- r. "''•■"" Black Muck'" 



Fig. 35. 



were put on in successive layers of 6" each until there was no 
material movement under the roller and then surfaced with the 
broken stone macadam. 



ECONOMICAL DESIGN i6l 

Under a heavy load the whole roadbed will vibrate for loo ft., 
but the shape remains intact. 

Economical Foundation Design Macadam Roads. — The econom- 
ical design of foundation courses may be summarized as follows: 

For moderate traffic use pit run coarse local gravel if available 
varying the depths to suit the soil. If gravel is not available use 
a macadam bottom for ordinary soils and field stone sub-base or 
sub-base bottom for bad foundations. The economy in the design 
of macadam roads is greatly increased by utilizing local material, 
preferably uncrushed, to its fullest extent. We wish to emphasize 
this point (see design report, page 274). If the supply of local 
material is limited it should be used for as much of the road as 
possible and advantage should be taken of the different local 
supplies by changing the design to allow their use with short hauls. 

Uniform designs which disregard limited amounts of local 
materials often raise the cost from $500 to $1000 per mile. 

Conclusions. — In the design of a road, the amount of material 
required for the foundation courses can only be approximated. 
This is the only item in the preliminary estimate that can not be 
figured within definite limits. It can be closely estimated if 
careful data on the soils is obtained from local people and from the 
preliminary survey (see page 330) but a certain leeway must be 
given the constructing engineer so that he may vary the estimated 
depths to meet the construction conditions and build a consistent 
road. It will be noted that the depths recommended in this 
chapter are greater than those shown in most of the state sections 
throughout the book. This increase in depth is based on the 
observed action of traffic on the older macadam roads, which unless 
recapped with from 3'' to 6" of additional stone are failing under 
heavy modern traffic. A macadam foundation is more suitable 
in northern climates for nine-tenths of the roads than a rigid pave- 
ment because it is flexible under frost action and with sufficient 
depth will hold the heaviest loads, but present practice in macadam 
design and maintenance is lagging behind the traffic requirements 
in the matter of depth while rigid pavement strength is well abreast 
of the times. The author has been amused at the recent compari- 
sons of the effect of Army truck traffic across New York State on 
rigid and macadam roads. A considerable mileage of old thin 
macadam roads failed in spots but where a reasonable depth of 
macadam prevailed no foundation failures occurred. A blare of 
trumpets hailed the failure of the old cheap inadequately main- 
tained macadams and great stress was laid on the fact that the 
rigid types held. This is mentioned to illustrate a phase of the 
present campaign for rigid types which the author considers 
unwarranted and dangerous from the standpoint of reasonable 
road design as it tends to discredit macadam construction. While 
we do not advocate macadam on Class I roads their use on Classes 
II, III and IV should be encouraged. (For traffic classification, 
see page 164.) 

i ^ Macadam foundation failures are due to insufficient depth, 
insufficient consolidation during construction and poor grade 



1 62 GRAVEL AND STONE FOUNDATIONS 

filler. The matter of filler is very important; coarse sand, peai 
gravel; or stone screenings are preferable and earth or loam that 
softens ivhen wet should never he allowed. Filler should be a separate 
item separately paid for. 

Macadam failures are due to the same cause as concrete failures 
of brick failures or any other failure — ignorance and carelessness. 



CHAPTER VI 
MACADAM TOP COURSES AND RIGID PAVEMENTS 






The scientific selection of the most suitable pavement for a 
given road is the hardest problem of Highway Engineering. This 
selection is often simplified by local prejudice, commercial interest 
or clever propaganda but purely as a matter of academic interest 
we will discuss the matter from the standpoint of the millemium. 

A reasonable decision depends on the requirements of the location, 
traffic, first cost, maintenance and renewal. Where the road is 
located in a village the elements of appearance, cleanliness, etc., 
have an important bearing. Where it is strictly a rural road looks 
have small effect and first cost usually governs. A large volume 
of extremely heavy load traffic makes a rigid type desirable and safe 
footing for team traffic limits the use of many pavements on steep 
grades. The relative economy of different pavements is theoretic- 
ally expressed by the sum of the first cost and the capitalized cost 
of maintenance and renewal. The first can be readily estimated 
but the cost of maintenance and renewal can not be figured with 
any degree of accuracy for single special cases and even on large 
systems it can only be approximated on account of the uncertainty 
of future labor and material costs and the inadequate and spas- 
modic legislative finance programs for the upkeep of highways. 

As stated in the introduction we believe that after the large 
decision has been made as to whether a rigid or flexible type is 
advisable, that the selection of special styles of construction within 
these classes has very little effect on the final cost of maintenance 
and renewal and that the problem can be confined to which of the 
types will utilize local materials to the best advantage and will be 
the cheapest in first cost, except as modified by footing on grades 
or appearance in villages and city streets which only applies to a 
limited mileage. The decision as to general type depends on the 
kind and volume of traffic. On any road the amount and class of 
traffic will fluctuate and roads that are designed for light travel 
will often fail under temporary heavy traffic which for some reason 
is diverted from its normal course. The first improved roads in 
any locality will for a time carry more than their share of the travel 
which is naturally reduced by the subsequent construction of 
adjacent improvements or may be increased by the linking up 
of isolated improvements into a continuous route of improved 
roads between large centers of population. It can be readily seen 

163 



1 64 MACADAM TOP COURSES 

that it is difficult to judge the amount of traffic a road will handle 
and that a short time traffic estimate is valueless as a basis for a 
definite conclusion. The design of the top course is usually based 
on a comparison of the action of different kinds of previously 
built roads that serve districts similar to that under consideration 
and this can be better determined by a study of the locality than by 
a localized traffic census. Roads on which high type macadams 
or rigid pavements are suitable may be divided into four general 
traffic classes. 

Class /.—Main trunk roads between large cities along natural 
transportation routes which accommodate through truck freight 
traffic. Main radial roads from 5 to 20 miles out of cities of say 
50,000 and upward and in the business section of villages which 
carry the concentrated farm and truck traffic of a large area and 
are subjected to continuous heavy load travel. 

^ Class II. — Main through automobile pleasure routes at greater 
distances from the cities which have a large touring car traffic and 
medium heavy farm traffic and some heavy trucking. 

Class III. — Secondary or feeder roads and cross roads having a 
medium heavy farm traffic and light auto travel. 

Class IV. — Pleasure or scenic roads that carry a large number of 
pleasure autos but light street tire traffic. 

Class I roads are better served by rigid pavements. Classes II, 
III and IV by flexible types. 

Rigid pavements are economical on perhaps 10% of the mile- 
age of improved roads that will be undertaken in the U. S. 
during this decade. They are destroyed by the action of the 
elements more than by traffic. They crack due to the settlement 
of new fills and frost heave; they shatter due to changes in tem- 
perature; they are harsh for horse traffic; they are comparatively 
difficult to repair and are prohibitive in first cost except for rich com- 
munities. They however handle heavy auto trucking more sat- 
isfactorily than macadam construction. They need comparatively 
little surface maintenance and for this reason traffic is inconven- 
ienced less than on macadams; they last a longer period without re- 
construction than macadams and traffic is therefore interrupted 
less; they bridge over small areas of weakness in the sub-grade, 
culvert, backfills, etc., better than macadams. There is no question 
but that they are desirable on Class I traffic roads. Under Class 
II traffic however from an economic point of view their selection 
is doubtful if macadam materials are available. Where they are 
used it is merely a tacit admission that the road authorities can not 
handle macadam maintenance and adopt the rigid type to tide 
over their terms of office. The flexible macadam type complies 
better with the^ usual conditions. It is generally cheaper in first 
cost, is' not seriously damaged by settlement of new grading or 
frost heave; can be easily repaired; can be gradually strengthened by 
the addition of stone to meet practically any loading and when 
necessary can be recapped with a higher grade surface which rids it 
of the continuous maintenance drawback. Macadam surfaces 



WATERBOUND MACADAM 165 

K however require continuous maintenance and more frequent re- 
construction and are the victims of a poor maintenance system. 
This last is the real reason for most of the dissatisfaction with 

,^ macadam roads and results in the harsh verdict of the doggerel. 

" Who builds a road for fifty years that disappears in two, 
Then changes his identity so no one's left to sue. 
c Who covers all the traveled way with a filthy oily smear, 

[ The bump providing rough on riding Highway Engineer." 

r This chapter describes the advantages and disadvantages of 
, the various types. The preceding discussion and Table 22, page 
; 190, indicate in a general way their economic limitations. The 
costs given are relative only and apply to New York conditions 
^ during 1910 to 1914. Labor $0,175 to $0.20 per hour. Teams 
^ $4.50 to $5.00 per day and cement approx. $1.20 net. Most of 
. the cost data given in Chapter XIV is for the same period. Main- 
r tenance methods are discussed in Chapter VII. 



WATERBOUND MACADAM 

'] Waterbound macadam is constructed of crushed fragments of 

suitable rock filled with rock dust and sprinkled and rolled until 

I firm and hard. The cost varies from about $3.50 per cubic yard 

, where local materials are available to $6.00 where the stone is 

imported and the haul is long. A fair average price for roads in 

Western New York would be $4.30 per cubic yard or $0.35 per 

I square yard for a 3" consolidated depth. 

I Depth of Course. — As the top stone is relatively more expensive 

' than the bottom course a good design calls for the least thickness 

j of top which can be successfully constructed and maintained. 

I In 1 90 1 the thickness used for top-course macadam in Massa- 

' chusetts, New York, Connecticut, and New Jersey was 2", and 

; the size of the top course stone fragments ranged from }4" to iH" 

in Massachusetts to i'' to 2" in New York. Experience demon- 

; strated that with a course as thin as 2", the larger stone fragments 

1 tended to ^'kick out'' under traffic and that the top wore out by 

raveling rather than by the abrasive action of the teaming. For 

I this reason the best practice at present calls for a 3'' depth of finished 

top course, using stone ranging in size from i J^" to 2%''; this depth 

I makes it possible for the large stone fragments to interlock more 

firmly than in a 2'' course. Where a pit run gravel bottom course 

is used a 4" depth of top is desirable on Class II roads. 

Crowns. — The crowns used on plain macadam range from 3^" to 

I i', to %" to i'. Mr. Charles Mills, Chief Engineer of the Massa- 

I chusetts Highway Commission reports the following loss of crown 

i on State roads in Massachusetts and concludes that an original 

crown of %" to i' is advisable on single track roads and J^'' to i' 

on double track roads. New York practice favors %'' to i\ on 

10' to 14' width of metaling and ^i" to i' on 16' to 20' pavement 

widths. 



1 66 MACADAM TOP COURSES 

Table 2ib. — Tests Made in December, 1901 




Date of Original 
Construction 


Number of 
Tests 


Original Crown 
(Inches per Foot) 


Present Crown 
(Inches per Foot) 




1895 
1896 

1897 
1898 
1899 


7 

9 

12 

7 
2 


0.694 

0.583 
0.645 
0.625 
0.688 


0.500 

0.514 
0.500 
0.500 
0.625 



From the Massachusetts Highway Report for 1901. 

Maximum Grades. — Waterbound macadam gives a good footing 
for horses on the steepest grades that are ever constructed; the limit 
of grade for this construction is determined by the cost of mainte- 
nance; on steep grades macadam washes badly and the cost of 
maintenance is high. Good practice limits its use to grades of 
5% or under, although it has been used and maintained success- 
fully on grades as high as 12%. 

Advantages and Disadvantages. — Waterbound macadam does 
not require particularly rigid inspection during construction and 
can be built under almost any weather conditions except freezing. 
By its method of construction the voids between the large stone 
fragments are completely filled with solid material and there is no 
tendency to squeeze or creep as in some of the asphaltic macadams. 
If carefully built it maintains its longitudinal and transverse shape 
and is an easy riding road for both team and motor traffic. 

Plain waterbound roads generally loosen up during the spring 
thaw and if subjected to much traffic at this time are liable to ravel. 
This trouble is not experienced with the bituminous macadams. 
Under heavy automobile traffic a plain waterbound macadam is 
not satisfactory as the machines remove the fine dust particles 
between the larger stones, leaving a rough surface which *' kicks 
out'' under team traffic. For this reason waterbound roads which 
are receiving much motor traffic are generally being treated with 
some kind of a dust layer or a bituminous protecting coat, that will 
better resist the wear of automobile travel. 

Waterbound Roads Treated with Dust Layers or Protected by 
Flush Coats. — If waterbound macadam is kept moist by sprinkling 
with water, rapid disintegration under light machine traffic, 
traveling at medium speeds is prevented. For light traffic, city or 
village streets, this is feasible, but the cost of sprinkling long 
stretches of country roads is prohibitive, and where the speed is 
high, as usually occurs on the main improved country roads, 
sprinkling alone will not satisfactorily protect a plain macadam. 

The application of calcium chloride ' to a road surface keeps the 
dust down for a longer period than sprinkling with water, as this salt 

1 We are indebted to Mr. Frank Bristow, Superintendent of Repairs, 
New York State Department of Highways, for much of the data on calcium, 
chloride, glutrin and cold oiling. 



OILING 167 

has the property of absorbing moisture from the atmosphere and 
condensing it on the road surface; on side roads two applications 
a season have kept the surface in good condition. The salt is 
applied with an ordinary agricultural drill, using about i }/2 pounds 
per square yard for the first application and less for the succeeding 
applications. In Western New York the cost of the first applica- 
tion 12' wide has been approximately $100 per mile. Complaints 
have been made that the application of too much calcium chloride 
has caused soreness to horses' feet, but using the quantities given 
above, no trouble has been experienced, to the writer's knowledge. 

The application of calcium chloride does not build up the road 
or form a wearing cushion that protects the stone; it merely prevents 
the fine surface dust from being blown away or removed by the 
machines. 

Glutrin. — Glutrin is a trade name for the liquid which is run out 
of sulphide tanks in the manufacture of pulp; it is distilled and the 
acids neutralized. It resembles molasses in color and consistency, 
is soluble in water, and is applied by sprinkling the surface of the 
road with one part glutrin dissolved in one or more parts of water, 
using from 0.3 to 0.5 gallons of the glutrin mixture per square 
yard treated. The road surface need not be swept if the dust is 
not more than Y/^' deep. It hardens the surface to a certain extent, 
and, apparently, prevents raveling if applied twice during a season 
on roads receiving a moderately heavy traffic. According to 
Hubbard an addition of 5% to 15% of semiasphaltic oil to the 
glutrin prolongs its efficiency, but such an addition tends to produce 
an oily mud in continued wet weather; glutrin alone does not produce 
this objectionable condition. Glutrin has been laid in New York 
State under an agreement with the Robeson Process Company of 
Ausable Forks, at a cost of $0,043^ to $0.06 K per square yard 
of surface actually treated. .' 

Cold Oiling. — Macadam surfaces treated with light refined tar or 
asphaltic oil give a nearly ideal surface after the slippery, sticky 
condition has disappeared. 

The road to be treated is swept clean of dust and the oil is applied 
by pressure sprinklers, using from o.i to 0.3 gallons per square 
yard. The surface may be dry or slightly moist when the oil is 
applied. It is then covered with a good quality of pea gravel, 
stone or slag screenings or a sharp, coarse sand. In Western New 
York the cost has ranged from $0.02 to $0.04 per square yard, 
including sweeping, materials (oil and cover) and the labor of 
placing. 

To derive a season's benefit from the application of light oil 
or tar, the surface of the macadam must by thoroughly impregnated 
with the bitumen. Some of the lighter oils will evaporate. The 
cover will absorb some more. To get the greatest degree of satura- 
tion of road surface therefore, with a resultant freedom from dust 
and disintegration, the cover should be the smallest amount of stone 
that will smooth out or eradicate that ''toothy" or mosaic" effect 
of small shallow voids between the firmly locked top stone (see 
page 202), 



i68 MACADAM TOP COURSES 

On medium traffic roads (Class II) one application a season 
is sufficient and on light traffic roads (Class III) one application 
will sometimes last for two seasons. 

Hot Tar and Asphaltic Residuum Flush Coats. — Bituminous 
flush coats are applied by sweeping the macadam carefully to 
remove all surface dirt as well as the stone or sand filler to a depth 
of about J^'' below the top of the larger stone fragments. On 
this rough, clean, dry surface a heavy refined tar or a bituminous 
residuum of the binder grade is spread hot, using from 0.2 to 0.8 
gallons per square yard. The binder is applied at temperatures 
ranging from 250° to 4oo°F., and is spread either by hand sprinkling 
pots or is sprayed on by specially devised pressure sprinklers. 
It is then covered with a layer of clean No. 2 stone (M'O or dustless 
screenings and thoroughly rolled. A well constructed surface of 
this kind resembles asphalt. It protects the macadam from ravel- 
ing, is waterproof, forms a surface which takes the wear of the traffic 
from the large stone fragments, and gives a pleasing appearance. 
However, it cannot be laid in wet or cold weather; like asphalt, 
it is slippery and will not give satisfactory footing for horses on 
grades over 4%, and, unless laid evenly, will develop short, sharp 
waves or humps, which are very disagreeable for fast-moving 
automobile traffic. Some engineers advance the argument that by 
successive applications of such a flush coat a road can be maintained 
indefinitely without recapping, but as far as the writer has been able 
to observe, the roads become so humpy from continued treatment 
of this kind that recapping will be necessary to even up the surface 
on the score of comfort alone. 

The use of hot tar application on a concrete road will be discussed 
on page 178. For use on an existing macadam road as repair, 
the authors believe that there is just one condition where a hot 
application should be specified; where an old road has begun to 
disintegrate unexpectedly, has passed the stage where cold oiling 
- would rejuvenate it and funds are not available in the current year 
for resurfacing, then the hot oil or tar treatment may be used as a 
stop-gap to save it from complete disintegration for another year. 

The cost of flush coats exclusive of covering ranges from $0.12 
to $0.16 per gallon, or about $0.09 per square yard. If applied to a 
macadam road during construction the cost of the plain macadam 
is increased approximately $0.10 per square yard, making $0.45 
per square yard a fair comparative figure for flush coat and water- 
bound macadam construction. 

The crown ordinarily used on flush coat roads is }4'' to i'. 

All bituminous binders have the following practical disadvantages 
whether applied as surface coats or as binders in bituminous 
macadams. The composition of residuum products is so complex 
and so easily varied that, to get uniform results, each shipment 
must be sampled and analyzed to insure certain required properties. 
In heating, care must be taken not to char the binder, as this 
destroys its life and effectiveness. They can not be applied in wet 
or cold weather, which reduces the length of the construction 
season, and unless evenly spread a rough, humpy road results. 



BITUMINOUS MACADAM 169 

Bituminous Macadam. — Bituminous macadams are constructed 
in two ways, by the penetration method and by the mixing method. 

Penetration Method. — Most of the bituminous roads in New York 
State have been built by this method. 

The larger stone fragments, ranging in size from 1" to 2" to 2 3^^'', 
depending on the depth of the course, are spread and rolled; a 
heavy grade of refined tar, residuum bituminous material, or 
fluxed natural asphalt, is then poured hot, either by hand or 
machines (see footnote) into the voids of the stone so that the 
stone fragments are covered with a thin coat of bituminous material; 
No. 2 stone, or dustless screenings are spread over the surface and 
broomed and rolled until the voids are filled; if a flush coat is to be 
used the excess filler is broomed off and the surface applied in the 
same manner as described for plain macadam. Where the flush 
coat is not applied, a wearing coat of clean screenings is spread over 
the surface. 

The amount of bituminous material used as binder varies from 
1.25 gallons to 1.75 gallons per square yard, depending on the depth 
of the course. The amount used for flush coats ranges from 0.2 
to 0.5 gallons per square yard. 

The cost of one-coat 2" bituminous top, using 1.25 gallons per 
square yard, will range. from $0.35 to $0.45 and a 2>" one-coat 
top, using 1.75 gallons per square yard from $0.50 to $0.60 a square 
yard. The flush coat using 0.4 gallons per square yard will add 
about $0.06 to the above costs. For the purpose of comparison 
with the macadam a fair set of prices is 

2" Bituminous top, one coat of bitumen $0.40 per sq. yd. 

2" '' '' flush coat 0.45 " '' " 

3" '' " one coat of bitumen 0.55 '' '' *' 

3" " '' flush coat 0.60 '^ " '' 

Depth of Top Courses for Bituminous Macadams. — In 19 10 
New York State adopted a depth of 2 " using 1.25 gallons as binder 
and 0.5 gallon as flush coat per square yard. 

In 191 1 a 2>" depth was used with 1.25 gallons per square yard 
as binder and 0.4 gallon as flush coat. 

In 191 5 a 3" depth was used with 1.75 gallons as binder and 0.5 
gallon as flush coat. 

A 2" bituminous top will not fail by raveling, the defect men- 
tioned for a 2'' waterbound macadam course, but it has certain 
constructional difficulties. To construct a 2" course no stone should 
be over 2" in its largest dimension. Because of the tendency to 

The author has had better success with hand pouring for the first coat 
than with machine work. For flush coats, however, a pressure machine is 
absolutely necessary. If bitumen is poured by hand it must be poured 
across the road (never along the road) as this method of work largely elimi- 
nates humps formed by overlap. It is much easier to control the hand spread 
than the machine spread as to amounts and the stone spread is not disturbed 
or rutted up during the pouring. While the machine spread is uniform 
this is in itself a drawback on the first coat as the rough stone sizing is never 
uniform and a hand spread can be varied to conform to the non-uniformity 
of the stone sizing. 



lyo MACADAM TOP COURSES 

crack under concentrated wheel loads, none of the stone forming 
the main body of the course should be less than one inch in size. 
These limits of size are so narrow that difficulty has been experienced 
in procuring sufficient stone for top when crushing local material, 
and even when the stone is obtained from a commercial plant 
the same difficulty is often encountered. Also in spreading such 
a depth with stone ranging in size from i" to 2" ^ there will be places 
where the metaling is only one stone deep and the fragments do 
not fit as closely together nor have the same chance to interlock 
as in a deeper course. The spaces between these stones are filled 
with No. 2 (%'0 size, which wears more rapidly under traffic 
than the larger pieces and the road tends to become rougher than 
would occur if the iK'' stone fitted closer together. This last 
argument does not apply to flush coat roads. 

The argument is often made that a 3'' top will last one and one- 
half times as long as a 2'' top because it has one and one-half times 
as much material, but the life of a top course rarely depends on its 
total thickness, as it will become so badly out of shape before the 
general elevation has worn down an inch that it will need 
recapping. 

In attempting to meet these difi5culties, 2 J^'' and 3" courses have 
been built; as far as the author has been able to judge, the 2}^" 
depth remedies the defects, and can be used where imported com- 
mercial crushed stone is available, but where the stone is crushed 
locally a 3'' depth is better with a slightly greater range in top stone 
size. 

When pouring bitumen in the penetration method, a pocket of 
fine stone, dirt, etc., will sometimes hold the binder near the top 
in too great quantities; during hot weather the bitumen swells and, 
as the voids are full in these spots, it rises to the surface and forms a 
hump or wave. This trouble is not so frequent on either 2}/^" 
or 2>" courses as on the 2" depth. 

The writer's present opinion is that while a 2^2' depth, using 
about 1.4 gallons bitumen per square yard in one coat, will give 
satisfaction that a 3'' depth using 1.7 gallons in one pour is better 
practice on a macadam bottom. On a pit run gravel bottom 
T^yi" with 1.8 gallons of bitumen is desirable. Where bituminous 
macadam is used to resurface an old worn out concrete road on 
steep grades 3'' to -^Yi" is the best depth. 

Crowns. — The crowns used on bituminous macadams range 
from 34" to I ' to %'' to i'; Y^' to i' is generally used and is ap- 
parently satisfactory. 

Footing. — A single coat road affords good footing on any grade 
that will be adopted as suitable for heavy hauling; such a top 
course will not wash, which makes it easy to maintain on hills. 

Advantages and Disadvantages. — Bituminous macadam without 
a flush coat provides good footing for horses; it will not ravel, is 
easy to repair for small depressions and ruts, is comparatively 
dustless and keeps its longitudinal and transverse shape well, 
making a comfortable riding road for fast travel. On the other 
hand, it will probably wear more rapidly than the flush coat 



TOPEKA MIX 171 

construction as the traffic comes directly on the stone; it is subject 
to the practical disadvantages of construction of all roads where 
bituminous materials are used; it is not waterproof when first 
constructed; this last defect, however, is remedied by the traffic 
which grinds up the surface wearing coat and forces it into the 
voids. As a matter of fact, the combined action of traffic and 
weather puddles the road, and after about six weeks' use we can 
say that the road has a bituminous bond and a water-puddle 
finish. 

Flush coat bituminous macadams are more dustless than the 
single coat, are more nearly waterproof when first built, look 
smoother at first, and will probably cost less to maintain. How- 
ever, they do not give as good a footing as the single cost and are 
liable to develop waves and humps disagreeable to fast traffic. 

If a flush coat is used there seems to be no advantages in a bitu- 
minous binder, as the flush coat alone prevents raveling, and, if 
such is the case, the binder used throughout the depth of the 
course is a waste of money; a waterbound bituminous flush coat 
course might better be used. In choosing between a flush coat 
construction or a single coat bituminous macadam, the author 
believes that a single cost bituminous macadam is the better 
design; although it will probably cost more to maintain, the in- 
creased safety and comfort to the traveling public is worth the expen- 
diture. Unusual care in construction is required (see Chapter XV). 

Gravel Bituminous Top. — A gravel bituminous bound top is 
rarely satisfactory as it lacks the interlocking action of broken 
stone which increases the stability of construction. The use of 
this type is not advised. 

Mixing Method — Open Mix. Type I. — The stone and bitumen 
are mixed hot in specially designed machine mixers. The mixture 
is then spread in the same way as sheet asphalt. A flush coat can be 
used if desired. The 191 5 New York State specifications call for 
No. 2 stone (^^'' to iJ^'O; when finished thickness is to be 2" or 
less and a mixture of No. 2 and No. 3 stone {j.}/^' to 2Y^')\ when 
finished top course is greater than 2", the stone to be proportioned 
as directed by the engineer. Approximately 18 gallons of bitu- 
minous material to each cubic yard of loose stone. %- 

In this "open" mix, it is unavoidable that pockets of mixed top 
material will be placed which have a greater percentage of voids 
than the average. Whether or not a seal coat is used, these pockets 
will wear more rapidly than the surrounding pavement. In a simi- 
lar manner, variations in the size of the stone will cause uneven 
wear. Both conditions tend to produce a humpy pavement after 
some use, but generally a smoother riding road is produced than is 
attained with carelessly built penetration roads. 

Mixing Method— "Tight Mix" or "Topeka." Type 11.— The 
stone, sand and bitumen are mixed hot in specially designed ma- 
chine mixers. The mixture is then spread in the same way as sheet 
asphalt. The thickness varies according to the foundation. It 
is generally a consolidated depth of 2" on a concrete foundation 
and 2y'2" on a firm macadam foundation. The various sizes of the 



172 MACADAM TOP COURSES 

mineral aggregate and the percentages of each are specified within 
certain limits varying slightly to meet gradations peculiar to the 
material available (see specifications, page 781). 

Because of the fine aggregate used in work of this type, there is 
not sufficient stability to withstand a mixed traffic and the surface 
ultimately forms in disagreeable waves. 

Attempts have been made to prevent this waving by using a 
high penetration asphaltic cement which will permit the pavement 
to iron itself out. However, if a heavy slow-moving trafiic be 
carried on this type of road, the surface will rut. 

Apparently, the best results in mixed bituminous macadam have 
been secured when the coarse aggregate was used — stone between 
three-quarter inch and one and one-half inches in size, which were 
filled with a matrix of fine material of sand and bituminous mate- 
rial. Such pavements have sufiicient "body" to materially de- 
crease the ''creeping" under use and take a more even wear than 
the open mixed type. Where used to recap an old concrete or 
macadam road an open binder coat is desirable to even up the old 
surface and allow a uniform depth of surface mix. 

The prices for this type of top course run from 

Type I, $0,615 , $1,105 :- . 

^ TT (n> /: to -X per square yard 

Type II, $0.60 $1.25 

Natural Rock Asphalts. — Sandstones and limestones containing 
a certain percentage of bitumen are known as rock asphalts. The 
most common source of supply for the Eastern States is Kentucky, 
and the product is known as ''Kentucky Rock Asphalt." It is a 
sandstone containing about 7% to 10% of maltha. It is pulverized 
at the mine and is shipped and applied cold in the following manner : 
2" to 2 J^" of stone, ranging in size from %^' to i^i'^ are^readand 
rolled slightly. The rock asphalt is run through a shredding ma- 
chine and spread over the stone, using approximately 40 lb. per 
square yard. The whole mass is the thoroughly rolled, preferably 
with a 6- or 8-ton tandem roller; 40 lb. per square yard of pure rock 
asphalt is then spread as a wearing coat and well rolled; the rolling 
is continued intermittently for a number of days after the traffic is 
turned on the road. The cost of such a course has been about $0.70 
per square yard in Western New York. 

The crown ordinarily used is 3^'' to i\ 

Advantages and Disadvantages. — The road is pleasing in appear- 
ance, is not as slippery as sheet asphalt, and will not ravel under 
motor traffic. However, it is hard to construct in cold weather, 
is not uniform, and will ravel in spots. It has defects in common 
with sheet asphalt of showing wear by developing short humps and . 
hollows disagreeable to fast traffic. The steepest grade on which 
it can be used advantageously is about 5%, as it becomes slippery 
in cold weather, and in warm weather it sometimes softens enough 
to make hard pulling for heavy loads. 

Amiesite. — Amiesite, a patented material made of crushed stone 
coated with asphaltic cement, has been used on many miles of 



BRICK PAVEMENT 173 

road with good results. It is shipped cold in a friable and granu- 
lated state, spread on either macadam or concrete base and well 
rolled. Amiesite screenings are then spread and rolled, forming 
the surface. This construction costs about $1.00 per square yard, 
3'' thick. It resembles asphalt in appearance and has the advan- 
tages and disadvantages of all roads of this class. It is particularly 
adapted for small jobs where it would not pay to set up an asphalt 
plant or where suitable asphalt materials are not locally available. 

For further information, see Chapter on ^'Cost Data and 
Specifications. " 

Other Surfaces of a Bituminous Nature. — There are any number 
of patented pavements that can be classed under this head to 
which we can not give space. 

Sheet Asphalt and Warren Brothers' Bitulithic are used in 
unusual cases, but constitute such a small percentage of the mileage 
that for information concerning them we refer the readers to books 
by Richardson, Hubbard, Tillotson, etc. We include some notes 
on inspection of construction, page 677. 

BRICK PAVEMENT 

The ordinary brick pavement construction is probably familiar 
to most readers. On a concrete foundation 5" to 7'' in thickness 
a sand cushion varying in depth from \" to 2" is spread and the 
paving brick are laid on this sand bed so as to break joints; the 
brick are well rolled and the joints are filled with sand, cement grout 
or paving pitch. Longitudinal expansion joints of bituminous 
material are provided next to the curb or edging; transverse 
expansion joints spaced 30' to 50' apart are used by some designers. 
The latest practice tends to make the cushion as thin as possible 
\" to ij-^'', acting merely as an evener of the concrete surface. It 
is also rare to find any material but cement grout used for filler 
though this tendency is not necessarily an improvement. The 
use of transverse expansion joints is being relegated to the back- 
ground but this also is open to argument. Premolded asphaltic 
strips form the best kind of expansion joints where they are needed. 
In the last few years the former theory that the i J^" sand cushion 
prevented crushing of the brick and gave the amount of resiliency 
necessary to a pavement of this type has been disputed and ap- 
parently successfully so, by the increased use of the cement sand 
cushion. Upon the finished concrete base a bed of dry cement 
and sand uniformly mixed in the proportion of one part cement to 
four parts sand is spread not over i" deep. This cushion is shaped 
by striking with a template and finished by rolling with a hand 
roller weighing about 300 lb. and restruck or luted. After the brick 
are laid theron, culled and rolled, the pavement is thoroughly 
sprinkled to set up the cement sand bed. The use of this kind of 
bed undoubtedly overcomes the loosening of bricks near cracks or 
expansion joints and prevents shifting of the sand cushion which 
sometimes occurred with pure sand and resulted in depressed 
areas. It is possible that the use of this kind of a cushion in con- 



174 RIGID PAVEMENTS 

junction with bituminous joint filler will help to overcome the 
serious fault of surface cracks which develop under frost action. 

In 191 5 several experimental brick pavements were constructed 
where the mortar cushion and brick were laid upon concrete which 
was still plastic. The concrete foundation was shaped by a tem- 
plate and the brick laid, inspected and rolled before the cement had 
taken its initial set. This is immediately followed by grouting. 
It is too early to say whether or not this so-called "monolithic" 
construction will be successful. The expense and difficulty of 
manipulation are increased and it is doubtful if any material advan- 
tages are attained. 

Brick pavement construction is essentially rigid, intended to 
withstand heavy traffic. The cost, including foundation and sur- 
facing, ranges from about $1.60 to $3.00 per square yard, the 
average price in Western New York being about $2.00. 

Brick pavements on heavy traffic roads have been extensively 
used in Ohio and New York. Macadam foundations for brick 
surfacing have not proved satisfactory in the Northern States, 
as the surface is too rigid and cracks under the heaving action of 

I -I yi^Pftth Expansion Joint 

'■^m^i-f'-' ' Note •■ Transverse Expansion Jowfs Spaced 
^I0\. 30foSOft:maybs(j6ect._ 

Fig. 36. — Brick pavement, flush edging. 

the frost. Even on a concrete foundation longitudinal cracks often 
develop from this same action. It is more difficult to prevent this 
on country roads than in cities where the sewers keep the earth 
sub-grade comparatively dry, and the necessity for a center drain 
under the concrete base is being recognized by many designers. 
Some engineers believe that the i to i cement grout in general 
use is too strong, and that if a weaker grout or a sand filler were 
adopted in its place the heaving frost action would merely separate 
the bricks slightly instead of breaking them and that as the road 
settled they would fall back into close contact. This is an attempt 
to make a theoretically rigid construction flexible and seems to be 
striving to adapt the construction to conditions for which it is 
not fitted. 

Longitudinal Cracks. — These cracks have been carefully studied, 
as they seem to be the most discouraging feature of brick pave- 
ment construction on country roads. 

Mr. Wm. C. Perkins, Chief Engineer of the Dunn Wire Cut 
Lug Brick Company^ states from a careful examination of a large 
mileage of brick roads built under his supervision, that longitudinal 
cracks have always occurred within 2' or 3' of the center of the 
road; that the cracks extend down through the concrete base and 
.that less difficulty is experienced in preventing them as the crown of 
the pavement is reduced. From these observations he has been 



STONE BLOCK PAVEMENT 



175 



led to experiment with a concrete base having a perfectly flat 
bottom, as shown in Figure 36 A, crowning the'road by making the 
concrete thicker in the middle than on the edges. The claim is 
made that this style of construction is helping to prevent such 
cracks. 

Transverse Expansion Joints. — The use of transverse expansion 
joints has not been successful locally. Difficulty has been expe- 
rienced with the brick loosening at these joints, and whenever a 
temperature heave has occurred it has appeared at the joint. 
Their use has been abandoned for rural roads in Western New 
York. This does not occur with a cement sand bed but excessive 
wear does occur at such a joint. 



Br/'cH'. 



, SandCush/on 



^^Lonqffvdinat 
Expansi'on 
Joint 




F1G.36A. 

CROWNS 

The crowns in use on brick pavements range from Y4!' to i 
to %'' to i'. For the methods of figuring ordinates for para- 
bolic crowns see page 551. 

Brick pavement does not give a good foothold for horses on grades 
above 5 % unless some special form of brick is used. For steep 
grades, on heavy traffic roads, it is better practice to use some form 
of stone block. 

Stone block pavement, including concrete foundation, costs 
from $2.70 to $3.30 per square yard. It is suitable for the steepest 
grades that are constructed and is the most durable pavement that 
can be used. 



>rfoi\ 



,' Pitch Expansion Jo/nf- 




Note : If Pitch Filler is used between Stone Block, 
no Special Expansion s/ofnf is needed. 

Fig. 37. — Stone block pavement, flush edging. 

Where stone blocks are used on hills it is better practice to use 
second quality blocks; these blocks are identical with the first 
quality blocks as to material but are not dressed as carefully and 
cost about fifty cents per square yard less; their rougher surfaces 
and wider joints afford better footing. For the difference in size 
and joints see specifications, Medina Block, page 736. 

The first cost of brick pavement for country roads restricts its 
use to roads where it can be conclusively proved that macadam will 
not be suitable. It is a reasonable design for Class I traffic in 
villages. 



176 



RIGID PAVEMENTS 



ASPHALT BLOCK 

The asphalt block pavement laid in New York has been very 
satisfactory. The proportion of ingredients is about 70% crushed 
rock, usually trap, which has passed a )^'' ring, about 20% limestone 
dust to act as filler and approximately 10% of asphaltic cement, 
molded under a pressure of 2 tons per square inch of block having 
a 2'' depth. This produces a dense asphalt much superior to the 
ordinary sheet. 

The asphalt used is Trinidad. This is refined and fluxed so that 
the resulting A. C. may be varied as to adhesiveness, penetration, 
etc., to meet varying conditions peculiar to different localities. 



ySfee/ Reinforcement- 


A 




J 



Plan 




Section 
Pig. 38. 



The penetration is made high enough to give a certain amount of 
pliancy to the block, to avoid crumbling at the edges and to make 
the joints self-healing. 

The use of blocks containing steel anchors, laid across the road, 
approximately 15 ft. apart, has eliminated any movement of the 
block under traffic. These blocks are placed at more frequent 
intervals on curves. Block pavements have been laid using a 
longitudinal row of these anchor blocks in place of edging. The 
results appear satisfactory. 

After the base is prepared a mixture of i to 4 Portland cement 
mortar is spread J^ in. thick. This mortar bed is carefully screened 
and the block laid thereon, joints being broken at least 4 in. 

An interesting comparison with brick occurs in the "pinning in" 
at curbs. Instead of bats being broken by hand, a large mechanical 
shear is used. Each fractional block is measured and cut to fit 
exactly. 



CONCRETE PAVEMENTS 
Asphalt Block Data 



177 



Highway No. 


County 


Mile- 
age 


Bottom 
per Sq. Yd. 


Top 
per Sq. Yd. 


Per Mile 
i6'-26' 


5357 


Westchester 


0.95 


$0.61 


$1.49 


$26,593 


5375 


n 


1-34 


Old Mac 




69 


18,114 


5388 


Rockland 


2. 16 


ii ii 




70 


^27,025 








0.59 




70 


^32,525 


1153 


Niagara 


0.97 


0.60 




37 


'31,800 


5482 


Westchester 


I. 16 


0.66 




50 


29,270 


1167 


it 


1.28 


0.61 




38 


24,245 


1053 


<< 


1.45 


Old Mac 




60 


21,205 


5528 


Warren 


0. 61 


0-59 




60 


35,990 


5356 


Westchester 


0.53 


Old Mac 




63 


^26,960 


5361 


n 


0.68 


0.61 




44 


'23,512 


5362 


ii 


0.25 


0.67 




37 


25,569 


5364-A 


it 


0.31 


0.47 




47 


23,166 


5373 


ii 


2.85 


0.58 


152 








Av. 0.599 


Av. 1.533 





1 Cost from preliminary estimate. ^ • 

All costs not marked with ^ from bid prices. 

After being laid, the pavement is given a light coat of sharp sand 
which is broomed into the joints. Traffic is permitted in four or 
five days. 

Advantages. — The pavement shows a smooth, uniform surface, 
dustless and practically noiseless. Its life has yet to be determined. 
Pavements that have been down ten or fifteen years are still in 
good shape. Within a reasonable freight radius from the point 
of manufacture, it can be laid for approximately the cost of brick. 

Disadvantages. — A mist or light rain makes the pavement very 
slippery. It should not be used on grades over 4%, 

CONCRETE PAVEMENTS 
Introductory 

Inasmuch as there is some difference of opinion as to the value 
of this type each author has written his interpretation of the avail- 
able facts. 

Concrete Pavements 

By W. G. Harger 

Many miles of these roads have been constructed in the last 
few years. 

The construction has varied from poor i to 6 pit run gravel 
concrete to first-class i : i J^ : 3 stone concrete 6" to 9" thick. 



178 RIGID PAVEMENTS 

There is enough data to conclude that cheap concrete is a failure. 
An effort was made to protect the surface of such a mix with a thin 
bituminous surface coat of asphaltic oils or tars. These coats have 
not been successful as they peel off and produce an unsightly, 
rough riding and a high maintenance cost road. 

The type of concrete road now being built and which has many 
enthusiastic supporters is a first-class i : i J'^ : 3 stone or screened 
gravel concrete which takes the traffic directly on its surface. The 
concrete is carefully manipulated (see specifications, page 785). 
The ordinary section used is shown in Figure 39. Expansion joints 
of premolded asphalt or patented steel plates with tarred paper filler 
are provided at intervals of approximately 30 ft.^ The cost of 
this pavement has been from $1.10 to $1.80 per square yard. 
They have the advantages" and disadvantages of all rigid types of 
construction. They should not be used on grades over 5%. 

Pavements of this class have been built on roads having light, 
medium and heavy traffic and are advocated by Cement Manu- 
facturers as an economical road under all classes of traffic. The 
author believes that while this type has its place that a great mileage 
is being constructed which from an engineering viewpoint is not 
justified. The roads have not been down long enough to obtain 



reliable data as to their length of life before resurfacing. Con- 
sidering in a general way, however, what we know of the material 
and the action of the weather and traffic on rigid types of pave- 
ment, an allowance of 10 to 15 years would appear liberal. When 
they arrive at the point when they need resurfacing a large expense 
is involved. It has been demonstrated that cheap thin bituminous 
coats have not been successful; it is not possible to successfully 
resurface with a thin layer of concrete which means that probably 
asphaltic concrete, asphalt block, brick or some other form of 
block or cube pavement will be used at a cost of from $9,000 to 
$16,000 per mile. The fact that resurfacing when it occurs re- 
quires such a large expenditure eliminates this type from use on any 
but the more important roads which constitute a small percentage 
of the mileage of any large system.* 

With the data at hand the indications are that this type is a good 
design for Class I roads outside of villages and possibly for the 
heavier Class II roads under special conditions. 

Under Class I traffic an average depth of 8" of concrete is recom- 
mended and a minimum width of 18' on account of the difficulty 
of shoulder maintenance (see Plate 9, page 60) . 

1 The author personally believes that better results will be obtained by- 
eliminating these joints altogether. The artificial joints are sources of 
weakness in that they tend to localize the wear. Apparently less wear 
occurs at a natural crack and it is certain that a smoother riding road is 
obtained. 



CONCRETE ROADS 179 

If used on Class II roads a depth of 7'' will probably be sufficient 
but no reduction in width is allowable. The fact that more width 
is desiraole for all rigid pavements than for macadams on Class II 
traffic is an added reason for the use of macadams under these 
conditions (see Chapter on ''Sections," page 42). 

Under climatic conditions free from frost an average depth of 6" 
is sufficient and under ideal soil conditions 4" to 5" have been 
built (see ''California Standards," page 50). 

First-class concrete is showing up better than anticipated under 
Class I traffic but the desirable depths, w^idths and necessary 
refinements of construction to insure success are increasing the cost 
per square yard and eliminate it as a competition for macadam 
on Classes II and III roads where macadam materials are available. 

CONCRETE BITUMINOUS ROADS 

By E. a. Bonney 

Some four or five years ago, a tremendous wave of publicity 
swept concrete roads into the limelight. The construction at that 
time consisted of a second-class concrete base with a skin coat from 
M" to %" in depth, composed of screenings, mixed with hot oil 
or tar, and sometimes a combination of the two. The base was 
laid without joints and gravel or any kind of stone was used for 
aggregate. 

Under this type at least a dozen patented pavements were 
developed practically none of which have to any degree borne out 
the extravagant claims made at that time. 

The bituminous skin coat has not been satisfactory. It is 
subject to all the disadvantages of other bituminous macadams and 
with few exceptions has not adhered to the concrete for any length 
of time. 

There is a road known as the Bedford- Goldens Bridge State 
Highway in Westchester County, on which 2.67 miles of concrete 
base has been laid when the original contract was canceled. The 
unfinished portion was covered with an experimental skin-coat 
treatment which today (1916) is as sound and intact as when laid. 
Work was finished in the early summer of 191 5. The road was 
subjected to the enormous automobile traffic peculiar to West- 
chester County all season. A brief description follows: 

The concrete was cleaned, all dust, dirt or caked material re- 
moved. It was then coated with a cold application of low carbon 
tar, very light grade, almost a creosote. This was spread about 
3^0 gallon per square yard and allowed to dry for two hours. About 
one- third of a gallon per square yard of Bit. Mat. " T " low carbon 
was then applied hot and covered with approximately 37 lb. binder 
of No. 2 stone per square yard. A second coat of H gallon per 
square yard was then applied and covered with about 32 lb. per 
square yard of No. i stone (screenings). 

This treatment so far looks extremely well and has not broken 
away from the concrete. It is still too early to classify as a success. 



lao RIGID PAVEMENTS 

The cost of the top course only was lyj^c per square yard. 
Base cost 68c. making total of 85c. 

CONCRETE PAVEMENTS 

By E. a. Bonney 

i:iJ'^:3Mix 

Concrete pavements are showing as each season passes by, that 
they are worthy of much more consideration than has been given 
them up to the present time. For roads subjected to heavily 
loaded and slow moving vehicular traffic or for roads so located or 
traveled that any type of macadam road would be subjected to 
costly maintenance, the concrete pavement has come to stay. 
The wear seems to be inappreciable and because of the flat crown, 
traffic is spread over the entire width of metal. 

Great care must be exercised in the selection of aggregates. 
Many sands that are considered good enough for ordinary concrete 
work will not give satisfactory results in concrete pavement. 
Stone or gravel should be limited to those . showing a high coef- 
ficient of wear. 

Considerable attention should be paid to the percentage of voids 
in the sand and stone. Experiments should be made to determine 
approximately the mixture giving the lowest percentage of voids. 
The authors do not believe in the blind adoption of a specified 
mix. It is often essential that the mix be varied to correspond 
to the gradation of available sand and voids in coarse aggregate. 

Several containers of uniform volume and a pair of scales are all 
the apparatus necessary to show whether or not the specified mix 
is the best mixture for the aggregates available. 

The approximate percentage of voids, may be found by water. 
By making up several concrete cubes or cylinders of the same 
volume, beginning with the specified mix and varying the others as 
indicated by the percentage of voids, the heaviest product will 
indicate the proper mixture. 

Any data given herewith is based upon a one-course road. The 
authors are not personally familiar with two-course roads. 

Bulletin No. 249 of the Office of Public Roads, U. S. Department 
of Agriculture, cites the advantages and disadvantages of concrete 
highways as follows: 

"Advantages. — i. As far as can be judged, they are durable under ordinary- 
suburban and rural traffic conditions. While it is true that there are no very 
old concrete pavements in existence, the present condition of many of those 
which have undergone several years' service would seem to warrant the 
above statement. 

"2. They present a smooth, even surface, which offers very little resistance 
to traffic. In the past the surface of concrete pavements have sometimes 
been roughened in order to insure a good foothold for horses. This practice 
has now been abandoned, except on very steep grades, because it tends 
greatly to accelerate deterioration of the pavement, and because the smooth 
surface has been found to afford a fairly satisfactory foothold under all 
ordinary conditions. 

"3. They produce practically no dust and may be easily cleaned. 



CONCRETE ROADS i8i 

*'4. They can be maintained at comparatively small cost until renewals 
become necessary. 

"5. They may be made to serve as an excellent base for some other 
type of surface when resurfacing becomes desirable. 

"6. They present a pleasing appearance." 

"The Disadvantages. — i. They are somewhat noisy under horse traffic. 

"2, There is no method of constructing necessary joints in the pavements 
which will entirely prevent excessive wear in their vicinity. Furthermore, 
joints do not altogether eliminate cracking and wherever a crack develops 
it must be given frequent attention in order to prevent rapid deterioration 
of the pavement. 

"3. They can not be readily and effectively repaired as many other types of 
pavements." 

This summation of concrete roads in general seems eminently 
fair. We believe, however, that to the disadvantages should be 
added the inevitable rut which appears between the edge of the 
concrete and the earth shoulder. These ruts are dangerous to 
fast-moving traffic and require constant maintenance for their 
elimination unless the shoulders are armored with crushed stone 
or gravel for 2 ft. or more from the concrete. 

The question of reinforcement -and joints are still the subjects 
of .much discussion among engineers. 

The item of reinforcement largely increases the cost of the roads 
and it is yet too early to sa3c.that the addeid expense is justified. 

Premolded Asphalt 
Joint as Laid 




The joint problem affords an unlimited field for a variance of 
opinions. Few engineers are satisfied with any of the existing 
armored joints, patented or otherwise. 

The author believes that experience to date has divided the 
problem of joints into two fields: i.e., on roads under continued 




maintenance a bituminous joint will prove satisfactory and is 
renewable at small cost; on roads which receive spasmodic main- 
tenance or none at all, some sort of steel joint should be used. 

On New York State work where maintenance is continuous 
the most satisfactory joint to date is of premolded asphalt, which 
is so placed that it projects from %" to 3^" above the surface of 
the concrete; as shown above (A). 

A combination of hot weather and traffic spreads the asphalt 
out, leaving a bituminous mat over the joint. 



i82 RIGID PAVEMENTS 

For concrete roads not under maintenance, the better joints 
are being made of soft steel tempered to the same relative hardness 
as the concrete. A hard steel joint simply transfers the point 
of wear from the joint-edge proper to the concrete back of the joint. 

The proper length of concrete slabs between joints is another 
subject of speculation. Many roads are now being built with 
varying distances between joints in an endeavor to determine how 
few can be used with success. 

The average cost of this type in New York State for 6" depth of 
pavement is $1,121 per square yard of pavement only. Total 
average cost for mile of completed highway, including excavation, 
drainage structures and pavement, is $15,320 (191 6). 

Small Stone Block Surfacing. — In Germany, Hungary, Austria, 
and England a surfacing made of granite blocks, ranging in size 
from 2^^" to 4", has been used successfully. This pavement is 
known as Kleinpflaster in" Germany, and as **Durax" armoring in 
England. The stone cubes must be cut with considerable accuracy 
in order to give a smooth and durable surface. 

The blocks are laid on a thin sand cushion of about %" depth, 
on either a macadam or concrete foundation; they are thoroughly 
rammed to give a firm bearing and the joints filled either with 
clean sand flushed in, or a bituminous filler. The joints do not 
exceed 3'^" in width. The courses of cubes are laid either diagon- 
ally to the direction of the traffic or in concentric rings. 

Where the stone is broken by hand the cost is high and it would 
be impossible to consider its use for rural roads in this country. 
A machine^ has, however, been developed in Europe for breaking 
these cubes which is claimed to produce a satisfactory product 
at a reasonable rate. It is a belt-driven friction drop-hammer 
having a stone chisel mounted on the anvil; the hammer head is 
shaped like a stone-cutter's sledge. The power needed for each 
machine is about i J^ h.p. 

About 400 of these machines are in operation, and a plant in 
Sweden is turning out 700,000 square yards of pavement per year 
with 62 machines. 

Provided the pavement can be laid for $1.00 to $1.25 per square 
yard, it seems a type that must be seriously considered. A price 
as low as this, however, would necessitate the use of convict labor 
in the manufacture of the cubes. 

McCLINTOCK CUBE PAVEMENTS 

By W. G. Harger 

This is a patented pavement devised by J. Y. McClintock, 
County Engineer of Monroe County, N. Y. It is very similar 
to "Kleinpflaster" except that under his patent artificial cubes 
as well as stone cubes are proposed. It appears to be a very promis- 
ing type. 

1 A detailed description of this machine is given in Engineering News, 
March 27, 19 12. 



McCLINTOCK CUBES 183 

The construction is essentially as shown in Figure 40 and consists 
of a top course of 2Y4!' cubes placed on a thin sand cushion sup- 
ported by either a macadam or concrete base. The cubes have 
been made of concrete, vitrified paving brick material and stone 
as in Continental practice. 

They are loaded, hauled and dumped like broken stone; laid 
in close contact by means of a pallet and rake 128 at a time on a 
sand cushion J^ to 3^^'' thick, no care being taken to br^ak joints. 
They are then rolled to bring to an even and firm bearing; the 
joints are filled with a sandy loam and the surface treated with a 
light coat of light road oil or cold tar if the foundation is macadam. 
The joints are grouted if the foundation is concrete. Temporary 
shoulders of 2" plank are put down during the laying of the cubes 
after which they are removed and replaced with broken stone or 
gravel as shown in Figure 40. 

The experience of the past six years has shown that this form of 
construction using a sand-tarred joint is flexible under frost action 
which makes it suitable as a surfacing on a macadam base. It 
keeps its shape under traffic and shows no tendency to ravel or 
break down at the edges and can be successfully held with 
a macadam or gravel shoulder without the formation of a rut 



OravelorSfone 

Shoulders-^ 



Fig. 40. 

along the edge which is a difficulty always encountered where a 
rigid edging is designed. It gives a satisfactory surface in both wet 
and dry weather and can be laid late in the season. The cubes 
require comparatively little inspection and can be successfully 
used as a patch in maintenance with simple manipulation. They 
reduce the tonnage and freight cost where imported materials are 
required. Concrete cubes have not served satisfactorily, failing 
in spots, but this is to be expected as it is not a reliable material 
for a road surfacing of this nature (that is for such small units). 
Vitrified shale cubes with wide sand joints laid on a macadam 
base have shown ability to stand medium traffic. Vitrified shale 
cubes with close tarred joints laid on a thick macadam base serve 
very satisfactorily under moderately heavy traffic, and the indica- 
tions are that these cubes laid on a concrete foundation and grouted 
will meet all but the heaviest traffic satisfactorily. 

Consider briefly the present tendencies in highway construction. 
There are two distinct types: the flexible form represented by the 
macadams and the rigid types, such as brick, asphalt, stone block, 
etc., having concrete foundations. Each has a distinct field and 
their relative economy depends largely on the traffic. 



1 84 TOP COURSES 

It is sufficient for this discussion to note that macadams are 
suitable for light and medium traffic (Classes II and III); that they 
are able to withstand climatic changes better than the rigid pave- 
ments and that with a moderate yearly expenditure they can be 
kept in good condition when used under the volume of traffic 
stipulated. 

They fail either under high velocity traffic or heavy hauling; 
the first being a surface failure and the second a foundation failure 
for most of the roads in this locality but a surface failure for some 
which have a thick well consolidated base. That is, if some 
better flexible surface can be used on a first-class macadam founda- 
tion, this type of road will be able to handle a heavier volume of 
traffic than at present with a moderate maintenance charge. The 
indications are that the brick cubes with sand-oiled joints will 
serve this purpose. 

The rigid roads develop defects due to temperature changes; 
frost heave and the settlement of fills. Subsequent movement 
is localized along these lines and eventually expensive repair and 
reconstruction is necessary. Under heavy traffic, however, the 
cost is less than for the macadam type and the inconvenience of 
continual repairs is avoided. 

The first cost of brick and asphalt block which are generally con- 
sidered the best of the rigid types is so high that designers often 
hesitate to use them where they are actually needed. If it were 
possible to reduce the cost and yet obtain practically the same class 
of improvement a larger mileage could be used to advantage. 

The indications are that the brick cubes on a concrete foundation 
will serve this purpose at a cost of about $0.40 per square yard 
less than the present paving brick. 

Highway designers do not hesitate to use macadam for the light 
traffic roads or expensive rigid constructions for the extremely 
heavy traffic; the great mileage that lies on the verge of either form 
of construction offers the real difficulty. It is for this class of 
road that the cubes are particularly adapted by reducing the cost 
of brick and increasing the efficiency of macadam. This applies 
also to the resurfacing of concrete and macadam roads. ' 

The author believes that provided this type fulfils its present 
indications that it will meet a recognized need in highway construc- 
tion and for this reason has given more space than perhaps is 
justified to a method which has not been tested out by a large 
mileage of construction. 

A reasonable cost of the brick 2" cube surfacing is approximately 
$0.95 per square yard in Western New York. This form of road 
material is adaptable to manufacture by convict labor. 

Rocmac. — Rocmac is another patented pavement which deserves 
mention, as the roads which the author has seen built by this 
method compare favorably with other types of construction. The 
claim is made that, under favorable conditions, it will cost only 
fifteen cents per square yard more than plain macadam. The only 
available example of cost details given below is hardly a fair sample 
of what can be done. 



ROCMAC 



i8s 



We quote an extract from the 1910 report of the New York 
State Highway Commission: 

"Experimental pavement according to the Rocmac System as laid over 
the westerly portion of Buffalo Road, Section No. 2, County Highway No. 
83, located in the Town of Gates, County of Monroe, New York. 

"The Rocmac system differs from ordinary macadam construction in 
that the aggregate of crushed stone is cemented together by a matrix com- 
posed of limestone dust (as rich as possible in carbonate of lime) mixed with 
a solution of silicate of soda and sugar, the silicate of soda combining with 
the carbonate of lime, an unstable compound, forming silicate of lime, which 
is a very stable compound. 

"The materials used in this experiment were Leroy limestone flour for 
the matrix, being the entire crusher product which would pass a screen of 
^4t in. mesh, and Akron limestone No. 3 size with some No. 4 size mixed for 
the aggregate. The No. 3 size being retained on a screen of iK in. mesh 
and passing a screen of 2 in. mesh, the No. 4 size being retained on a screen 
of 2 in. mesh and passing a screen of s'^i in. mesh. 

"The delivery point for material shipped by rail being Cold water Sta- 
tion, a dead haul of one mile to the beginning of the work. 

"The supervision given this work consisted of occasional inspections by 
the divisions superintendent of repairs and the inspector in charge of this 
section, neither of whom could devote much time to this particular work 
without interfering with other duties. Had the work been constantly 
directed by a competent foreman more progress would have been made 
and the cost probably would have been decreased. 

"The method pursued during the laying of this surface was to scarify by 
hand the original foundation course, removing all loose material by brooming, 
upon this prepared foundation so spread the matrix composed of limestone 
dust and solution, to an average depth of about 2 inches, upon this spread 
the crushed limestone aggregate to such a depth as would give finished 
rolled thickness averaging about 3^i inches when properly crowned, then roll- 
ing same until thoroughly consolidated and continuing rolling and sprinkling 
with water by hand until the matrix which flushed to the surface in the 
form of grout has nearly disappeared, when the pavement is covered with a 
light coat of screenings and considered complete. 

"The total length of this resurfacing extending from Station 237 to 
Station 275-76 is 3876 lineal feet, aggregating an area of 6890 square yards 
surface upon which was used 1004 tons of No. 3 and No. 4 crushed lime- 
stone, 520 tons of limestone flour and 4050 gallons of silicate of soda solution. 

"Deducting from total expenditure materials not used and expense of 
labor trimming shoulders and ditching would leave total cost of this re- 
surfacing, including all material and labor necessary to form pavement 
complete in place $6400.82 or $0.9288 per square yard. 

"This expense is itemized as follows: 



Item 


Total 


Per Square 
Yard 


Cost of stone f.o.b. cars delivery point 


$2026.59 
617.28 

1408.79 
408.61 
547-28 

1341.64 
50.63 


$0.2941 
0.0896 

0.2044 
0.0593 
0.0794 
0.1947 
0.0074 


Cost of Rocmac solution 


Cost of teams hauling stone, solution, water and 
coal 


Freight and duty on solution 


Roller and coal 


Labor 


Tools, tanks, blacksmith, oil and wood 




Total 


$ 6400.82 


$0.9288 





' * The averstge price paid per ton for all stone f.o.b. cars at delivery point 
is $1,253'^; price paid per hour for labor $0.22; for teams $o.56H per hour; 
roller rent $10 per day. 

"During the progress of this resurfacing traffic was not intefered with at 
all, all traffic being permitted to go over the work in whatever stage of 
progress. This is an advantage worthy of consideration. 



1 86 TOP COURSES 

**The finished surface after five months' traffic has the appearance o£ a 
well-constructed macadam road, being hard, smooth, well bound, and clean, 
no discoloration being apparent except immediately after a rain, when it 
shows light brown in spots, due to the solution, which being soluble in 
water comes to the surface. 

"No ravel developed during continued dry weather when freshly laid 
and under traffic; road is relatively dustless; this, however, depends upon 
the percentage of silica in the stone used. The theory being that whenever 
the pavernent becomes wet the solution is brought to the surface, resulting 
in absorbing and hardening down any fine material which had been pro- 
duced by the abrasion of tires. 

"It can be laid in all excepting freezing weather, and while smooth yet 
it is sufficiently rough to afford good footing for horses and rubber tires. 
There is nothing entering into the construction to soften under high tem- 
perature and nothing to form mud in wet weather. It is claimed to be 
s»lf-healing, due to continual chemical reactions taking place whenever the 
road becomes wet." 

Conclusion. — In this chapter the authors have attempted to show 
the approximate cost of the different styles of construction in 
general use or such experimental tops which they have seen which 
promise well. The costs given are relative only, to be used in the 
comparison of the various constructions and are based on roads 
in New York during the period of 191 2 to 1915. 

The data may be summarized as follows, showing the desirable 
requirements, location and approximate first cost of the different 
constructions. The comparative yearly costs including main- 
tenance and renewal are shown in Table 22 compiled from 
maintenance data. The type selection shown in Table 21 C does 
not consider the requirements of steep grades. 

On steep grades stone block is the best solution, hillside brick 
second, penetration one coat pour bituminous macadam third, 
and waterbound macadam fourth. The last two become slippery 
if maintained by surface oiling and it has been necessary in some 
cases to build a specially wide shoulder treated with gravel or 
stone for horse traffic. 

Classification for Safety of Traffic 

The sheet asphalts, topeka mix and similar constructions are 
dangerous for high speed traffic even on fairly level grades during 
sleet storms or light rains and are not recommended for roads 
outside of villages. 

Bituminous macadams, concrete, brick, stone block, waterbound 
macadams and small stone or brick cubes can be ranked as safe 
surfaces for high speed traffic. 

Recommended Types. — Bituminous macadams are recom- 
mended for Class II and IV traffic and resident village streets. 

Waterbound macadam for Class III traffic. 

Concrete for Class I outside of villages. 

Brick for Village business streets. 

Stone block for hills on Class I traffic. 

Asphalt block for extremely heavy Class I traffic. 

Sheet Asphalt, Topeka, etc., are to be avoided where traffic 
travels at high speed. Its most suitable location is a resident 
village or city street. 



FAILURE OF PAVEMENTS 187 

FAILURES 

The common causes of failure of different pavements due to 
structural defects are as follows. The details of inspection are 
taken up in Chapter XV. 

Stone Block. — Failures rare; will stand lots of abuse in 
construction. 

Asphalt Block. — Failures rare. When they occur due to poor 
block. 

Waterbound Macadam. — Failures rare. When they occur are 
generally due to poor rock, small sized stone in top courses, and 
insufficient rolling or puddling. 

Penetration Bituminous Macadam. — Failures not uncommon 
due to the use of too much soft binder; unequal application and 
overheating of Binder. The asphalt companies advocate the use 
of too much bitumen. 

Concrete. — Failures not uncommon due to inferior materials 
particularly dirty sand and to poor manipulation, weak mix, 
and too much water content. 

Brick. — Failures not uncommon due to poor brick and careless 
grouting. 

Sheet Asphalt and Topeka Mix. — Failures not uncommon due to 
overheating and poor mix. 



1 88 



TOP COURSES 



Best Location if Used 


Anywhere except resi- 
dent sections of 
villages. 

Anywhere. 

Outside of villages. 

Village streets. 


Outside of villages. 
Anywhere. 


< 


Approx. Cost 
per Mile In- 
cluding all 
Grading, 
Draining, 
Incidentals, 
Etc. 


$36,000 

28,000 
20,000 
26,000 
22,000 


$18,000 

17,000 
14,000 
12,000 


88 
0^ 0^ 

c>oo" 


Approx. 

Cost per sq. 

yd. Includ- 
ing Base 


0000 

CN vO t^ 

crj (S H <S w 


C 

$1.40 

1.50 
I. 20 
I. 00 


t^OO 


9s^a 
Suipnpui 


M H 


< M M M 


<lj OS 


Recommended 

Min. Width of 

Pavement 

Proper 


00 


OC 


OC 


OC 


OC 




>— 1 
1— 1 

U 

• OC 


15' plus stone shoulder 


1— t 
(-H 
(— i 

cn 
U 

H 


10' plus gravel 
shoulder 


■M 

c 

g 

> 

0) 




(J 

2 

C/5 


i 



1 

a 
< 


0. 

a 


B 
8 

en 

J?. 

V 

4-> 
. <^ 

E 




8 



'C 
PQ 


4-) 



<J 

en 

< 




<u 

CJ 

8 

m 

S 

i 




a 

1 
1 



en 

u 

as 


t 

en 



'§ 
;=( 


B 

a 

s 

B 

Ci 

1 


Waterbound macadam treated with 
calcium chloride or light oil. 



COST OF PAVEMENTS 



189 



< 



o 

o _ 
o o 



88 



o 
o 

TO to lO 



< 



000 


00 


M M M 


M 


00 "t^"b 


M M 



o 



:3^ 



vO vO O to to 



«£ 8 6 j^ 

^ O ^ ^ —, 

P. ^ ^ 5 § 

^ c/3 ,, O 5 



g3 



o 






c3 
03 



a 



> 



> t-i 
O to 
fe en 

+j O 

<u o 



J1 



c3- 

o 



IQO 



TOP COURSES 



•—; jj> (h 


o o o o 


o 


o o o o 


o 


o 


rt-g uo ^H S 


o o o o 


»o 


O lO lO M 


o 


>o 


o O ^•'^ ^ S 


fO M Tt ro 


q_ 


O rt"^ M^ 


q 


CM 


pT pT (N cT 


pT 




M 




flS .'d 1 « 












ost of R( 
lurfacing 
istribute 
ver orob 
ble life o 
Road on 
Yearly 
Basus 












o o o o 


o 


o o o o 


o 


o 


o o o o 


o 


o »oo o 


>r5 


lO 


H H 


M 


00 lOiO ':t 


^5 


to 


O ^''d o rt 












nd 












0^^ <D W 












ssum 
lengt 
of lif 
Year 


\n\no m 


<N 


»o O t^ O 


O 


lO 


f<5 CS M M 


M 


MM. M 


M 


M 












1 < 












Approx. 

Yearly 
Mainte- 
nance in- 
cluding 

Oiling 


o o o o o 




O O O O 


o 


o 


lio »o o »^ ir> 


O »0 IT) lO 


ITi 


o 


w M ro M H 




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ro 


pi 


«»% 










>> 












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rt to to , 


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CN 


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" ^-^ w 


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00 


t>.io -^ fO 


fO 


^ 


>HfefeO 


MM M 










^^sg^ 


*% 










T^ 












CO 












First Cost 
per mile 

including 
Grading, 

Pavement, 

Drainage 

and all 

Incidental 


o o o o 


o 


o o o o 


o 


o 


o o o o 


o 


o o o o 


o 


o 


9. 9. ^. 9. 


o 
d 


o^ q q^ q_ 

00 rf ci C^ 


q^ 

00* 


q 
pT 


PO N cs (N 


cs 


M M M 




M 








> 






to^ 






^l 








> 

1 




< 1 t-l 

HHt-HI-t l-H 




h-l 




t-HI— It— ll-H 


1— 1 


(— IhHhH t— 1 


*"* 


HH 


Ji 


, 


V ^ V ^ 


;[ 


V V V 






o bfl 


r^ CO 












•jS.S 


O CO 


roOvoo O 


00 


l^ N N 0\ 


o 


O 




M M 




M M 






_ 3 (U 


g§ 






































X! 












^ to 














'S 


00 00 00 00 


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o 


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M 


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a 
o 


^ CO CO «-(.S 


o 


fe^m^^°"^ 


^fo 


o 



YEARLY COSTS 



191 



To afford a comparison of high and low type roads the following 
data is inserted at this point for Earth, Gravel, and Sand Clay 
roads. 









Approx. 






Approx. 


4% 


Yearly 


Total 


Type 


Cost per 


Interest on 


Mainte- 


Yearly Cost 




mile 


First Cost 


nance and 
Renewal 


Per mile 


Earth . 


$2000 


$ 80 


$ 50 


$130 


Sand Clay. . . . 


3000 


120 


75 


200 


Gravel 


4000 


160 


240 


400 



CHAPTER Vn 



MAINTENANCE 

Maintenance will be divided into two classes: the care of low 
type (earth, sand-clay and gravel) roads and the more costly 
attention required to keep the higher type macadams and rigid 
pavements in good condition. Maintenance is a relative term and 
the costs given in reports mean very little unless each man person- 
ally understands the conditions under which the work was done 
and the degree of perfection in maintenance attained. 

The authors have had no personal experience in earth or sand- 
clay maintenance work; the data pertaining to these types is 
compiled data and while the explanation of methods are clear and 
definite the general costs must be accepted merely as approximate. 
The data on maintenance of high type roads is based on our personal 
experience and while this may limit its general application some- 

I ill. Iron Brace A.. -7>1^'^- 




\ ''-J Jron/^oct. ' 
Iron Sfr'ip, :;fx3xd\ 



Fig. 41. 

what it is more definite in the matter of costs and more valuable 
than the ordinary State Reports which often are difficult to in- 
terpret correctly, due to indefinite bookkeeping and to the transferral 
of charges between various funds. 

Low Type Roads. — The maintenance of these roads consists 
in keeping the grass and weeds cut, the ditches clean, culverts 
clear, overhanging trees trimmed and the surface of the traveled 
way scrapped and dragged. One shaping with a blade road machine 
in the spring generally is all the heavy work required the rest of the 
work being done with road drags, hones, planers, etc., at frequent 
intervals during the balance of the year. On sand-clay and gravel 
roads surfacing material is added to fill holes and ruts or better the 
wearing surface. 

192 



EARTH ROADS 



193 



There are two general systems: the contract system which 
lets short strips of road not over 4 miles in length to farmers - long 
the road and the patrol system which is taken care of by a steady 
patrol gang which handles from 10 to 20 miles. The contract 
system is explained in the quotation from the 191 7 Year Book of 
the American Highway Association, page 196. The patrol system 
is referred to throughout the chapter in various quotations. 

Earth Roads. — Road machine blade scrappers are familiar to all 
readers. The road hones, planers, etc., are not so well known and 
their construction is shown in Figures No. 41-41 D. Steel drags 
ican now be obtained. Their use in earth or gravel road maintenance 
is explained in the following quotation from the United States 
Forest Road Manual. 




^^v-1§" Fig:.4l.A 

Plank Drag 




S^-rg'' Fig.41-B 

Split Log or"King" Drag 




Fifir,41-C 

Lap Drag gp Smootber 



-***" Shod with Iron 

F.rfi:.41-D 



MAINTENANCE 



"Maintenance is the most important item of work to be considered in 
road management. The smaller allowances for systematic maintenance, 
as they are being included in the annual road budget alongside the unlimited 
number of those for periodical repairs, tend to give it a place of least con- 
sideration and again its consideration and planning is evaded as much as 
possible for it is the never-ending consideration of continuous annual work 
and expense. It is always admitted that the degree of efficient use we 
derive from anything constructed for practical utilization, depends on the 
amount of effective maintenance it receives. Therefore, roads which are 
most widely used and exposed in all their parts to the worst of elements 
relatively should receive the highest degree of such attention, and moreover 
the higher the type of construction and the more it costs, the more marked 
attention will it require. 

"However, it is most gratifying to find that the old ideas of taxpayer and 
user are rapidjy disappearing, _ making way for the installation of practical 
system for the efficient retention of the better roads — as they are now being 
constructed. Gradually are we beginning to learn that the stability and 
usefulness of a road is not forever established, even when the best of super- 
vision and authorities declare and approve or have made the construction 
strictly up to the standard and with ample drainage provided — but that 
each mile of construction should be followed immediately, with a mile of 
maintenance. Besides eliminating the difficulties and discomforts of travel. 



194 MAINTENANCE 

which seems only a benefit to the traveler, but is in reality an economical 
benefit to everyone, directly or indirectly — maintenance will do away with 
all the worries to the management and effectively prevent so much of this 
misapplied criticism to construction features. Finally the results of main- 
tenance encourage more road-building, whereas its lack discourages it. 

"There is no type of road that can be considered permanent, and an 
earth road or one bedded in the natural material, which is wholly as im- 
portant as the higher grade roads, or even more so — is the cheapest to main- 
tain in its original condition. The complete maintenance of an earth road 
means simply the retention of the drainage facilities that were provided 
in a completed and properly constructed piece of road work. Furthermore 
the experience of and the attention given to the road in constant rnain- 
tenance will show where ample drainage was not sufficiently provided; 
and again showing its importance, constant maintenance secures this 
necessary drainage with the least costs and at the proper time — before 
serious damage is done and heavy repair costs result. The time to begin 
the maintenance is immediately after the road is constructed, and its degree 
of efficiency will depend on what in the way of money or assistance is con- 
stantly provided or made available to meet sudden contingencies. The 
work must be done at the right time and in the right way to get the best 
results. 

"Ample drainage begins with taking the water off the road and continues 
with taking it along the road and away from the road._ Constant main- 
tenance by dragging secures this primary step in the drainage system, and 
also a hard and smooth surface for travel. The dragging preserves the 
crown, which is kept in the traveled way for no other purpose than to shed 
water. It then follows that this water will be taken away from the road 
through the further efforts of constant maintenance in keeping the ditches 
and culverts open. 

' * To properly and economically maintain -a certain road or set of roads 
an organization for doing the work should be effected. On a country or 
mountain road a patrol consisting of two teams and two men for one part 
and one team and one man for the other part of the season should be able 
to care for 15 to 20 miles. It will be found though that a newly constructed 
road will require heavier maintenance for the first year or two, thus re- 
ducing the number of miles for this patrol. One or more such outfits could 
be applied to a longer road or a larger system and kept under the same 
supervision. These patrols keep the ditches clean and the culverts open, 
haul surfacing materials, i.e., clay onto sandy portions and sand or gravel 
onto clay, keep the right-of-way open to sun and wind; and are on hand to 
drag the road after each rain. Two teams are provided only in cases where 
there is no extra help available along the road to^ assist in the dragging, 
otherwise one team would be sufficient. However, if the teams are govern- 
ment-owned, two teams should be had, as the added costs for the extra 
team are small and will in most cases prove cheaper than hiring. The two 
teams can be used on one drag or two depending on the ruling grades in 
the road. 

"In early spring when the winter snows are going off, the supervision 
and such extra assistance as is necessary should be made available early 
to see that the snow water is being cared for — that it is running down 
the ditches and into the culverts, and not down the wheel tracks and over the 
banks of the road. Later he should have a small gang of men making 
the necessary repairs that might occur while the frost is coming out of the 
ground and from wash and water-breaks. A light grader should be at 
hand especially on sidehill roads to clean the ditches of material broken off 
or rolled down the banks and to restore badly depleted crowns, after which 
the drag can be used for the remainder of the season to preserve this perfected 
condition. 

"A good foreman for this should be a man who as well as to take a hand 
in the work, should be able to plan the work and keep in touch with the 
maintenance needs and move his men economically to the first necessary 
pieces of repairs. 

" Dragging is the cheapest and most effective method of maintaining roads 
constructed of earth, top soil, sand-clay or gravel. The drag is a very simple 
and inexpensive implement and when used properly gives surprising results. 

"Properly used and at the right time the road drag performs four distinct 
offices, (i) By moving at an angle to the traveled way it tends to produce 
or preserve a crowned cross- section; (2) if used when the material of the 



DRAGGING 195 

surface is not compact and .hard, it tends to reduce ruts and other irregu- 
larities in the road by moving material from points which are relatively- 
high to those which are relatively low; (3). when used after a rain it acceler- 
ates the drying out of the road by spreading out puddles of water and thus 
increasing the surfaces exposed to evaporation; (4) if the surface material 
is in a slightly plastic state, dragging smears over and partially seals the 
so-called pores which naturally occur in earthy material, and thus makes the 
road surface more or less impervious to water. 

"If used improperly or at the wrong time, the drag may do actual injury 
to a road. Dragging a very dry road, for example, serves to increase the 
quantity of dust and may do additional damage by destroying the seal 
produced during previous draggings.^ If, on the other hand, the road_ is 
very wet and muddy, the irregularities in the surface are likely to be in- 
creased rather than diminished. The common defect in road dragging is 
to regard the road drag as a road-building tool, and to expect one or two 
trips to put the road in shape for the season. 

Notes on Maintenance 

"i. In filling bad ruts and mud-holes, it is best to use the same material 
that the roadbed is composed of, otherwise an uneven surface will result, 
oftentimes, of course, the roadbed of clay can be improved by scattering 
sand or gravel over it more or less evenly, or if of sand by the same use of 
clay, but not by filling the ruts with these appHcations. ^ Filling with rock 
will effectively close a mud-hole but the next season will find two more 
mud-holes, one on either side of this hard place formed by filling the first. 

"2. On sidehill roads, after light snows have fallen during the season, 
the inside ditches should be opened of the snow immediately in order that 
the water from the melting snow will run down the ditches instead of the 
wheel tracks. This is especially necessary where steep grades occur to 
prevent heavy wash and loss of crown in the traveled way, and water break- 
ing over the outside bank. The snows, usually, being light, this can be 
done by drawing the drag down the ditch with a large skew angle or better 
with a small ditch-cleaner, the A-drag or go-devil. 

"3. In a grazing country very often it occurs that salting grounds have 
been used near or along the roads. These should be removed for cattle 
climbing up and down the banks and walking along the ditches can cause 
considerable unnecessary damage to the road. During the season of cattle 
or sheep drives the men on maintenance should see to it, that the herds or 
bands, if they have to use the road, use the traveled way and not the banks 
and do as little damage as possible. If serious damage is done they can make 
immediate reports, if owners are obligated to repair such damages on public 
roads. 

"4. Outer bank slopes of earth that are- continually eroding, should be 
protected by sowing to grass, or any other plant that will mat and not be 
objectionable to occupants of lands along the road. 

"S. Keep the ends of the culverts free from drifting weeds and d6bris 
and clean the catch-basins of silt and other deposits. 

"6. Remember that the chief repairs should be looked after in the spring 
when the soil, being moist and easily worked, will compact readily under 
the drag and traffic. There is little use in attempting to do much in July 
and August to the roadbed proper, for the soil is so dry that it is difficult 
to shape properly anctmost of that moved will blow away in the first wind. 

Notes on Dragging 

"i. Use the drag often and if the very best results do not come at first 
trial, do not quit. First-class results can be attained. 

"2. Dragging is always done after rains, melting snows, or thaws, just 
after the ground has lost its stickiness, when the material will slide easily 
along the face of the drag and pack well; but not when it becomes dry in 
any one place. Different road surfaces and varying conditions will demand 
different times of application, the knowledge of which will come through 
faithful and persistent use and observation. 

"3- It requires a careful and skilful operator to get good and quick 
results, one who knows or can learn how to hitch to it, and where and how 
to ride it. Hitch so that the drag will travel at an angle of 45° with the 



196 



MAINTENANCE 



center line of the road, and do not try to cut too much material at one 
operation. The amount moved depends wholly upon the length of hitch 
and position of driver. A long hitch will move more earth than a short 
one. When a hard spot must be cut, the driver throws all his weight on 
the front blade; when a low place must be filled he moves back. These 
operations on patented steel drags are facilitated by changing the angle of 
the blades from a vertical. Step quickly to the opposite end of the drag 
from which you wish to deposit material into low spots. 

"4. Drive the team at a walk and ride the entire distance. The drag 
should begin at the ditch line and proceed toward the center or crown. 
If the crown becomes too great, reverse the skew angle of the drag. Do not 
try to drag too wide a section at one operation. 

"S. Do not try to drag too long a section. So much depends on the 
time the drag is used, that there is danger of dragging the road too wet at 
- one end and too dry at the other. Learn to select those sections which 
dry before others and drag them first. 

"6. Drag the road during or directly after one of the light snow falls 
just before it freezes up for the first time, as it will be in better condition to 
go through the winter and better able to shed water during the spring thaw. 

"7. Very little improvement will be noticed after the first trial, and many 
trips will have to be made the first year after construction. The second year, 
less dragging will be required and the road ought to improve continually." 

The following quotation from the 191 7 Good Roads Year Book 
shows the Kentucky methods and approximate cost of 
maintenance. 

"Maintenance by dragging is most successful when well organized. The 
results obtained by good rnanagement in Hopkins County, Kentucky, are 
frequently cited as indications of this, and for this reason the following 
account of the work there is quoted from a report by the Kentucky depart- 
ment of highways. 

"In 191 2 a county engineer was appointed. The* county roads were 
pleasured under his supervision and 2 mile sections designated, and in 
January, 19 13. drags were started on about 100 miles of the county roads. 
This original contract was only for dragging the roads, which work was to 
be done four times between January ist and April ist, at a cost of $10 to 
$12 per mile. As the sections dragged were not continuous, the citizens 
at once appreciated the difference between the maintained road and that 
which was not maintained. Consequently the next contract, which called 
for dragging and also for cleaning the ditches for six months, until November, 
1913, resulted in contracts for 150 miles of road and at a reduced cost. In 
November, 1913. a contract substantially like that now in use was adopted 
and the time of the contract was for one year, or until . November, 1914. 
Over 200 miles were maintained this year at an average cost of $28 per 
year per mile. For the year from November, 1914, to November, 1915. 
the benefit of the maintained roads was so well understood by the citizens 
that 560 miles were under contract at an average cost of $24.35 per mile 
per year. 

"In November, 1915, a two-year contract was entered into, which the 
county may revoke for non-performance of the obligation at the end of the 
first year. About 520 miles are now under contract, at prices ranging 
from $12 to $40 per mile per year, the average being $22.10. It is expected 
this mileage will soon be increased.^ Originally a contractor was allowed 
to have charge of 8 miles, but now he is not allowed to contract for more than 
4 miles of road. Under the 191 5 contracts the contractor must trim the 
branches which overhang and interfere with travel on the roadway; keep 
the roadway between ditches free from shrubbery and weeds; keep ^e 
ditches clean, free from obstructions, and at all times capable of carrying 
the water. 'He shall by June ist each year grade the roads with dump 
scraper, grader, drag and ditcher, or in any way he may see fit, so that 
the center of the roadway shall be crowned so that the water will flow from 
the center of the road to the side ditches, and at no place will the water stand 
on the road or run down the road. The road shall be dragged from ditch 
to ditch at each dragging, when the road is wet, but not sticky.' 

"A record of the number of draggings is kept by the county engineer on 
cards which, before mailing by the contractor, are countersigned by the 



GRAVEL ROADS 197 

rural route carrier or a reliable citizen. The contractor also hauls material 
and constructs all culverts and bridges of 10 ft. span or under, and keeps 
the approaches to and the floors and abutments of all bridges and culverts 
on his road in good traveling condition. An analysis of these contracts 
shows that where the contract has been faithfully executed there is a decrease 
each year in the cost per mile, mainly because the farmer contractor has 
learned from experience that continuous maintenance makes a lower cost 
of time and labor each succeeding year." 

Cost. — The cost of earth road maintenance ranges from $20 
to $200 per mile per year. A fair average is approximately $50 
per mile per year for ordinary farming county and $100 per mile 
per year for mountain roads. 

Sand -clay Roads. — The methods and character of work are the 
same for the sand-clay maintenance as for ordinary earth roads. 
The cost is generally less. The following quotation from the 
Alabama State Highway Report indicates the usual procedure. 

Sand-clay Roads 

"No cheap road can be maintained as easily and at as small an annual 
cost as a well constructed sand-clay road. It responds readily to a road 
machine and the surfacing material is usually very convenient. Like all 
others though it is neglected until extensive and expensive repairs become 
necessary. If a sand-clay road which has been intelUgently constructed 
is kept dragged at reasonable frequent intervals, say three times a month 
during December, January, February, March and April, and during rainy 
periods in the other months, it will give excellent service and serve all 
practical purposes. If too much sand is in the surfacing material the road 
will tend to ravel or disintegrate and it becomes necessary to add a small 
amount of clay to the sandy section. A thorough harrowing should then 
be given the surface, after which the road should be thoroughly machined 
or dragged until the proper cross-section is obtained. Likewise, too much 
clay may develop in wet weather and the addition of sand becomes necessary. 
Sand can be incorporated in like manner as the clay. In very wet weather, 
traffic will incorporate the sand fairly well and it frequently becomes nec- 
essary to add sand to prevent slipping, when artificial mixing would be 
difficult." 

Gravel Roads. — Gravel roads require patrol maintenance for 
good results. The road should be shaped with a road machine 
blade grader in the spring while soft and plastic and kept in shape 
by dragging. Gravel must be added continuously to fill holes and 
ruts. Shoulder, ditch and culvert routine cleaning is the same as for 
any maintenance. • 

The following quotation is from Instructions to Patrolmen in 
New Hampshire which is famous for its gravel roads. 

•'Each patrolman must supply a horse and dump cart, shovel, pick, hoe, 
rake, stone-hook, axe, iron bar, iron chain and tamp. Special tools are 
furnished by the State Highway Department. 

"One dragging in the spring is worth two in the summer. It is better 
to drag a mile of road several times and get it in good condition, than to 
drag 2 or 3 miles and not finish any part of it. Don't drag a soft section 
when it is so wet that the first vehicle to pass will rut it all up. First fill 
the holes and ruts with new material and then drag as the surface dries out. 
Every patrolman should have material dumped in small piles along the 
side of his section so that on a rainy day he can at once fill all holes and ruts 
in which water is collecting. 

"When the weather is unsuitable for dragging, as during a dry spell, 
all patrolmen should cart on all the new material possible in order to fill 
all ruts and holes and resurface worn sections. Carting is very essential 



198 MAINTENANCE 

during dry periods and should never be neglected. Whenever a patrolman 
IS in doubt as to what to do next the general rule is to cart new material 
for all roads are wearmg out under travel and it is necessary that the surface 
be contmually renewed to take the place of the old material that is thrown 
out as mud or blown away as dust. 

"Save all the sods, leaves, rubbish, stones and refuse that you clean off 
your road and dump this waste material in places where the bank is steep 
so that by flattening the side slope there will be no need of a guard-rail 
or dump the material back of a present guard-rail so that later this guard- 
rail can be removed." 

The necessity for patrol maintenance is shown by the following 
extract from the Iowa Specifications. 

Maintenance of Gravel Roads 

V "iP^^*^ ^^^^^!^^^! and supervisors' attention is called to the fact that 
both Class A and Class B gravel roads require constant and systematic 
maintenance at all times. Special attention should be given such roads for 
the hrst year following their construction. During this period the gravel 
IS sure to become rutted, wavy, and scattered if it is not maintained in the 
most careful manner. 

"Haxiling gravel and dumping it on the road does not produce a gravel 
^°i?- 1- 1^ "^°^^ important part of the construction work lies in the attention 
which the road received while the gravel is being compacted. A road newlv 
surfaced with gravel is nothing but a possibility. The success or failure 
of such a possibility depends very largely on the attention which it receives 
during Its first year. The frequent use of a planer or blade grader will 
prevent the formation of ruts and waves. This work should be done while 
the gravel is wet, as better results will be secured. 

''The scattered gravel should be brought back on the surfacing and the 
^?^^ i/u°^^^/^^^^^* "P *° ^°^^ *^^s material in place. Additional gravel 
should be added to replace that worn away and to fill any depressions due 
to settlement. 

u "The Commission strongly urges that the patrol system of maintenance 
be adopted for all gravel roads. The patrolman should spend all his time 
on the road. It is only by such a system that definite responsibility can 
be fixed. Patrol maintenance should extend not only over the first year 
after the gravel surface is placed, but also throughout the succeeding years. 
It should extend to the side ditches, earth shoulders, culverts, and all other 
parts of the road as well as to the gravel surfacing. 

"While the patrol system of maintenance is urged for all gravel roads, it is 
absolutely necessary for Class B gravel roads. These specifications have 
been prepared with that idea in mind. 

"The Commission will approve the construction of Class B gravel roads 
on the county system only on condition that an adequate patrol mainte- 
nance will be established promptly after such road is placed in service." 

Iowa Hiqhway Commission. 

Cost.-- We are indebted to Mr. F. R. White, Road Engineer of 
the Iowa Highway Commission for the following information 
in regard to the construction and maintenance cost of about 400 
miles of Class B gravel roads (see Plate No. 39, page 140). These 
roads were constructed at a cost slightly above $1000 per mile. The 
cost of maintenance depends very largely on the volume of traffic 
and the location of gravel. However, where there is an average 
of 200 to 300 vehicles per day and the gravel can be obtained within 
3 miles of the road the yearly cost of maintenance is about $150 
per mile. 

In New York State where the roads are oiled to care for a some- 
what larger volume of traf&c 200 miles of high-class gravel roads 
cost approximately $550 per mile per year to maintain. 



MACADAM ROADS 199 

A fair average maintenance cost per mile per year for double 
track gravel roads is probably from $200 to $300 under fairly 
heavy travel. 

HIGH TYPE ROAD MAINTENANCE 

In the development of any system of highways the methods and 
cost of maintenance become increasingly important. The rapid 
growth of motor traffic in the last few years has changed both 
methods and cost making it necessary to give new figures which are 
reliable for present traffic conditions. We have therefore confined 
ourselves in the discussion to recent costs with which we are familiar 
in order that in stating general conclusions proper allowance is 
made for unusual conditions not shown in the reports of various 
State Highway Departments. 

The discussion will be based on the general maintenance costs 
and methods employed on 6000 miles of New York State improved 
Highways of all types for the years 1915 and 191 7 and detail costs 
on 600 miles of roads in Western New York for a term of years. 

We are indebted to Mr. Frank Bristow for the following discus- 
sion of general maintenance methods and summarized costs. It 
should be borne in mind that the discussion and costs apply to 
territory subjected to severe winters. 

MAINTENANCE OF MACADAM AND RIGID PAVEMENT 
HIGHWAYS 

By Frank W. Bristow 

N. Y. S. Dept. of Highways, Division on Maintenance 

Maintenance comprises keeping the paved roadway surface in as 
nearly perfect condition as possible, keeping the earth shoulders 
smooth and safe for traffic; the drainage system free from obstruc- 
tions; all structures in good repair; removing obstacles to vision as 
brush or overhanging branches; and cutting tall weeds and grass. 

If the work of maintaining improved roadways is consistently 
performed through successive years it is certain that the efficient 
life of such roads will be lengthened. Maintenance should com- 
mence when construction leaves off, because in order to effectively 
and economically maintain improved roads it is necessary that the 
roadway be in a good state of repair at the time the maintenance 
work begins, and should the pavement be so worn as to be structur- 
ally weak it is not economy to postpone resurfacing. 

Maintenance work, including surface treatment with bituminous 
material and cover, should be distinguished from extensive repairs 
involving replacing of wearing course or reconstruction. 

Maintenance of Macadam Roads 

It is especially desirable that all surface treatments be completed 
as early in the season as possible; say by mid-summer to permit 



200 MAINTENANCE 

traffic to enjoy the greatest benefit from such treatment, the season 
of heaviest motor traffic being from the middle of July to the middle 
of September. So far as practicable the correction of surface 
defects such as ruts and depressions should precede the surface 
treatments. 

While the elimination of dust on macadam roads is desirable 
as adding to the comfort of the traveling public, it is necessary 
from the maintenance point of view, inasmuch as dust means 
deterioration of the road which if permitted to continue results in a 
raveled condition and the macadam will disintegrate. Surface 
treatment with oil or tar also tends to seal or waterproof the pave- 
ment. Horse-drawn steel-tired traffic tends to destroy an oiled 
surface mat, while rubber- tired motor traffic is beneficial. 

It is good practice not to oil macadam roads upon which horse- 
drawn traffic greatly predominates or new waterbound macadam 
which has not been under traffic at least two months, or extremely 
shady roads. 

The usual foundation defects which develop in gravel and 
macadam surfaces are ruts, due to a soft condition in the earth 
sub-grade, depressions due to settlement of fills which commonly 
develop at locations where new culverts were constructed and 
frost boils. 

Shallow ruts and surface depressions are corrected by being filled 
in with crushed stone of as large size as the depth of depressions 
will permit, the same being well tamped into place, and piore lasting 
results are obtained if a proper grade of bituminous material is used 
to firmly bind the new stone; light asphaltic oils and tars have been 
used for this purpose with unsatisfactory results, in that patches 
made by this method do not endure, the experience being that the 
material forming the patch is pushed ahead by traffic leaving the 
original depression exaggerated by the bunch of new patching 
material at the end. Heavier binder grade material has been used; 
a patch by this method is durable but does not wear away as 
rapidly as the adjacent surface resulting in a high spot in time. 
To date our experience is that an asphaltic emulsion for cold patching 
is most satisfactory, being nearly fool proof and requiring no equip- 
ment but a broom and shovel. This material is not recommended 
for use with stone of greater size than will pass a one and a quarter 
inch ring. In using this material the depression to be repaired 
should be swept clean, so as to be free from mud or loose material, 
and tamped full of a mixture of the emulsion and broken stone. 
Such a patch will require an hour or two to set. The proportions 
of the mixture required are, where the stone used are uniform in 
size, about three-quarters of a gallon per cubic foot of stone ; jvhere 
the stone are graded about a gallon per cubic foot. This mixture 
may be made in moderate quantities as stock for use is required. 
Ruts in gravel surfaces may be eliminated by the use of a hone 
early in the season. Deep ruts indicate necessity of either sub- 
drainage or reinforcement of the foundation; an inspection should 
determine which is the proper remedy. On side hill roads frequently 
a deep drain in the upper side ditch to intercept the ground water 



OILING 20I 

will be effective; where reinforcement is decided as necessary, 
usually sub-base construction about eight feet in width will be 
sufficient. Field stone, quarry spalls, broken stone, slag or gravel 
are proper materials for such reinforcement. . 

Frost ooils so-called are caused by wet spots in the earth founda- 
tion freezing and heaving; later when the frost leaves and the 
foundation soil is soft the thin macadam crust tends to break through 
under loaded wheels. These spots which usually occur where 
the road construction is in a cut, should be excavated, and drained 
if practicable; any wet clayey soil or silt removed and replaced by 
gravelly material, field stone, quarry spalls or other good' material ; 
the macadam is then replaced. 

Ravel is the .term applied to describe the condition where the 
fragments of broken stone become loosened from the body of the 
road, due to the binding agent failing to perform its function. 
Bare, toothy or a pitted condition of surface are the varying degrees 
of a slightly rough surface due to the interstices between the frag- 
ments of stone not being filled flush with the binding material or when 
the wearing surface has innumerable extremely slight depressions. 
Dust, which is self-explanatory. 

The remedy for raveled, pitted or dusty condition is a surface 
treatment of bituminous material and cover. 

These treatments are generally made using a grade of asphaltic 
residuum oil or a refined tar product which can be applied cold, or 
which requires very little heating, and better and more uniform 
results are obtained where a pressure distributor is used. If a 
pressure machine is used not less than twenty pounds pressure 
^should be required. 

Asphaltic base oils, or tar products having a bituminous content 
of from 40 to 60 per cent, may be applied by gravity sprinkler, 
but 60 to 75 per cent, asphaltic oils or tars containing 60 to 70 per 
cent, of pitch are preferably applied by pressure. Uniformity 
in application is important. 

As to the relative merits of asphaltic residuum oils, cut back 
asphalts, high carbon, or low carbon tars there is a diversity of 
opinion (see also page 210). Relative cost and durability will 
naturally be the considerations controlling the selection. The 
material which is the cheaper at one delivery point may not be at 
some other. As to the durability it is doubtful if there is any ad- 
vantage as between the asphalt and tar products. When applied, 
the tar material appears to take a set faster than the asphalt, which 
is a decided advantage, but more criticism is made as to slipperiness 
of the tarred surfaces during freezing weather. It is thought that 
the tars have the greater adhesive quality, but that the exposed 
surface due to evaporation of volatile constituents becomes crumbly 
or dead in a shorter time than a similar grade of asphalt. 

Regarding rate of application per unit area, this will vary with 
the porosity of the surface to be treated; for the cold, or light hot 
application ranging between one-sixth and one-third gallon per 
square yard. Experience is that from one-fifth to one-quarter gal- 
lon will produce good results on the average surface. 



202 MAINTENANCE 

Preliminary to the applying of the bituminous material the 
surface to be treated should be swept clean if necessary, to free it 
from all loose and organic matter; after this has been done the 
application can proceed regardless of whether the surface is wet 
or dry, providing there are no pools of standing water on the surface, 
a slightly damp surface apparently gives better penetration than 
an absolutely dry surface, the object sought being to get the mate- 
rial into the texture of the road. The surface treatment should be 
confined to one side or half width of the road at a time, leaving 
the other side available for traffic. Some little time should be 
allowed for proper penetration, but within one hour after the 
application it should be lightly covered with suitable mg^terial. 
Traffic can now use this side and the treatment continued on the 
opposite side. 

The materials recommended for cover are crushed stone or slag 
which will pass a M-in. mesh and are free from dust; ore tailings, 
fine screened gravel or coarse sharp sand. The toughness of the 
mineral aggregate used for oiling cover is an element in the dura- 
bility of the mat formed by the treatment. Relative cost will 
determine the selection of material to be used for cover. The quan- 
tity of cover necessary will vary with the rate of application of the 
bituminous material and with the porosity of the surface treated. 

Where the rate of application of oil is from one-fifth to one-quarter 
gallon per square yard the range of cover may be stated as being 
between 35 and 70 cu. yd. per mile of road 16 ft. wide, and gen- 
erally 40 to 50 cu. yd. will be ample. 

This cover should be uniformly applied either by hand or by 
mechanical spreader; however, only sufficient to cover the oil lightly 
should be applied at one time. It will require two or three separate* 
spreadings from time to time as the surface becomes shiny and 
sticky to produce a perfect mat. Any excess unused material 
delivered for cover should finally be gathered up and stored in 
neat piles back of the ditch line where possible. These treatments 
do not require rolling, although rolling tends to turn any coarse 
sharp fragments of cover material onto their broader sides, reducing 
danger of tire cuts to a minimum. 

Thick mats^ formed of binder and %-inch stones while durable 
are not generally satisfactory; they are expensive, costing from 
$1000 to $2000 per mile and frequently become rough under traffic, 
although they do serve at times to carry a road along for a few years 
which would otherwise be a resurfacing matter. This treatment 
also is used to restore a crown to a road worn flat. 

On gravel and new waterbound macadam and upon roads where 
there is little motor traffic, maintenance by calcium chloride is 
effective. Where this treatment is used the applications may be 
of the granulated crystals applied by hand or by a mechanical 
spreader, at the rate of i lb. to i J^ lb. per square yard; preliminary 
sweeping is not necessary unless there is excessive dust say M-in. 
depth or more upon the surface proposed to be treated. Should 

1 The authors wish to emphasize the danger of using thick mats for 
ordinary maintenance. 



RIGID PAVEMENTS 203 

this treatment be made immediately preceding a rain, a consid- 
erable quantity of material would be lost. Two or three treat- 
. ments as above should suffice for the average season, and the width 
treated may be confined to the width of the traveled way. This 
treatment has cost in New York State about $150 a mile a year. 
Surfaces which have previously been oiled are not recommended for 
calcium chloride treatment. 

In cases where continued surface treatments of bituminous 
material through successive years has built up an excessive depth 
of mat, which has a tendency to be unstable and rut, it is suggested 
that such mat be removed and spread upon the shoulders, which 
will cost from $50 to $150 a mile, and that surface treatments be 
again^made upon the macadam itself. Should it be found that the 
macadam has become uneven, as to crown and grade, or is badly 
worn or has numerous holes, it is suggested that the road be scari- 
fied and thoroughly dragged with a heavy spike-tooth harrow, after 
which an agricultural weeder should be repeatedly hauled over the 
road, the object sought being to work all of the finer particles to 
the bottom of the scarified course, leaving fairly clean coarse stone 
at the surface; this should be shaped up by hand or scraper and 
rolled to develop any irregularities in the surface which should be 
corrected by the addition of new crushed stone. Any pockets 
of fine material should be removed and replaced by new top course 
stone, the weeder should again be used to loosen the stone, which 
will then be ready for the first application of binder, which may be 
at the rate of three-quarters of a gallon per square yard, application 
being made by a pressure distributor, the surface then to be covered 
with a layer of M-in. broken stone and thoroughly rolled. During 
the rolling, additional ^^-in. stone shall be applied and broomed 
about until the voids in the top course are well filled; all loose stone 
shall then be swept from the surface and a sealing cost of one-half 
gallon of binder per square yard shall be applied and immediately 
covered with a layer of J-^-in. stone and again rolled; surface will 
then be ready for traffic. This treatment is probably better 
adapted to waterbound macadam than to the penetration bitumi- 
nous type; however, if found necessary to break up and reshape 
penetration macadam, it is suggested that the latter loosening by 
the weeder qe omitted and a spread, one stone thick, of 2-in. broken 
stone be applied and the first application of binder be increased to 
one gallon or one and a quarter gallons. This method is not ap- 
plicabe to an extended mileage as it is generally better to resur- 
face Iwhen a road reaches this stage. 

Concrete Roads with Thin Bituminous Surfaces. — The second- 
class concrete with thin bituminous wearing surface is a difficult 
type to maintain; the bituminous surface under traffic patches off, 
and as the concrete is usually not strong enough to resist abrasion, 
holes develop in the concrete; patching results in a rough riding 
surface and probably the best way to secure a smooth riding road 
is to resurface, using a 2-in. bituminous mixing type top. 

Asphalt, Topeka Mix, Amiesite, Etc. — The holes which develop 
in the bituminous mixing method type wearing surfaces should be 



204 MAINTENANCE 

repaired as follows: Excavate the old material at the defective 
spot the entire depth of course, so that the edges will present 
clean, vertical surfaces, these surfaces and the exposed foundation 
to be swabbed or painted with hot asphaltic cement or paving 
pitch, the hole then to be filled, with a mixture similar to that used 
in original construction, whenever practicable, using sufficient 
quantity so that after consolidation by rolling (or tamping in case • 
the extent of repairs is limited) the surface of the new patch will 
be flush with the adjacent pavement. In case there is no local 
mixing plant available, or the limited extent of repairs do not jus- 
tify expense of treatment as above, holes may be repaired with 
the mixture of crushed stone and cold patch asphaltic emulsion, as 
outlined for macadam surfaces. 

Concrete Pavements. — The cracks which develop in concrete 
pavements may be the result of either frost action, settlement of 
foundation or contraction, and are properly treated by being 
poured with hot paving pitch or asphalt binder. If spots disinte- 
grate, the defective material should be removed and replaced by 
new concrete. 

Brick Pavements. — Block pavements of brick, stone, asphalt, etc., 
properly constructed should not require repairing for a considerable 
term of years; cracks which develop should be grouted with hot 
paving pitch or asphalt binder; areas which settle, thereby breaking 
the bond of the grouted joints resulting in crushing or cobbling 
the blocks, should be taken up, the sand cushion reformed, all sound 
blocks cleaned and relaid, being turned over where necessary, any 
broken blocks to be replaced by new whole ones, joints then to be 
grouted with Portland cement grout preferably, if the original 
pavement was so constructed, otherwise the joints may be poured 
with hot paving pitch. It should be noted that repairs with fresh 
cement grout require to be protected by barricades for a period 
of about a week, so that such repairs should be confined to one side 
of the pavement in long stretches, leaving the other side available 
for traffic; where the repairs are limited in extent and barricades are 
especially undesirable, the patch may be covered with two inches 
of earth and further protected by planking during the time required 
for the grout to set. Where joints are poured with paving pitch, 
traffic need be diverted only during the time of actually making the 
repair; this is a decided advantage. 

Observation demonstrates that horse traffic on steep grades leave 
the pavement and seek the earth shoulder, so that so far as prac- 
ticable these shoulders should be improved by widening, and by 
graveling or covering with broken stone to avoid excessive rutting, 
also that on sharp curves the tendency of motor vehicles is to cut 
close to the inner edge, making it well for this reason to stone or 
gravel the shoulders at these points. 

Along the edges of the rigid types of pavement, block and con- 
crete especially, traffic usually develops a deep rut which if neg- 
lected becomes dangerous, to rapidly moving traffic; this rut should 
be kept filled with gravel or broken stone. Excess material when 
removed from the shoulders should be so disposed of as to widen 
embankments and flatten slopes. 



MAINTENANCE COSTS 205 

General Organization Methods. — There are three general plans 
for performing the work of general maintenance, the patrol system, 
the repair gang and by contract. The nature of the work renders it 
difficult to estimate in terms of labor and material with precision, 
so that except in the case of surface treatments, repair by contract 
is not advised. By the patrol system the roads patrolled are under 
• constant supervision and the responsibility for neglect is 'fixed. 
The repair gang may be used to supplement the patrol system when 
it is desired to expedite extensive small repairs, and also to perform 
all necessary repairs upon any roads not patrolled. A patrolman 
living in the vicinity of his work, equipped with a single horse, one- 
yard wagon and small tools, costing $3.00 a day," can make all minor 
repairs on. a section of between 5 and 7 miles of macadam. The 
repair gang should be equipped with a small motor truck, say of 
one and a half tons capacity, to be used in transporting the men and 
tools within a radius of about 25 miles from their headquarters 
base; this truck can also assist by hauling some material required 
in the work. 

It is concluded that a combination of the patrol and repair gang 
systems is an improvement over the adoption of either plan of or- 
ganization exclusively, also that the success of either plan depends 
entirely upon the experience, good judgment and ability of the man 
in direct charge and control of this work. As nearly all of the 
hauling in connection with maintenance work is over hard-surfaced 
roads, motor equipment for delivering stone, oil, etc., would natu- 
rally be considered. The writers' opinion is that for short hauls 
teams are economical, also that the motor tractor and trailers sys- 
tem of equipment are more efficient than the complete single unit 
system. 
' Summarized Costs for the Season of 1915 New York State. — 
1 In order that the following figures may be more easily understood, 
I it is well to outline the development of the use of the different types 

of pavement. 
' From 1898 when State highway improvement began until 1909 
[ to which time 1787 miles had been constructed, practically the 
I entire mileage consisted of waterbound macadam. Up to this 
I time there had been no systematic maintenance, which resulted 
in a large mileage of road requiring more than ordinary expenditure 
I to bring it up to standard. 

Beginning in 1909, penetration bituminous macadam was gener- 

j ally used on the main roads with brick near cities and villages. 

About 191 2 the department tried out concrete roads with thin 

I bituminous oil tops. . This type proved unsatisfactory in that the 

bituminous surface peeled in spots and the concrete used was not 

sufficiently strong to stand the traffic directly. The high cost of 

I maintenance can be seen from the following table. The type has 

\ not been used since 19 14. The department is now designing 

( first-class concrete roads where roads of that class are economical. 

I In the following tabulation of maintenance and renewal costs, 

I therefore, the average per mile represents approximately a fair 

( sample of both yearly maintenance and renewal for waterbound 

i 



2o6 



MAINTENANCE 



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MAINTENANCE COSTS 



207 



macadam, gravel and concrete bituminous and represents only 
ordinary yearly maintenance for bituminous macadam, concrete 
pavements, brick and other high -class rigid pavements; none of 
these latter classes have been down long enough to yet require 
renewal, which makes their cost as sho\\Ti much less than will ulti- 
mately be required. 

Of the mileage shown in the preceding table, the following table 
shows the amount of resurfacing. 

Table Showing Resurfacing Costs 191 5 ^ 



Type of Road Resurfaced 


No. 
Miles 


Total Cost 


Cost 
per mile 


Gravel 


12.88 

176. 29 

43-72 

24-85 

0.36 

258.10 


$ 77,686.27 

997,776.66 

243,760.22 

160,321.37 

4,003.40 


$ 6,000 

6,000 

6,000 

6,400 

12,000 


Waterbound Macadam 

Penetration Bituminous. . . 
Concrete Bituminous top . . 
Block Pavements 


Totals. 


$1,483,547-92 





1 The type of resurfacing is not necessarily the same type as the original 
road as shown in column No. i. 



Supplementary Explanation of Mr. Bristow's General Costs and 

Discussion 

The authors wish to call attention to two points in the general 
cos t tabulation. The average cost of maintenance and renewal 
for 191 5 is given as $750 per mile for the total system. This system 
includes approximately 1000 miles of road recently built on which 
there is practically no charge except minor repair aggregating not 
over $200 per mile per year. For a completed system of this char- 
acter all of which is under normal maintenance and renewal, the 
average cost per mile would be approximately $900 per mile, as is 
evident by excluding the thousand miles from the tabulation of 
total cost. 

In the resurfacing table it is evident from the cost per mile that 
better grades of top courses were generally placed on the water- 
bound and gravel roads than originally constructed; this means that 
in some cases the original design was not proper for the class of 
traffic the road served. 

The most evident faults of the usual maintenance are in delaying 
the work till late in the season and in careless mending of ruts and 
depressions before the application of surface treatments. It is 
well to emphasize the necessity of using a coarse grade of stone 
preferably ij^^" to 2}^." size in mending noticeable depressions. 
The hole should be dug out, the edges squared up, the depression 



208 



MAINTENANCE 



filled, bound with heavy binder and screened and rolled. Careless- 
ness in this regard has resulted in a large amount of justifiable com- 
plaint. The following quotation from the 191 7 report of Mr. 
Fred Sarr, 2d Deputy Highway Commissioner of New York 
State is very reliable and up to date data as the bookkeeping on 
which it is based is of a high order. 

"The cost of maintenance, repair and reconstruction of a large mileage 
has been segregated and charged against the roads of various types of im- 
provement, following the plan of the last two years in order to determine 
the cost of maintenance of the several types of pavements which have been 
used in the improvement of the New York State and county highways, and 
the results are indicated in the following tables. 

"The pavements are arranged in two groups. In the first group are the 
types represented by at least 100 miles, or those that by reason of the large 
mileage and wide distribution should represent with a reasonable degree 
of accijracy the average cost of maintenance of pavements of the particular 
typed. In the second group are the types represented by less than 100 
miles and too much weight should not be given to the tabulated costs of 
maintenance of such mileage, in that the results of one year with a small 
mileage do not fairly represent the actual average cost per mile of mainte- 
nance of the particular type. 



First Group 



Type of Improved Surface 


Miles of 
Improved 
Highways 

of Each 
Type 


Expenditures 
per Mile dur- 
ing 191 7 for 
Maintenance 
and Repair, 
Exclusive of 
Reconstruction 
to Different 
Type 


Total Expendi- 
tures per Mile 
during 191 7, 
Including Re- 
construction 
to a more Per- 
manent Type 
of Surface 


Bituminous macadam, 
penetration method, as- 
phalt binder 

Waterbound macadam. . . 

Brick pavements 

Concrete: 

First Class 


2,793.77 

2,534.34 

280. II 

257.46 
226.48 
167.72 

164.34 


$412.00 
970.00 
222.00 

1 1 2 . 00 

1,127.00 

918.00 

352.00 


504 . 00 
1,154.00 

1,443- 00 


Second Class 

Grave] 

Bituminous macadam, 
penetration method, tar 
binder 



"An expenditure of ^34,392 which was required to restore to normal con- 
dition sections of improved highways that were damaged by cloudbursts 
and floods, has not been distributed to the particular type of pavement in- 
volved, in that the type of construction had no bearing upon this extra- 
ordinary expense. 



MAINTENANCE COSTS 



209 



Second Group 



Type of Improved Surface 



Miles of 
Improved 
Highways 

of Each 
Type 



Expenditures 
per Mile dur- 
ing 1 91 7 for 
Maintenance 
and Repair, 
Exclusive of 
Reconstruction 
to Different 
Type 



Total Expendi- 
tures per Mile 
during 191 7, 
Including Re- 
construction 
to a more Per-' 
manent Type 
of Surface 



Block pavements: 

Asphalt, concrete base. , 

Asphalt macadam base. 

Wood 

Stone 

Brick cubes, macadam 

base . 

Concrete : 

Hassam 

Bituminous Macadam: 
Mixing Method: 
Amiesite, concrete base. . 
Amiesite, macadam base, 
Topeka, concrete base. . . 
Topeka, macadam base. . 
Open mixed, concrete 

base 

Open mixed, macadam 

base 

Bitulithic, concrete base 
Henderson, macadam 

base 

Sheet asphalt, concrete 

base 

Gravel mixed, gravel 

base 

Penetration Method: 

Asphalt binder, concrete 

base 

Sub-base, bituminous. . 
Kentucky rock asphalt. . . . 
Rocmac 

Total all types 



13-55 
2.52 
o. 24 
2.93 



58.52 



3-73 

4.33 

33-74 

12.64 

13.32 

3-58 
13.63 

I . II 

1 .22 

11.47 



4.80 
14-39 
17-55 

1-39 



$240 . 00 
163.00 

30 . 00 

76.00 

619.00 



32 .00 

1,131.00 

245 - 00 

393- 00 

29.00 

109.00 
2 I 6 . 00 

1,380.00 



738.00 



I 74 . 00 
1,079.00 

387.00 
3,884.00 



$9,811 .00 



6,639.21 



$643 . 00 



$767.00 



The cost of maintenance having been segregated and charged against 
the various types of -Davement for the past three years, in order to secure a 
more reliable comparison of maintenance costs, the experience of the three 
years has been combined for the types having a material mileage in our 
system of improved highways with the following results: 



2IO 



MAINTENANCE 



Type 


Average of the Past Three Years 
Experience 


Average Mileage 
Maintained 


Average Expendi- 
ture per Mile-year 


Bituminous penetration method 

Waterbound macadam 

Gravel. 

Brick pavement 

First Class concrete 


2,6s9 
2,408 
178 
280 
164 
2S3 


$464 . 00 
976.00 
824.00 
196.00 
124.00 

1,082 .00 


Second Class concrete 

All types 


6,099 


678.00 



General 

"Efficient maintenance of macadam pavements, particularly of the water 
bound type, of which there are 2535 miles in the State system of improved 
highways, necessitates frequent surface treatments with bituminous mate- 
rials or constant patching of the holes that rapidly develop under the present 
day motor vehicle traffic. 

"Frequent surface treatments are objectionable not only from a traffic 
standpoint, but from the fact that such treatments tend to build up an un- 
stable mat of bituminous material and mineral aggregate on the surface of 
the pavement that is displaced by the fast moving motor vehicle traffic, and 
develops a rough and uneven surface. , 

"It has, accordingly, been the policy of this Bureau to restrict the use of 
surface treatments and wear the surface mat down as this is possible before 
giving another general surface treatment. ^ 

"This method, while tending to provide a smoother surface, requires 
constant patching during the latter stages of the wearing down process. 

" Much time and thought have been given to the study of the results ob- 
tained by various methods of manipulation and materials used in patching 
macadam surfaces. 

"In making these patches to pavements carrying any considerable amount 
of motor vehicle traffic, it is necessary to bind the mineral aggregate with 
some form of bituminous material. 

"Light asphaltic oils and refined tar products, similar to those used for 
surface treatments, have been used extensively for light, thin patches, paint- 
ing the area to be patched with the bituminous material and covering with 
stone chips or sand. 

"Heavy binders that require heating have been used in the same manner. 

"The most satisfactory results have been obtained, where the required 
patch must be cme-half inch or more in depth, by mixing the mineral aggre- 
gate with a heavy asphalt or tar binder, cut back with light voltaic oils to a 
consistency that will mix readily with the mineral aggregate when cold, also 
with an emulsified asphalt binder used in the same manner. 

'' The bituminous material and stone aggregate, being mixed either by hand 
or in a small concrete mixer, permits of a proper ijrcportioning of the mate- 
rials which has been demonstrated to be about 6 % in weight of solid biturnen 
or mineral aggregate used, or about one gallon of the cut bacK or emulsion 
per cubic foot of crushed stone. 

"With asphalt cut back the best results have been obtained by using a 
material made from an asphalt binder, having a penetration of about 165, 
cut back with about 33 % in weight of naphtha. 

"With tar cut back the best results have been obtained with a material 
made from a refined tar binder having a melting point of about 70°C., cut 
back with about 40 % in weight of tar oils, of which at least 60 % shall distil 
up to 235°C. 



MAINTENANCE MATERIALS 21 1 

"A very satisfactory material for patching purposes is an emulsified 
asphalt containing about 65% of asphalt binder having a penetration of 
about 165. 

' ' This material may be diluted with water if desired, and may be mixed 
with wet mineral aggregate when found in that condition. It readily sepa- 
rates from the emulsified state when combined with crushed stone in the 
so-called open mix. 

"The resultant adhesive qualified of an emulsified asphalt appear to be 
better than can be obtained by the same asphalt in any other form. 

"The only tangible reason advanced for this result is that the water in 
the emulsion may carry the binder into the pores of the material or pavement 
to which it is applied. 

* ' The patch made with emulsified asphalt hardens to a condition of stabil- 
ity much quicker than one made with cold oils or tars or cut back binder 
that we have used, and is, for this reason, preferable to those materials for 
patching work on heavy traffic highways. 

"Very good results have been obtained with the cut back tar cold patch 
material, particularly on medium to light traffic highways, where the patch- 
ing material is not thrown about by traffic to any great extent. 

"In order to obtain efficient results in patching with a tar binder, it is 
necessary to make a so-called close mix, by using a graded mineral aggre- 
gate having arninimum amount of voids, which, however, will not permit 
the volatile oils to evaporate as fast and the patch to become stable as 
quickly as may be obtained with asphalt emulsion when used in the open 
mix. It is, accordingly preferable when using tar, to mix same with the 
mineral aggregate and leave in shallow piles for about two days before apply- 
ing to the road surface. . 

"The necessity for using the close mix with tar binders, is due to the 
fact that tar products are more susceptible to the heat and cold than asphalts. 

•' ' In other words, if starting with the two materials of the same consistency 
at 6o°F. and the temperature is raised to that of a pavement on a hot sum- 
mer day, say I30°F., the tar is much more fluid than the asphalt and tends 
to flow away from the open mineral aggregate, and the open patch will show 
a tendency to ravel. Again when the temperature is reduced to that of a 
pavement on a winter day, the tar becomes much more brittle than the 
asphalts and again the open patch with tar binder is more liable to ravel out 
than one made with asphalt binder. 

' [ A comparison of the result obtained with the two materials each of 
which contains a quantity of the semi-volatile oils sufficient to permit them 
to be applied to the surface of the pavement at 6o°F. as a surface treatment, 
demonstrates that the tar, by reason of its greater fluidity en a hot summer 
day, will penetrate the old pavement to a greater extent than the asphalts, 
and thereby serves more as a binder to the old pavement. It is for this 
reason that cold tars are generally used as the first and second treatment of 
a waterbound macadam pavement, subsequent treatments of heavy as- 
phaltic oils carrying about 65 % of solid bitumen, will give more efficient 
and lasting results if used conservatively, that is, if the successive treatments 
do not follow each other too closely. 

"_When successive treatments are given every year as a dust layer or to 
obviate the necessity for patching, cold tar is preferable in that it does not 
build up a mat on the surface of the pavement to the extent obtained with 
asphaltic oils. 

"Providing a mat is built up with successive tar treatments, the same will 
generally lie flat and not shove u«ider traffic, and develop a wavy and corru- 
gated surface as is often obtained with too frequent surface treatments with 
asphaltic oils. 

"This resulting difference is due to the aforesaid difference in consistency 
at summer temperatures of the pavements. 

"The tar being so fluid at summer temperature, it appears to retain a 
smooth surface by the effect of gravity, while the asphalt simply softens 
sufficiently to permit the surface mat to be displaced by traffic, which dis- 
placement increased from day to day and often necessitates the entire 
removal of the old mat. 

' ' Another factor to be considered in deciding upon the material to be used 
for the surface treatment is the condition of the old pavement. 

Where the old macadam is composed largely of small particles of crushed 
rock and dust, and is in a more or less loosened condition, and is subject 
to displacement by traffic, a light asphaltic oil is preferable to cold tar for 



212 MAINTENANCE 

surface treatments. The asphaltic oil treatment develops into a mat or 
carpet over the macadam which remains more or less plastic, even at low 
temperatures, and displacement of the macadam under traffic does not result 
in the shattering and the ultimate destruction of the mat to the extent ob- 
tained under similar conditions with tar treatments. 

"Also for the same reason, asphaltic oils give the best results on pavements 
where steel shod traffic predoniinates. 

' ' The best results obtained with tar treatments are where the old macadam 
pavement is clean or free from dust and where the pavement is firm and 
sound, and the stone fragments do not displace under traffic, and where 
motor vehicle traffic predominates, also where a minimum amount of cover 
material is used in conjunction with bituminous material. 

"Macadam pavements surface treated with tar are, however, much more 
slippery for horse traffic in cold weather than those treated with asphaltic 
oils. 

"In my report of a year ago, I discussed to some length the subject of 
the extensive breaking through of many of the pavements during the spring 
months. 

"Referring to such report it will be noted that the total area actually 
broken during the spring of 19 16 was equivalent to 82 miles of pavements 
16 feet wide, and that the broken areas were distributed over many projects 
aggregating to a total of i939 miles, of which an average of 4.2% was 
broken through. 

"During the season of 1916, about 75% of the total broken areas were 
substantially repaired, and about 238 miles of the weaker pavements were 
resurfaced. 

"The spring of 191 7 appeared to be a repetition of the previous year as 
to the amount of broken pavements. 

"The result of a survey to determine the extent of the broken pavements 
when tabulated indicates that the total broken areas were, however, but 
60 % of the total of the previous year. 

"The total length of the various projects involved aggregating 2090 miles 
about 9 % larger than those reported in the previous year. _ Of this total 
length the equivalent of about 48 miles of pavement 16 feet wide was broken 
»up or about 23^ % of the total length involved." 

Snow Removal. — On main roads between large cities snow 
removal in winter has become part of the regular program. In 
many districts automobile trucking relieves rail congestion and is 
needed even more in winter than in summer. The Maintenance 
Departments are in a position to handle this work with their 
organized forces and equipment which are idle at this time of 
year and the necessary expense is certainly worth while to make the 
main roads passable for trucks the year round. 

Typical Maintenance Costs of Different Types. — From a detailed 
study of 600 miles of road in Western New York with which we 
are personally familiar, the following typical costs are derived. 

It is assumed that the type used is suitable for the class of traflfic . 
served as indicated on page 164. 

The maintenance system is a combihation of patrol, gang work 
and contract. A one man patrol with horse and wagon is used 
to keep the shoulders in shape, the ditches and culverts clean and 
small holes in the pavement repaired. Gang work with proper 
machinery under State control to paint guard rail and make more 
extensive surface repairs and contract work for oiling and surfacing. 
Detail oiling costs are given under cost data (page 653). This 
system is not highly efficient as the executive heads are changed 
at short intervals for partisan reasons; the department is a con- 
venient means of dispensing minor patronage and the maintenance 
money is rarely available early enough in the spring to be used to 



DETAIL COSTS 213 

advantage, but it represents about as good a method as can be 
expected in doing public work on a large scale and as such is of more 
practical value as a guide of costs than figures based on maximum 
efficiency. 

Patrol Work Macadam Roads. 

Regular patrol labor '. $70 per mile per year 

Extra labor 40 " '' '' " 

Maintenance material 45 " '' '^ " 

Guard rail, incidentals, etc 20 " " '' " 

Total per mile per year $175 " *' *' " 

Say $200 for waterbound roads 

Say $150 for bituminous penetration roads. 

Patrol Work Rigid Pavements. 

Regular patrol labor $30 per mile per year 

Extra labor 15 " " " " 

Shoulder material, etc 30 " " " " 

Guard rail, incidentals, etc 20 '' " '^ " 

Total per mile per year $95 

Say $100 

15' Waterboimd Macadam, Class n and IV Traffic. 

Life of top course 4 to 12 years; Say 7 years Class II and 9 
years Class IV. 

Class 11 Traffic. 

Yearly patrol including materials for minor repairs and painting 

guard rail at $200 per mile per year $1400.00 

Calcium chloride, ist and 8th years @ $125 per mile 

per year 250 . 00 

Cold oiling, 2d year 200 . 00 

" 3d '' 200.00 

" ;^- 5th '' 250.00 

Hot oiling 6th '' 1000 . 00 

Cold oiling 7th '' 250 . 00 • 

Resurfacing with waterbound macadam 8th year 4000.00 

Eight year total $755o . 00 

Cost maintenance and renewal per mile per year 950.00 

Cost of ordinary maintenance per mile per year 450.00 

Class IV Traffic. 

10 years total approx $8000 . 00 

Cost of maintenance and renewal per mile per year 800.00 

Cost of ordinary maintenance 400.00 



214 MAINTENANCE 

15' Penetration Bituminous Macadam Class 11 and IV Traffic. 

Life of top course 6 to 12 years. Say 10 year average. 

Yearly patrol @ $150 per mile per year $1,500.00 

Cold oil 3d year 200 . 00 

" "5th '' 250.00 

. " "7th " 300.00 

Hot " 9th '* 1,000.00 

Cold '' loth '' 250.00 

Resurfacing nth year with bituminous macadam 6,000.00 

1 1 year total $9,500 . 00 

Cost maintenance and renewal per mile per year 900.00 

Cost ordinary maintenance 350.00 

18' Cement Concrete Pavement Class I and 11. 

Class I Traffic (12 year life). 

Yearly patrol and incidentals @ $150 $1,800.00 

Resurfacing the 13th year with either asphalt, brick, 
clay cubes or rebuilding with concrete @ $10,000 to 
$16,000 per mile 14,000.00 

13 year total $15,800.00 

Cost maintenance and renewal per mile per year 1,220.00 

Cost ordinary maintenance 150.00 

Class n Traffic (15 year period). 

Yearly patrol and incidentals $ 1,500.00 

Resurfacing 13,000 . 00 

16 year total 14,500.00 

Cost of maintenance and renewal per mile per year $ 900 . 00 

Cost of ordinary maintenance 100.00 

18' Brick Pavement Class I Traffic 

Probable life 15 years based on reports from 80 cities. 

Range of life 10 to 25 years. 

Yearly patrol and incidentals $ 2,250.00 

Replacing brick surface 18,000.00 

16 year total $20,250.00 

Cost of maintenance and renewal per year $ 1,250.00 

Cost ordinary maintenance 150.00 

Maintenance Conclusion. — The indications are that the yearly 
cost of maintenance and renewal of a well designed high-class 
road system will run about $900 per mile per year. The effect 
of bad design is evident from resurfadng costs, for if waterbound 
macadam is built on a Class I traffic road the life is easily halved, 
increasing the maintenance and renewal cost to $1500 per mile 
per year and causing continual inconvenience to the traveling 
public by repairs and reconstruction. 

Probably the most feasible method of reducing maintenance 
cost will be the utilizing prison labor to manufacture and in a limited 
way apply the maintenance materials. 



CHAPTER VIII 



MINOR POINTS 

Under this heading are included right-of-way widths, guard rail, 
bridge rail, snow fences, retaining walls, toe walls, curbs, guide and 
danger signs, cobble gutters; rip rap, catch basins, grates, dykes, 
storm sewers; flow of water in ditches and cattle guards. 

Right-of-way Widths. — Many of the older communities are 
handicapped in road improvement by narrow right-of-ways which 
require widening at a large expense and considerable legal difficulty. 
Where right-of-way is acquired for new locations future develop- 
ment should be considered. The width acquired must be sufficient 
to include all cut and fill slopes. Where these considerations do 
not increase the normal width the following normal widths are 
recommended : 

Mountainous regions (cheap land) loo ft. 

Farming country (moderately cheap land) 80 ft. 

Thickly settled districts (expensive land) 60 ft. 

Clearing Widths. — Clearing of trees, brush, etc., depends on 
height and thickness of growth; the object of clearing is first to 




(TopandBofhm No.9^ allofher Wires No.lh dSirands-fedf-ausperRod, 
Locusi- Posis, leasi- Piame-her cdl&wecf is 'finches. 
All Corner and End Po^H are 12 inches in leasf Diameter and Braced 
as shown above. 

Pig. 42.— jRight-of-way fence. 

remove growth within the slope lines, second to provide a clear 
view and third to clear sufficient width to allow the sun to reach 
the road and dry it out and melt snow. This last depends a good 
deal on the direction in. which the road is running and the altitude 
and geographical location. It is entirely a matter of judgment 
but should be liberal in the forest districts and ranges from 30 
ft. for low scrub growth to 150 ft. in adverse location and thick 

215 



2l6 



MINOR POINTS 



high growth. In high altitudes the roads are at their best closed 
in winter and if careful location and liberal clearing will increase 
the length of open season it is well worth while as in effect it increases 
the usefulness of the road by 15% to 25%. 

Guard Rail 

Wooden Guard Rail. — The construction generally used is shown 
in the following sketch. 



7nis Jign every lOOft(approx.)wifh BfacHram t 




\ii ^ Rails and Posts Painted 

uJ .=% 3 Coats White Lead and Oii. Lj 






2 "Steel or Wt. Iron Pipe -. 



>6< 



..<?'(?::.. 




^^ I 



< 



AsOrdered)^a 
bytnqineery^^ 



lronPin,^'Diam; 6"lonq'' 
Fig. 43. 




The posts are cedar, white oak, or chestnut, and the rails are 
hemlock, yellow pine, or white pine. Such guard rail costs from 
25c. to 40c. per foot, about 5c. per foot per year for maintenance, 
and needs renewal every 8 to 10 years; the capitalized cost at 
4% is approximately $1.25 as figured by the New York State 
Highway Commission, and on this basis they have decided that 
it is cheaper to use a fill slope of i on 4 up to a seven foot depth 
eliminating the guard rail than it is to use a i on ij-^ fill slope with 
guard rail. 

The wooden guard rail as built acts as a warning only. If a 
machine or rig becomes unmanageable and hits the rail, it generally 
breaks or the posts tear out, allowing the vehicle to turn turtle on 
the fill slope. So many accidents of this kind occur that there is a 
demand for a rail that actually gives protection as well as 
a warning. 

Concrete Guard Rail. — Because of this demand and the high 
cost of maintenance and renewal of the common wooden rail, 
concrete guard rail is being adopted. The simplest and best 



GUARD RAIL 



217 



design of this kind that the author has seen was tried out by the 
New York State Department of Highways on the Ridge Road, 
near Rochester, N. Y. in 19 10. A sketch is given below. This 
construction has been specially commended by the automobile 
associations (Fig. 44). 




Pig. 43A. — Minne3ota guard rail. 



£S 






-8-0- 



nH' ^/- 



Diaphragm io \ " 
'• Prevenf Slipping '^} 



=^': NOTE. -"^ ''^l^:=:"f=^\~/:rn:^i~ ~;^fj=i-S'~ ■ 



I 1 1 Fences should ^^ \ 
\ \b€ set Lower ^^\ 

l _ J y^^'Ofi Double Rail. ^>1> 




fieinforcemenf.} 



Mesh 
Reinforcement 



Pig. 44. — Concrete guard rail. 



The rail was invented by J. Y. McClintock, County Engineer 
of Monroe County, N. Y. It is neat in appearance, durable and 
strong, and is specially adapted for a combination bridge and ap- 
proach rail. The old design of an iron bridge rail connected with 
a wooden road rail has been an eyesore. 

The actual cost of manufacture and setting was from 50 to 
60c. per foot. The contract price for such rail would, probably, 
run from 8dc. to $1.00, depending upon the length of the haul, 
freight rate, and difficulty of digging post holes but even at the 
high figure it is cheaper in the end than wooden rail and is a 



2l8 



MINOR POINTS 



safe construction. The anchor and rod shown on the sketch is 
used on curves or even on straight stretches where new fill is en- 
countered, to prevent the posts being torn out by impact from runa- 
way machines. 




y. 2.. Q U:. >k— ... S-'-—^ 



Cedar, Chesfnuf, 
Locust, OahfSf one 
or Concrete. 

dark Removed 
belowSurface. 



^XpbleWfre} 

4- 




vmn 




ASirandsofHo£ 1^2' EijeboH-nv^and Washer,Thread9dt6'.^ OnSecHons oiRaitin^LessfhanlOOFf. 
eakWire.-.^^ \ , GakmrtClips. \\ in Unqth the Pandas shown shall be 

\ H--- —10 ;^--- -H :. UsedafOne End and on fh9 other £nd 

^~^^—\^^''6alv.Shel or IronWlre Cable. ^ jjjjij;, the Pipe Brace and 4 Strand wire 

\ Brace mau be omitted and 3' Eue bolts 




substituted for I'Eyebolfs 
^ ■ Not Less than 12 Strands of NoA 
/ 6a I V. Wire. 

"^ "" jT' OeadHan. 



wmTTTPr:^ 



• *■ After Erection, Posts and Parts not \ 
J \^ 6a Ivan ized to hare two coats o^ White j 
; \ Lead and Linseed Oil Painf. \ 

■ ^ V^ ^^ I I Poststol>€ not Less than d'Round or 6%q. | 
dark to be removed from Posts and Knots 
hewn flush mth Surface. 



1 I 



\MPbsh tobeHtavtj'Bnish^^'^'^.^^ r^\/J 
\ Coated with Creosote T'^"^ 

1 fbint on Bottom anct Sides . .^ / 
\ up not less than 4^ Feet. ^^ 

Area of Face to be not 
Lessthan4S<j.Ft.^.^'' 



^-j? 



Fig. 45. — Cable guard rail. 

The rail proper has a web and bar reinforcement; it is designed 
to stand a 6 ton horizontal load at the center of the panel. The 
rails and posts are molded separately and allowed to set for, at 






^^^ 



Jlc 



;:^n: 




Turn bo l-h with 
:^^y^PBHers. 

.f...-;-!'. Place one Leg 
ateach 



Support. 







Z'k4"Hemloch. ''- 1x6 "Hemlock, 

P ^ ^ "- End View. Fence in Position. 

Fig. 46. — Snow fence. 



least, a month; they are then put together in much the same manner 
as the wooden rail. The rounded top of the post makes it possible 
to erect on any grade. 



GUARD RAIL 



219 



A considerable mileage of this rail has been erected in New York 
and New Jersey and has prevented many serious accidents. It has 
been hit by autos, tar kettles, rollers, traction engines and rigs and 
in no case has the vehicle gone over the bank — which is the general 
cause of fatal accidents. The rails and posts will break when hit 
by a heavy machine, but the reinforcement merely bends (does 
not snap) and continues to exert enough resistance to hold the ma- 
chine on the roadway. > 

Guard rail has two distinct purposes; first as merely a warning, 
at culverts, curves, low embankments, etc., where the danger is not 
great and second, as an actual protection in dangerous places. 




□ffi 






-7'Q 



"U..... 



End Ekvafion. 



Section C-JX 



Pig. 47. — Showing raised parapet on skew bridge extended over 
straight parapet retaining wall. 

Concrete guard rail is not advocated where warning alone is 
sufficient. 

Wire Cable Guard Fence. — Figure 45 illustrates this construction. 

Snow Fences. — Sketch No. 46 shows a typical snow fence used 
to prevent drifting in bad locations. 

Bridge Rail and Raised Parapets. — Bridge rail for small span 
bridges is of two types, iron pipe rail (see Figure 43) or solid raised 
parapets (see Figure 47). The solid parapet is to be preferred. 

Retaining Walls. — In unusual cases retaining walls are needed 
in road construction. Plain or reinforced concrete walls are gener- 
ally used, the selection depending upon the relative cost. The plain 
concrete wall is considered the best type for heights up to 12 ft.; 
the reinforced cantilever form from 12 to 18 ft. and above 18 ft. 
the buttressed design. We give, page 220, examples and rules for 
the plain and reinforced cantilever types only, as the necessity for 
walls higher than 18 ft. is very rare. For the design of buttressed 
walls the reader is referred to the standard works of reinforced 
concrete. 

Retaining walls are usually built in monolithic sections of 20' 
to 25' in length; expansion joints are provided between these sec- 
tions. The expansion joints may consist of simply a plane of weak- 
ness between the sections produced by allowing one section to set 



2 20 



MINOR POINTS 



RoundiolfRad.-^. k^-^ ^ 



ffoundtolkRad.^^ . * 




,Weep-Hole5of3"7ife 
; /o i4?f Spaced 6' 
■C.toC. 



Pig. 




2> 

Type R. 

48. — New York State standard retaining walls. 



H 


Reinforcing Steel Bars of Deformed Section 


SXEMl 


Heel 


Toe 


Net 
Area 


Spacing 
C-C 


Length 


Net 

Area 


Spacing 
C-C 


Length 


Net 
Area 


Spacing 
C-C - 


Length 


11' 


0.601 


6r 


I2'-2 ' 


0.442 


i¥ 


4'-iir' 


0.442 


Qr 


,s'-3r 


12' 


0.601 


5r 


i3-3i" 


0.442 


6r 


5'-5r' 


0.442 


H" 


,^-8" 


13' 


0.601 


5" 


i4'-5 " 


0.442 


sV 


6'-o" 


0.442 


i¥ 


4'-oi" 


14' 


0.601 


^V' 


i5'-6|" 


0.601 


6F 


6'-6" 


0.601 


8/ 


4'-44'' 


i.S' 


0.601 


a" 


i6'-8 " 


0.601 


s¥ 


7'-o'' 


0.601 


1-" 


4'-q" 


16' 


0.994 


6' 


i7'-9 " 


0.601 


aV 


i'-(>¥ 


0.601 


6/ 


s'-ir 


17' 


0.994 


5r 


iS'-ioi" 


0.785 


$¥ 


^'-o¥ 


0.785 


i¥ 


sr^" . 


18' 


0.994 


,s" 


20'-0 " 


0.785 


a¥ 


8'-7" 


0.785 


6/ 


S'-ioi" 


iq' 


0.994 


4^' 


2l'-ir' 


0.785 


a¥ 


9'-i" 


0.785 


6i" 


6'-2i" 


20' 


0.994 


a¥ 


22'-3 " 


0.785 


A " 


9'-f 


0.785 


sr 


d'-?" 



1 In each set of 3 bars in stem, first bar which is of length given, extends to top 
of wall, second bar to height f H, third bar to height | H. 

When Type W is used as a bank wall (that is, above the roadway), max. H = 20'; 
min. X = 2' for H of 5 to 10'; and 0.2 H for H greater than 10'. 

When Type W is used as a sustaining wall (that is, below the roadway), max. 
H = 13'; and min. X = 3', except where foundation is rock or entirely below frost. 

When Type R is used as a bank wall, max. H = 20'; min. X = 0.15 H for H 
greater than 10'. 

When Type R is used as a sustaining wall, max. H = 13'; min. X = 0.25 H for H 
greater than 10'. 



RETAINING WALLS 



221 



H 
M 

O 

o 


1 

eg 


pq 


? 


eq 


1 


CO 


1 

T 

CO 


J 


o 

y 


H 


y 


t 


y 


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:? 




2 


ffi 




:? 

"3 






:? 

00 


:? 

OS 


I 


1° 


m 


? 


fe 

? 


J 


J 
CO 


& 

^:i 


J 

CO 


J 

CO 


H 






ft: 

z 


2 


% 

2 


2 


? 


ffi 


5; 


5: 


I 




:? 

00 


7 


1 


>< 

% 

o 

n 

• > 

oi 

Q 


1 


pq 




CO 


:? 


ft: 




fc 
T 

o 




H 








ft: 


ft: 

o 


:? 

CO 


:? 

CO 


W 










00 


OS 


1 






ISIS 
;i o 

o 


pq ■ 


:? 




CO 


CO 






lb 


H 




C<1 






:? 

CO 


CO 


CO 


ffi 


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5: 

«3 


CO 




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ft: 


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< 

H 

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CO 


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lb 


% 

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cq 


ft: 


CO 


CO 


CO 


w . 


ft: 

o 








? 

00 


ft^ 

? 

bi 


3 




PQ 


oo 








CO 


CO 


ft: 




2 


*: 

cq 






:? 

CO 


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lb 




:? 


oo 


bi 


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C! 


(^ 


c 


^ 


s 
ts 




Tl 


rU 


« 


o 


'd 


Xi 


^ 


'd 


^ 


n 


•s 


•+J 


^ 


u 


^ 


w 


rt 




o 


;3 


^ 


O 


o 




,^ 


^ 


f^ 


a 


a 





ft -^ 



11^ 

Q> 0) rt 
4^ ^ ^ 

rt o o 

TT f) 






oV. 



05 ^ ^ 

..2 ^ 

^^ 

1 'd 



a . 

a 

■■2§ 



O (U 



c.25.?'^^ 

S (U C _, -, w 
Ph ^ ft 



222 



MINOR POINTS 



before building the adjacent wall, or it may be a key joint as shown 
in Figure 49A and the plane of separation may be made more pro- 
nounced by coating the concrete with a thin layer of asphaltum 
or pitch. 




Cemen+ and Dry Rubble. 

Pig. 49. — State of Pennsylvania retaining walls. 




Plan. 



Key Expansion Joint. 
Fig. 49A. 



Toe Walls. — Toe walls are nothing more than low retaining 
walls or very substantial curbs. They are used in cuts on the out- 
side of the gutters to prevent unstable side slopes from filling the 
gutters or heaving them out of shape by sliding pressure. Figure 



CURBS 



223 



50 gives a section of Eden Valley Hill near Buffalo, N. Y. where a 
clay quicksand cut was successfully protected in this manner. 

Curbs. — Curbs are constructed of stone and of concrete. 

Stone Curbs. — The cuts given show the methods of setting; 
the size of curbstones for first-class work range from 16" to 22" 
in depth, 5" to 6" in thickness and 3' to 5' in length. For small 
villages, curbstone of 4" width set in the simplest manner shown, 



Brick Outter.^ 




miosl- 



Drain 
Fig. 50. — Showing concrete toe wall. 

is satisfactory. The stones most used are granites, bluestones of 
New York State, and the tougher sandstones such as Medina, 
Berea, Kettle River, etc. The prices range widely, depending on 
the locality of the work. Mr. William Pierson Judson, in his 
"Roads and Pavements," gives the following range of costs: 



Cinders, 
Oravelor 
Crushed^ 
^fone-'"' 




K/55{ 



Simple Stone Curb 
for Light Traffic Village Streets. 



Round to ("i^ad.^. 
Sand- 



J<6\ .'Round to I 'Rad. 

! fe, 

Cinders, Oravelor Crushed ... ^ 

«»« Stone Cinders, Onrvel 

Z'Porous '^^"^' orCrushe^Stone'i 

''^^ 2"PorousVie" 

Concr.Curb and Gulter. 



'Round to TRad. 
. ■^.A'i'Joints Filled with Paving Fitch 

'^ J.4..^ i|^S^ 

\ilOli ^5" Concrete Ba^e 

Simplest Form of Concrete Curb. 
(Shbwing also Form of Expansion Joint 
where Brick are Laid Longitudinally 
in Gutter.) ' 




Fig. 51. 



Straight curbs set, cost about as follows: with 30% to 50% added for 
curves; granite, $0.50 to I0.90, unusual case $1.25 per foot. 

Ulster and Oxford bluestone, $0.40 to $0.80, unusual case $1.00 per foot. 

Medina and Berea sandstone, I0.35 to I0.90. 

Concrete usually costs from I0.40 to $0.50 with $0.35 added for a combined 
gutter, though combined gutter and curb have been built for $0.50. 

Simple concrete curb (Figure No. 51) has been built during 191 1 in different 
parts of Western New York at a cost of $0,30 to $0.40 per foot. 



224 



MINOR POINTS 



Where stone curbs can be built for less than $0.70 per foot, it seems good 
policy to use them through the business sections of small villages. For the 
residential Dortions or where the cost of stone curbing is high, a concrete 
curb of the simplest design is the best practice, as city conditions and require- 
ments are neither necessary nor expected. 

Curb Radii. — A good radius for drives is 4 ft. For right angle 
Main Street intersections 13 ft. For acute or obtuse angles 10 to 20 ft. 



/.^"Kd'C/eafs 



CJMei- 
Boh-s- 




•^^^^^"'' <22m-HUDS0N >: ALBANY lOi^J l^ 

<4^M-NA5SAUT>'^""^-^^^^^ I^^"^ 



I5.H.N0.37: 

' ' A 






Cylinder of 2"J Clas$ „ 
Concrete; Diam. 6 , , 




Letters to be of '^^ ^ 
Aluminum on a Black Field. 



• /. 9 "Galv. Iron Pipe, 
(Outside Diam.) 






; P- 



HI 



\ Iron Pin 

\ tiiroughPipe 



K- 6"--- — >i 

Cast Iron. Filler. 



<-^:^ 



-:i 




jRivet 



^"Carriage Bolt 
•Upset Thread after Nut is in Place. 
Fig. 52. 



Guide Signs and Danger Signs. — A good sign must be easy to 
read, pleasing in appearance and permanent. The drawing (Figure ; 
52) shows one of the designs in use; the posts are of galvanized 
iron and cost about $5.00 in place; the background for the alumi- 1 
num is a japanned metal; the signs cost approximately $0.15 per 



COBBLE GUTTERS 



225 



letter including the board. Danger signs should be used only where 
no doubt exists as to their necessity, as their indiscriminate use 
decreases their effec^veness. 

Riprap and Dykes. — Well constructed riprap protects stream 
banks and bridge approaches from stream wash except in unusual 
cases where a solid masonry or concrete protection is required. 



^{^ou/der 




4cSand 
Cushion 



( Sand-Cushion not Required in Sandy Soil 
Size of Stone 5-9") 
Cobble Gu-tter. 




Third Class Concrete 
Ditch Lining. 




• tiuisuai %idth)'y 
Concrete orSand Foundation; Grouted 

orSandJo/nts. 
Brick Gutter. 




No.4 Crushed Stone 
Ditch Protection. 

Fig. 53. 



I The sizes of stone suitable for riprap are usually specified at a 

i minimum of 3^ cubic foot and 50% or more of the material to be 
over 2 cubic feet. 
Where the road is located in bottom land and is covered with 
backwater in the Spring, it can be protected by riprap paving 
i on both sides or a dyke and riprap paving on one side as shown 
J in Figures No. 55 and No, 56, 



226 



MINOR POINTS 



Cobble Gutters, Brick Gutters, Ditch Linings, Etc. 

Cobble gutters are used to protect the ditches from wash on 
steep grades and at entrances to intersecting roads where there is 
not sufficient headroom for a culvert. 

Also at the entrances to private property where the grade line 
of the ditch might be badly cut by vehicles. 




Fig. 54. 

The usual cost of such construction ranges from $0.40 to $1.00 
per square yard. 

Where cobblestones are not available, ordinary building brick 
may be used or No. 4 crushed stone as shown on page 225. 





Fb odElev. of Back Watery q^^^ l^aterial 

Coarse Oravel Preferred. 

'*ri7pT777r7T7ff^^''''" ' 

Fig. 55. — Method of protection where road can be built above 

flood level. 

Grates. — Cost of cast-iron grates about $0,065 per pound. 
Cost of wrought-iron grates about $0.08 per pound. 
Repointing Masonry and Refacing Old Walls. — Old masonry 
structures can often be used complete or in part by repointing the 

,' Layer of Dead Water ( Prevents Wash) 
Elevation of Flood Water 




•Stone Fill 

Fig. 56. — Method of protection where road cannot be raised above 

flood level. 

joints; they should be cleaned out thoroughly with a chisel and 
filled flush with a i to i Portland cement mortar. 

The author does not believe in facing up old masonry abut- 
ments if it can be avoided; however, if it seems advisable, because 
of shortage of funds, the old joints should be weil cleaned out and 



STORM SEWERS 



227 



hook dowels used as shown in cut No. 58. One dowel every 6 sq. 
ft. is good practice. 

The concrete facing should be at least 12 in. thick, have a good 
footing course and be reinforced to prevent settlement and tem- 
perature cracks. 

Storm Sewers on Hills. — For the convenience of designers the 
approximate flow capacity of ordinary sized pipes on different 
grades are given below in Table 23. 

C 6„o-'g|&-o-Ji-<:?-0 -Q-&-0-:j| 

P'?" ri^f^oundBars 






j<...27---->i;<> 



Standard 
Orating 





hr"-^'fi 



Upset 
Ends 
ofBars 
and f fat- 
ten to f 



\ 






III 



^'>-Z7V 



Section. 



^ Standard 
Onating- 



Standard Orate. 




Leachin9 5asin. 



Table No. 23. 



Circuhr Opening''' 

Catch Basin. 

Fig. 57. 

-Approximate Flow Capacity in Cubic Feet 
Per Second 

Value oi N = 0.013 



Grade 


Capacity of Flow of Different Sized Pipe 


12" 


15" 


18" 


20" 


24" 


36" 


0.5% 
I.O 

I si 

2.0 

30 
4.0 

6.0 
7.0 
8.0 


2 

3 
4 
4 
5 
6 

7 
8 
8 
9 


4 
3 
2 
8 
8 

I 

I 
8 
5 


4-4 

6.3 

7.6 

8.8 

II. 

13.0 

14.0 

15.0 
16.0 
17.0 


7.5 
10.5 
13.0 

150 
18.0 
22.0 
24.0 
26.0 
27.0 
28.0 


9-5 
14.0 
17.0 
19.0 
24.0 
27.0 
30.0 

330 
350 
38.0 


16.0 
23.0 
27.0 
31.0 

390 
46.0 
Si.o 
56.0 
60.0 
65.0 


42.0 

60.0 

75.0 

86.0 

105.0 

122 .0 

137.0 

1500 
162.0 

1730 



1 Computed from diagram Ogden's Sewer Design. 



228 



MINOR POINTS 



Flow of Water in Ditches. — Multiply area of flow by velocity. 
Velocity can be roughly approximated by the formula 



R 



V 



velocity in feet per second 

constant = 60 for ordinary cases 

, , ,. ,. cross-sectional area of flow in sq. ft. 

hydraulic radms = — ^ -. — : — : — r; — ~ 

wetted perimeter in lin. ft. 

S = slope of stream per foot. 



J Reinforcing Bars-^ 
Spaced IZ"C.toC. 




Pig. 58. — Facing tor old masonry. 



Yling Fence Guards 




Pit with 51 af Oraf/nj. 

Cattle guard driveway. 

Cattle Guards. — In western territory ranch owners will often 
grant road right-of-ways for a nominal sum but stipulate that the 
right-of-way shall not be fenced as it would cut off part of their 
range from water. The boundaries of these ranges are generally 
fenced and where the road passes this fence a gate must be used to 
prevent straying of cattle; it is more or less of a nuisance for every 
user of the road to open and close the gate and generally a gap is 
left in the fence across which a shallow pit 2' to 3' deep is dug and 
this is covered with a slat grating which cattle will not walk but 
which can be driven over by automobiles. 



CHAPTER IX 

MATERIALS 

The selection of materials is an important part of the design. 
Most municipal and State Departments have well equipped labora- 
tories for testing stone, gravels, brick, bitumens, cements, etc. The 
object of these tests is to determine the physical and chemical prop- 
erties that have a particular bearing on the action of the materials 
under construction conditions. While these conditions are not 
attained they are approximated and by a comparison of the labora- 
tory results with the actual performance of the different materials in 
practice a relation can be established that is useful as a basis for 
judgment : 

We are greatly indebted in this edition to Mr. H. S. Mattimore 
and Mr. J. E. Myers who have rearranged and brought up to date 
much of the material on tests and their significance. 

This chapter gives a brief statement of the desirable qualities and 
' the tests for: 

I. Top course, macadam stone. • 
! 2. Screenings, 
i 3. Bottom course, macadam stone. 
j 4. Bottom course and sub-base fillers. 
; "- 5. Brick. 

I 6. Bituminous binders. 
7. Concrete materials. 

I. STONE FOR THE SURFACING OF MACADAM ROADS 

Stone for use in the surfacing of a macadam road should be hard 

and tough to withstand the abrasive action of team traffic and the 
, vibratory action of high-speed motor vehicles and should not 

contain any minerals that are likely to disintegrate rapidly under 

influence of weather conditions. 
I To determine the relative hardness, toughness and power to resist 

abrasive and impact action of traffic, stones are subjected to the 

following tests: 

1. Abrasion. 

2. Hardness. 

3. Toughness. 

4. Specific gravity. 

5. Absorption. 

6. Fracture. 

7. Geological classification. 

229 



230 



MATERIALS 



Abrasion Test.^" — The machine shall consist of one or more hollow 
iron cylinders; closed at one end and furnished with a tightly fitting 
iron cover at the other; the cylinders to be 20 cm. in diameter and 
34 cm. in depth, inside. These cylinders are to be mounted on a 
shaft at an angle of 30 deg. with the axis of rotation of the shaft. 

At least 30 lb. of coarsely broken stone shall be available for a test. 
The rock to be tested shall be broken in pieces as nearly uniform in 
size as possible, and as nearly 50 pieces as possible shall constitute 
a test sample. The total weight of rock in a test shall be within 
10 g. of 5 kg. 

All test pieces shall be washed and thoroughly dried before weigh- 
ing. Ten thousand revolutions, at the rate of between 30 and S3 
per minute, shall constitute a test. Only the percentage of mate- 
rials worn off which will pass through a 0.16 cm. (J^g in.) mesh 
sieve shall be considered in determining the amount of wear. This 
may be expressed either as the percentage of the 5 kg. used in the 
test, or the French coefficient, which is in more general use, may be 

given; that is, coefficient of wear = 20 X — = ■ — , where w is the 

WW 

weight in grams of the detritus under 0.16 cm. (J^g in.) in size per 
kilogram of rock used. 



Conversion 


Table % of 


Wear to French Coefficient 


F. Coef. 


% of Wear 


F. Coef. 


% of Wear 


20 

13.3 
10 


2 

3 

4 


8 
6.7 

5.7 


5 
6 

7 




Deval rattler. 

Hardness. — Hardness is determined by a Dorry machine. A 
stone cylinder 25 cm. in diameter, obtained by a diamond core drill 
from the material to be tested, is weighed and placed in the machine 
so that one end rests on a horizontal cast-iron grinding disk with a 
pressure of 25 grams per sq. cm. Th« disk is revolved 1000 times 
during which standard crushed quartz sand about ij^ mm. in 
diameter is automatically fed to it. The cylinder is then removed 
and weighed and the coefficient of hardness obtained by the formula 
20 — }i the loss in weight, expressed in grams. In order to get 

1 American Society of Testing Materials. 



ROCK TESTS 231 

reliable results two cylinders are generally used, each one being 
reversed end for end during the test. 

Test for Toughness.^ — i. Test pieces may be either cylinders or 
cubes, 25 mm. in diameter and 25 mm. in height, cut perpendicular 
to the cleavage of the rock. Cylinders are recommended as they 
are cheaper and more easily made. 

2. The testing machine shall consist of an anvil of 50 kg. weight, 
placed on a concrete foundation. The hammer shall be of 2 kg. 
weight, and dropped upon an intervening plunger of i kg. weight, 
which rests on the test piece. The lower or bear-surface of 
this plunger shall be of spherical shape having a radius of i cm. 
This plunger shall be made of hardened steel, and pressed firmly 
upon the test piece by suitable springs. The test piece shall be 
adjusted, so that the center of its upper surface is tangent to the 
spherical end of the plunger. 

3. The test shall consist of a i cm. fall of the hammer for the first 
blow, and an increased fall of i cm. for each succeeding blow until 
failure of the test piece occurs. The number of blows necessary to 
destroy the test piece is used to represent the toughness, or the centi- 
meter-grams of energy applied may be used. 

Determination of the Apparent Specific Gravity of Rock.^ — 

The apparent specific gravity of rock shall be determined by the 

following method: First, a sample weighing between 29 and 31 g. 

and approximately cubical in shape shall be dried in a closed oven 

for I hour at a temperature of no degrees C. (230 degrees F, ) and 

then cooled in a desiccator for i hour; second, the sample shall be 

rapidly weighed in air; third, trial weighings in air and in water of 

another sample of approximately the same size shall be made in 

order to determine the approximate loss in weight on immersion; 

fourth, after the balances shall have been set at the calculated 

weight, the first sample shall be weighed as quickly as practicable 

in distilled water having a temperature of 25 degrees C. (77 degrees 

F.); fifth, the apparent specific gravity of the sample shall be 

calculated by the following formula: 

W 

Apparent specific gravity = :^ ^jr- in which W = the weight 

W — W I 

in grams of the sample in air and Wi = the weight in grams of the 

sample in water just after immersion. 

Finally, the apparent specific gravity of the rock shall be the 
average of three determinations, made on three different samples 
according to the method above described. 

Determination of the Absorption of Water per Cubic Foot of Rock.^ 
— The absorption of water per cubic foot of rock shall be determined 
by the following method: First, a sample weighing between 29 and 
31 g. and approximately cubical in shape shall be dried in a closed 
oven for i hour at a temperature of no degrees C. (230 degrees F.) 
and then cooled in a desiccator for i hour; second, the sample shall 
be rapidly weighed in air; third, trial weighings in air and in water 

1 American Society of Testing Materials. 

2 American Society of Testing Materials. 

3 American Society of Testing Materials. 



232 MATERIALS 

of another sample of approximately the same size shall be made 
in order to determine the approximate loss in weight on immer- 
sion; fourth, after the balances shall have been set at the calculated 
weight, the first sample shall be weighed as quickly as possible in 
distilled water having a temperature of 25 degrees C (77 degrees 
F.); fifth, allow the sample to remain 48 hours in distilled water 
maintained as nearly as practicable at 25 degrees C. (77 degrees F.) 
at the termination of which time bring the water to exactly this 
temperature and weigh the sample while immersed in it; sixth, the 
number of pounds of water absorbed per cubic foot of the sample 
shall be calculated by the following formula : 

]^^2 — Wi 
Pounds of water absorbed per cubic foot = ^fz- — — — X 62.24 in 

W — Wi 

which W = the weight in grams of sample in air, Wi = the weight 
in grams of sample in water just after immersion, W2 = the weight 
in grams of sample in water after 48 hours' immersion, and 62.24 = 
the weight in pounds of a cubic foot of distilled water having a tem- 
perature of 25 degrees C. (77 degrees F.). 

Finally, the absorption of water per cubic foot of the rock, in 
pounds, shall be the average of three determinations made on three 
different samples according to the method above described. 

Fracture. — Stone suitable for- road work should crush in cubical 
shapes rather than in thin, flat pieces and preferably with rough, 
jagged fracture that it may interlock firmly under action of the 
roller. 

Geological Classification. — The geological classification is 
determined from an examination with a microscope or powerful 
hand glass, and a consideration of its origin. Great refinements 
are avoided as the general classification is all that is necessary 
to the highway engineer after the physical qualities are ascertained 
by test. 

Cost of Tests. — The cost of collecting and testing stone as given 
in the 1909 Report of the New York State Department of High- 
ways is $8.55' per sample. 

The following tables show tests on the more common rock: 



ROCK PROPERTIES 



233 



Table. 23a. Taken from Bulletin No. 31, United States 
Office of Pl^lic Roads 



Rock varieties 



Per cent 
wear 



Tough- 
ness 



Hard- 



Cementing 
value 



Granite 

Biotite-granite . . . . 
Hornblende-granite 
Augite-syenite . . . . 

Diorite 

Augite-diorite 

Gabbro 

Peridotite 



Rhyolite 

Andesite 

Fresh basalt . . 
Altered basalt . 
Fresh diabase . 
Altered diabase 



Limestone 

Dolomite 

Sandstone 

Feldspathic sandstone 
Calcareous sandstone 
Chert 



Granite-gneiss . . . . 
Hornblende-gneiss 
Biotite-gneiss . . . . 

Mica-schist 

Biotite-schist . . . . 
Chlorite-schist . . . 
Hornblende-schist 
Amphibolite 



Slate 

Quartzite 

Feldspathic quartzite 
Pyroxene quartzite . . 

Eclogite 

Epodosite 



3-5 
4.4 
2.6 
2.6 
2.9 
2.8 
2.8 
4.0 

Z'7 
4.7 
Z'2> 
S'^ 
2.0 

2.5 

5.6 
5.7 
6.9 
2>'2> 
7.4 
10.8 

3.8 
2>'7 
3-2 
4.4 
4.0 
4.2 

2>-7 
2.9 

4.7 
2.9 

3.2 

2.4 
3.6 



15 
10 
21 
10 
21 

19 
16 
12 

20 
II 

17 
30 
24 

10 
10 
26 
17 
IS 
15 

12 
10 

19 
10 



21 
10 

12 
19 
17 
27 

31 
16 



18.1 
16.8 
18.3 
18.4 
18.1 
17.7 
17.9 
15.2 

17.8 

13.7 
17.1 

15.6 
18.2 

17-5 

12.7 
14.8 
17.4 
15-3 

19.4 

17.7 
17.1 

17.5 
17.8 



16.S 
19.0 

II. 5 

18.4 

18.3 
18.6 

17.4 
16.0 



20 
17 
30 
24 
41 
55 
29 
28 

48 
189 
III 
239 

49 
156 

60 
42 
90 
119 
60 
27 

26 
30 
41 
30 
16 
24 

53 
29 

102 

17 
21 

17 

21 

47 



*NoTE. — To convert % of wear to French coefficient, see Table on page 230. 



234 



MATERIALS 



Table 2^b 
From Annual Report N. Y. State Highway Comm. 



1914 



County 



Number 
of com- 
plete 
tests 



Number 

of 
. partial 

tests 
(no core 

piece) 



Weight 
lbs. per 
cu. ft. 



Water 

ab- 
sorbed, 
lbs. per 
cu. ft. 



French 
coeffi- 
cient of 
abrasion 



Hard- 
ness 



Tough- 
ness 



Erie 

Saratoga. . . 
Steuben . . . 

Clinton 

Dutchess 

Essex 

Franklin . . . 

Fulton 

Herkimer . . . 

Monroe 

Montgomery 

Niagara 

Saratoga .... 
St. Lawrence 
Washington . 

Dutchess . . , 
Herkimer . . . 
Montgomery 
Niagara .... 
St. Lawrence 
Washington 
Wayne .... 



Essex... 
Warren. 



Clinton 

Dutchess 

Essex 

Franklin 

Fulton 

Hamilton . . . 
Jefferson .... 

Lewis 

Orange 

Putnam 



St. Lawrence 

W^arren 

Washington. 
Westchester. 

Essex 

Franklin. . . . 
Hamilton . . . 
Jefferson. . , . 

Lewis ... 

Oneida 

St. Lawrence 
Warren 



46 
4 



Calcareous Sandstone 

167 I 0.65 

169 0.31 

162 I 1.44 

Dolomite 



s 




167 


0.65 


95 


12.9 


13-4 


6 




169 


0.31 


lO.I 


15-9 


13-8 


4 


I 


162 


1.44 


9.4 


15. 1 


13.1 



6 




175 


0.41 


11.9 


15.8 


12.7 


4 


I 


174 


0.43 


12.4 


17-3 


11.9 


4 




173 


0.42 


13.5 


16.9 


15.8 


4 




174 


0.51 


9-5 


14.9 


12. 1 


4 




176 


0.15 


II. 8 


16.1 


14.4 


17 




173 


0.67 


8.4 


131 


6.7 


13 




171 


1.07 


10.3 


14.8 


8.2 


8 




Hi 


0.39 


10.6 


14.7 


II-3 


II 




168 


1.50 


6.5 


14.0 


7.0 


8 




174 


0.33 


8.6 


15.5 


9.2 


^l 




174 


0.65 


lo.S 


15.7 


9.9 


6 




175 


0.29 


10.7 


iS-i 


lo.s 



Dolomitic Limestone 



8 


I 


176 


0.46 


9.0 


14.9 


10.9 


4 


I 


170 


0.47 


II-3 


16.7 


8.2 


8 


I 


175 


0.41 


13.0 


IS.8 


12.4 


7 




166 


2.19 


95 


13.I 


7.8 


7 




168 


0.38 


9.2 


16.8 


6.8 


4 




175 


0.36 


13-7 


16.1 


10.8 


4 




173 


059 


10.2 


15.S 


8.7 



Gabbro 
176 I 0.29 

183 1 0.37 

Gneiss 



7.6 

lO.I 



17.3 
17.7 



Granite 



6.9 
9.8 



5 




i8s 


0.27 


10.5 


17.2 


11.3 


8 




172 


0.58 


7.0 


17. 1 


9.1 


29 




176 


0.31 


8.4 


17. 1 


8.1 


8 




178 


0.50 


6.2 


16.1 


7^ii 


12 




169 


0.2s 


II. I 


17.8 


ii.S 


II 




173 


0.37 


8.2 


17.0 


5.8 


26 




171 


0.23 


II. I 


17.3 


12.0 


6 




167 


0.27 


9.6 


17.9 


10.6 


7 




179 


0.38 


7-1 


17. 1 


6.4 


10 




172 


0.32 


8.5 


16.6 


7-5 


7 




180 


0.20 


lO.O 


17.0 


8.5 


52 




172 


0.27 


9.7 


17.5 


10.2 


30 


2 


173 


0.30 


7-5 


17.3 


6.5 


4 




170 


0.29 


8.5 


17. 1 


10.9 


37 


2 


171 


0-39 


8.3 


16.9 


7.8 



S 


... 


171 


0.38 


7.5 


18.0 


5.1 


6 




165 


0.31 


8.7 


17.9 


9.4 


5 




165 


0.36 


9.9 


18.1 


9.0 


23 


I 


166 


0.23 


12. 1 


18.4 


lO.I 


8 




166 


0.36 


10.9 


18.4 


9.2 


6 




166 


0.13 


10.2 


18.9 


8.2 


30 


. . . 


165 


0.2s 


9.9 


18.3 


8.1 


s 


... 


165 


0.45 


7-9 


17.9 


7.7 



ROCK PROPERTIES 



235 



From Annual Report N. Y. State Highway Comm. 191 4 



County 



Number 

of com 

plete 

tests 



Number 

of 

partial 

tests 

(no core 
piece) 



Weight, 
lbs. per 
cu. ft. 



Water 

ab- 
sorbed, 
lbs. per 
cu. ft. 



French 
coeffi- 
cient of 
abrasion 



Hard- 
ness 



Tough- 
ness 



Weighted 
value 



Albany 

Cayuga 

Clinton . . . . . 
Columbia . . . 

Erie 

Fulton 

Genesee. . . . 

Greene 

Herkimer. . . 
Jefiferson. . . . 

Lewis 

Madison. . , . 

Monroe 

Montgomery 

Niagara 

Oneida 

Onondaga . . . 

Ontario 

Otsego 

Rensselaer. . 
Saratoga .... 
Schoharie . . . 

Seneca 

Ulster 

Warren 

Washington , 



Dutchess... 



Allegany. . 
Broome. . . 
Cayuga. . . 
Chenango. 
Clinton. . . 
Delaware . . 
Erie .... 
Franklin. . . 
Greene . . . 
Herkimer . 
Jefferson. . . 
Livingston . 
Madison . 
Niagara . . 
Orleans. . 
Otsego.. . 
Saratoga . 



14 
53 
8 
S 
6 
4 
8 
4 
5 
7 



Limestone 



13 


7 


168 


0.60 


7-9 


14.3 


6.4 


34 


6 


170 


0.49 


8.8 


14.9 


7.8 


14 


2 


170 


0.28 


8.2 


14.1 


5-3 


12 




170 


0.28 


9.1 


15-3 


9.2 


9 


3 


167 


0.57 


8.1 


16.6 


8.3 


6 


I 


168 


0.21 


7-7 


15-5 


6.5 


6 


3 


169 


0.26 


8.0 


I5-0 


8.2 


II 




160 


0.36 


II. I 


16.4 


8.9 


17 


9 


169 


0.26 


8.7 


14.8 


8.2 


105 


44 


169 


0.28 


7.6 


15.1 


6.4 


26 


20 


169 


0.32 


6.9 


14.1 


6.2 


16 


I 


169 


0.23 


8.4 


14.7 


7-7 


4 




168 


0.27 


8.1 


14.1 


7-4 


12 


2 


169 


0.24 


8.5 


15-3 


8.0 


II 


I 


168 


0.84 


7-1 


12.8 


6.5 


31 


19 


169 


0.29 


7.8 


13.8 


6.6 


25 


I 


170 


0.38 


8.9 


15-7 


8.4 


II 




169 


0.39 


10.2 


15-9 


10.2 


7 


2 


169 


0.32 


8.1 


14.1 


6.3 


4 


I 


171 


0.21 


7-5 


I5-0 


5-3 


5 




170 


0.24 


8.7 


13-7 


7.0 


29 


2 


169 


0.34 


8.1 


14.9 


6.7 


7 


3 


169 


0.21 


?-^ 


15-3 


7.9 


12 


3 


170 


0.25 


8.1 


is.o 


7.4 


5 




170 


0.24 


8.9 


1S.7 


7-4 


S 


3 


169 


0.34 


7.9 


15.5 


6.9 



Marble 
178 I ^.30 



7.3 I 14.2 



Sandstone 



156 
i6s 
167 
164 
163 
167 
159 
157 
169 
160 
156 
160 
163 
158 
155 
162 
163 



2.10 
1.29 
1.16 
1.58 
0.71 
1.4s 
2.10 
1.06 
0.62 
2.50 
1.46 

3-02 

2.15 
1.78 
2.18 
1.75 
0.36 



8.4 
7.8 

7.8 
8.7 

II. 7 
7.0 
6.3 
9.7 
8.6 

10.9 
8.3 
8.8 
9.9 
9.0 

11.8 
8.4 

IO-7 



13.4 
12.9 

12. 1 

11. 2 
18.5 
12.7 

5-1 
17.9 
14-5 
16.4 
16.2 

9.6 
13.9 
16.4 
14.4 
11.9 
18.0 



6.0 









Quartzite 








Columbia . . . 

Dutchess 

Rensselaer. . 
Washington . 


16 
8 

10 
12 


2 


168 
166 
166 
167 


0.28 
0.36 
0.49 

0.40 


I6.S 

13-5 
12. 1 
14.6 


18.3 
18.8 
18.7 
18.9 


17. 1 
II. 8 
14.8 
16.3 



9.1 

10.5 
10.5 

10.4 

II.O 

8.5 
7.8 

7.1 

8.1 
10.7 
6.3 
8.8 
8.6 
8.2 
8.1 
9.6 
8.7 



236 



MATERIALS 



From Annual Report N. Y. State Highway Comm. 19 14. — Cont, 



County 



Number 
of com- 
plete 
tests 



Number 

of 

partial 

tests 

(no core 
piece) 



Weight, 

lbs. per 

cu. ft. 



Water 

ab- 
sorbed, 
lbs. per 

cu. ft. 



French 
coeffi- 
cient of 
abrasion 



Hard- 
ness 



Tough- 
ness 



Weighted 
value 



Schoharie . . 
Schuyler. . . 

Seneca 

Steuben 

St. Lawrence 
Sullivan . . . 

Ulster 

Wyoming . . 

Albany ..... 
Columbia . . . 
Dutchess .... 

Greene 

Montgomery 
Rensselaer . , 
Saratoga.. . . 
Schenectady 
Ulster 

Essex 

Franklin .... 
Herkimer. . . 
Jefferson. . . . 

Rockland . . . 





Sandstone 


. — Continued 






6 


3 


i6s 


1. 21 


9.4 


15.2 


II. 7 


4 




162 


2.14 


8.1 


II.6 


10.6 


5 




165 


0.86 


IT.O 


13.9 


IS.8 


22 


3 


157 


2.79 


8.3 


9.3 


lO.O 


16 




I5Q 


0.79 


lO.O 


17.8 


7.2 


30 


4 


164 


1.26 


6.5 


14.9 


8.2 


8 




166 


0.64 


8.0 


14-3 


8.1 


7 




159 


2.54 


6.0 


5.1 


7.9 



Sandy Grit 



5 




167 


0.75 


7-5 


13.2 


7.2 


12 




168 


0.32 


10.7 


15.9 


11.7 


10 


2 


168 


0.57 


8.1 


16.2 


II-5 


13 




169 


0.48 


7.1 


1S.6 


9.5 


4 




166 


1-39 


lO.I 


II. 3 


11.8 


10 




169 


0.44 


9.1 


15-9 


9.4 


5 




168 


0.99 


11.8 


15.2 


11.9 


4 




165 


1. 10 


9.2 


14.6 


95 


7 




169 


0.59 


7-5 


13.8 


10.2 



183 



Syenite 
0.5: 
0.4: 

O.K 

0.3^ 
Trap 
I 0-39 



7 




184 


0.52 


7.7 


17.1 


6.7 


4 




171 


0.45 


lO.I 


18.3 


8.0 


13 




174 


0.16 


12.5 


18.0 


11.6 


7 




176 


0.34 


12.4 


18.1 


14.5 



70 

S8 
77 
54 
73 
58 
61 
36 

56 
76 
68 
62 
65 
69 
78 
66 
60 

64 
75 
85 



13.2 I 17.6 I 1.64 I 



Table 2^bb 




Geological Classification 


Class 


Type 


Family 


I Igneous 




I Intrusive 
Cplutonic) 


f a Granite 
b Syenite 

i c Diorite 
d Gabbro 

I e Peridotite 






2 Extrusive 
(volcanic) 

I 


[ a Rhyolite 
1 b Trachyte 
' c Andesite 
[ d Basalt and diabase 






I Calcareous 


f a Limestone 
\ b Dolomite 


II Sedimentary 






f a Shale 






2 Siliceous 


\ b Sandstone 
[ c Chert (flint) 






I Foliated 


f a Gneiss 
\ b Schist 
[ c Amphibolite 


III Metamorphic 


\ 


[ a Slate 


■ 




2 Nonfoliated 


1 b Quartzite 
1 c Eclogite 
[ d Marble 



1 Bulletin No. 31, United States Department of Public Roads. 



IGNEOUS ROCKS 237 

The following quotation from bulletin No. 31 O. P. R. & R. E. 
describes the characteristics of the three groups: 

Igneous Rocks. — "All rocks of the igneous class are presumed to 
have solidified from a molten state, either upon reaching the earth's 
surface or at varying depths beneath it. The physical conditions, 
such as heat and pressure, under which the molten rock magma 
consolidated, as well as its chemical composition and the presence 
of included vapors, are the chief features influencing the structure. 
Thus, we find the deep-seated, plutonic rocks coarsely crystalline 
with mineral constituents well defined, as in case of granite rocks, 
indicating a single, prolonged period of development, whereas the 
members of the extrusive or volcanic tj^es, solidifying more rap- 
idly at the surface, are either fine-grained or frequently glassy 
and vesicular, or show a porphyritic structure. This structure is 
produced by the development of large crystals in a more or less 
dense and fine-grained ground mass, and is caused generally by a 
recurrence of mineral growth during the effusive period of magmatic 
consolidation. 

"In the arrangement of the rock families from a mineralogical 
standpoint it will be noted that the plutonic rock types, granite, 
syenite, and diorite, are represented by their equivalent extrusive 
varieties, rhyolite and andesite, and that diabase has been included, 
I somewhat arbitrarily, with basalt, as a volcanic representative of 
I gabbro. These latter rocks are of special interest, owing to their 
; wide distribution and general use in road construction. They occur 
; in the forms of dykes, intruded sheets, or volcanic flows, and vary 
[ in structure from glassy-porphyritic (typical basalt) to wholly crys- 
! talline and even granular (diabase). Their desirable qualities for 
I road-building are caused to a large extent by a peculiar interlocking 
of the mineral components (t)phitic structure) , yielding a very tough 
I and resistant material well qualified to sustain the wear of traffic. 
\ "Igneous rocks vary in color from the light gray, pink, and brown 
I of the acid granites, syenites, and their volcanic equivalents (rhyo- 
lite, andesite, etc.) to the dark steel-gray or black of the basic gab- 
bro, peridotite, diabase, and basalt. The darker varieties are 
I commonly called trap. This term is in very general use and is 
' derived from trappa, Swedish for stair, because rocks of this kind 
j on cooling frequently break into large tabular masses, as may be 
seen in the exposures of diabase on the west shore of the Hudson 
! River from Jersey City to Haverstraw. 

I Sedimentary Rocks. — "The sedimentary rocks as a class repre- 
1 sent the consolidated products of former rock disintegration, as in 
' the case of sandstone, conglomerate, shale, etc., or they have been 
, formed from an accumulation of organic remains chiefly of a cal- 
I careous nature, as is true of limestone and dolomite. These frag- 
\ mental or clastic materials have been transported by water and 
j deposited mechanically in layers on the sea or lake bottoms, pro- 
I ducing a very characteristic bedded or stratified structure in many 
! of the resulting rocks. 

j "In the case of certain oolitic and travertine limestones, hydrated 
i iron oxides, siliceous deposits, such as geyserite, opal, flint, chert, 



238 MATERIALS 

etc., the materials have been formed chiefly by chemical precipita- 
tion and show generally a concentric or colloidal structure.^ Oolitic 
and pisolitic limestones consist of rounded pealike grains of calcic car- 
bonate held together by a calcareous cement. Travertine is the 
so-called 'onyx marble' of Mexico and Arizona. It is a compact 
rock, concentric in structure and formed by the precipitation of car- 
bonate of lime from the waters of springs and streams. 

"Loose or unconsolidated rock debris of a prevailing siliceous 
nature comprise the sands, gravels, finer silts, and clays (laterite, 
adobe, loess, etc.). Shell sands and marls, on the other hand, are 
mainly calcareous, and are formed by an accumulation of the marine 
shells and of lime-secreting animals. Closely associated with the 
latter deposits in point of origin are the beds of diatomaceous or 
infusorial earth composed almost entirely of the siliceous casts of 
diatoms, a low order of seaweed or algae. 

*'This unconsolidated material may pass by imperceptible grada- 
tions into representative rock types through simple processes of in- 
duration. Thus clay becomes shale, and that in turn slate, without 
necessarily changing the chemical or mineralogical composition of 
the original substance. 

"Such terms as flagstone, freestone, brownstone, bluestone, gray- 
stone, etc., are generally given to sandstones of various colors and 
composition, while puddingstone, conglomerate, breccia, etc., apply 
to consolidated gravels and coarse feldspathic sands. 

"The calcareous rocks are of many colors, according to the 
amount and character of the impurities present. 

Metamorphic Rocks. — "Rocks of this class are such as have been 
produced by prolonged action of physical and chemical forces 
(heat, pressure, moisture, etc.) on both sedimentary and igneous 
rocks ahke. The foliated types (gneiss, schist, etc.) represent an 
advanced stage of metamorphism on a large scale (regional meta- 
morphism), and the peculiar schistose or foliated structure is due 
to the more or less parallel arrangement of their mineral components. 
The non-foliated types (quartzite, marble, slate, etc.) have resulted 
from the alteration of sedimentary rocks without materially affect- 
ing the structure and chemical composition of the original material. 

"Rocks formed by contact metamorphism aftd hydration, such as 
hornfels, pyroxene marble, serpentine, serpentineous limestone, etc., 
are of great interest from a petrographical standpoint, but are rarely 
of importance as road materials. 

"The color of metamorphic rocks varies between gray and white 
of the purer marbles and quartzites to dark gray and green of the 
gneisses, schists, and amphibolites. The green varieties are com- 
monly known as greenstones, or greenstone schists." 

Interpretation of Tests. — It has been found impractical to specify 
definite qualities of stone for use in macadam highways. Economy 
and practical engineering demand that all available sources be con- 
sidered. Tests are made to determine the relative qualities of 
stone from these different sources and the results used as a guide 
for selection. 

1 G. P. Merrill's "Rocks, Rock Weathering, and Soils," 1897, PP- 104-114. 



ROAD VAI.UE OF ROCKS 239 

In the work of the New York State Highway Commission all tests 
are tabulated geographically, using a county as a unit. Table No. 
23& is compiled from the records of this department. It will be 
noted that comparisons are made in different classifications only, 
as it is considered that conclusions should not be drawn from 
a comparison of tests procured from materials having different 
origins and composed of different minerals. 

For the purpose of ready comparison, there has been introduced 
a figure known as the ''weighted value." (See last column Table 
236.) This is computed by giving relative weights of three to 
the French coefficient, two to the hardness, one to the toughness 
values and adding the three together. These relative weights were 
determined from a consideration of the amount of material used in 
the different tests and the personal equation in running them. 

By consulting these tables the available rocks of different classi- 
fications in various sections throughout New York State can be 
determined readily, and as new tests are completed they are com- 
pared with good average material from that section. 

Conclusions. — Trap (diabase), granite, gneiss, quartzite, sand- 
stone and limestone are the most common rocks and w^hen found 
in a good state of preservation make good surfacing materials. 

As generally found, trap is uniform in hardness and toughness, 
making an excellent material for use in top course. 

Granite and gneiss, where they occur with hornblende replacing 
a large percentage of the quartz, make an excellent surfacing stone. 

Quartzites when found in good State of preservation are hard and 
i tough. They should not be confused with crystalline quartz which 
I is hard but brittle. 

Sandstones are extremely variable and only the better varieties 
should be used. 

Limestones range from the fine grained dense products whick are 
hard and tough to the coarse grained soft products which are not 
suitable for surfacing. 

Screenings. — Screenings act as a filler and binder for waterbound 
macadam and as a partial filler for bituminous macadam. For use 
in waterbound construction the main mineral constituent is the most 
essential feature to be considered as this must be a material that 
will from a binder and "puddle" readily when subjected to the 
action of a road roller and water. 
I Limestone screenings have proved the most efficient as a binder in 

I j waterbound construction, although trap and some other igneous 

I I rocks can be bound with their own dust by repeated puddling. 
Screenings consisting mainly of quartz have never been used suc- 
cessfully in waterbound construction except by the addition of some 

': i limestone screenings. The use of a percentage of clay or loam as a 
*i binder is not advisable except where the cost of limestone screenings 
(would be prohibitive. 

I Laboratory methods for testing the cementing power of rock 
'powders are available but the results obtained are erratic and unde- 
pendable. 

In plain waterbound roads it is often necessary to mix some lime- 



240 MATERIALS 

stone screenings, fine sandy loam, or even a small percentage of 
clay loam with trap, granite, sandstone, quartzite, or gneiss screen- 
ings to get a good bond and prevent raveling in dry weather. 

3. BOTTOM COURSE MACADAM STONE 

As the bottom stone simply spreads the wheel loads transmitted 
through the top course and is not directly subjected to the traffic 
action, almost any stone that breaks into cubical irregular shapes 
that will not air or water slake and that is hard enough to stand the 
action of the roller during construction will be satisfactory. 

Any of the materials listed above in Table 24 except shale and 
slate can be used, provided that they are not rotten from long ex- 
posure in the air. The different available varieties are usually tested 
in the same manner as for top stone in order to pick the best. Acid 
blast furnace crushed slag makes an excellent bottom course but 
s not uniform enough for top course, 

4. FILLERS 

Fillers are used in the bottom course to fill the voids between the 
crushed stone and to prevent rocking or sidewise movement of the 
larger pieces. 

They should be easy to manipulate in placing, should not soften 
when wet, or draw water up from the subgrade by capillary action. 

The materials most used are 

Coarse sandy loam 

Coarse sand 

Gravel with large excess of fine material 

Stone screenings 

The fitness of the material can be determined by inspection and 
by wetting a handful; if it gets sticky or works into a soft mud it 
should not be used. 

5. VITRIFIED BRICK 

Bricks must withstand the same destructivelagenciesjas described 
for top stone. They must be uniform in size, tough, hard, dense, 
evenly burned, and, on account of their peculiar shape, must have a 
high resistance against rupture. These properties are tested by the 
standard methods adopted by the American Brick Manufacturers' 
Association, as described in the New York State specifications on 
page 730- 

It should be understood that bricks suitable for paving are manu- 
factured in a different way and of different materials than ordinary 
building bricks. 

"The materials for molding any paving brick must be of a 
peculiar character which will not melt and flow when exposed to an 
intense heat for a number of days but will gradually fuse and form 
vitreous combinations throughout while still retaining its form. 

*^The resulting brick must be a uniform block of dense texture in 



BITUMENS 241 

which the original stratification and granulation of the clay has 
been wholly lost by fusion which has stopped just short of melting 
the clay and forming glass. 

"The clay while fusing must shrink equally throughout, thus 
causing the brick to be without laminations or of any exterior 
vitrified crust differing from the interior."^ 

The great majority of paving brick are made in Ohio, Illinois, 
Indiana, Pennsylvania, West Virginia, and New York. They are 
classed as shale or fire-clay brick. 

6. BITUMINOUS BINDERS 

The subject of bitumens is an intricate one and the reader is re- 
ferred to the works of Clifford Richardson, Prevost Hubbard, and 
others, for detailed information, as a book of this character can give 
only an outline. 

There are a number of dust preventives and road binders on the 
market which depend for their effectiveness on a bituminous binding 
base. The term bitumen is applied to a great many substances. 
Hubbard arbitrarily defines bitumens as "consisting of a mixture of 
native or pyrogenetic hydrocarbons and their derivatives, which 
, may be gaseous, liquid, a viscous liquid, or solid, but if solid melting 
^ more or less readily upon the application of heat, and soluble in 
I chloroform, carbon bisulphide, and similar solvents."^ 
( The bitumens may be classified as native and artificial. The 
( native bituminous materials, that are used in road work, are the 
asphaltic and semi-asphaltic oils (dust layers). Malthas (the binding 
base of Rock Asphalts), Trinidad, Bermudez California, and Cuba 
asphalts, Gilsonite, and Grahamite (which, however, are too brittle 
in their natural state and require fluxing with a suitable residual oil 
I before they can be used as binders). The natural asphalts are 
refined to remove water and any objectionable amount of impurities 
by heating until the gases are driven off, skimming the vegetable 
matter which rises to the surface, and removing the mineral constitu- 
ents which fall to the bottom. 

The artificial bituminous materials are derived by the destructive 
distillation of coal, or by fractional distillation of crude coal tars, 
or the native petroleum oils. They comprise the crude coal and 
water gas tars, the refined tars, the residual oils and semi-solid 
binders derived from the petroleum oils. They vary greatly in 
consistency and binding power. 

The following material is briefed from Bulletin No. 34, United 
States Office of Public Roads : The light oils and tars have a rela- 
tive small percentage of bituminous base and are effective only so 
long as it retains its binding power; the more permanent binders 
contain a larger percentage of bitumen; these are the heavy oils and 
\ semi-solids. 

Artificial Bitumens 

Crude Tars. — Coke ovens and gas plants produce most of the 
coal tars in use. These tars contain various complex combinations 

1 Judson's "Roads and Pavements," page 87. 

2 " Dust Preventives and Road Binders." John Wiley & Sons. 



242 



MATERIALS 



of carbon, hydrogen, and oxygen and small amounts of nitrogen and 
sulphur. They vary in composition according to the material from 
which they are made and the temperature at which they are distilled. 
The percentage of free carbon ranges from 5 per cent, to 35 per cent., 
and the bitumen from 60 per cent, to 95 per cent., depending on the 
temperature of manufacture. Tars produced at high temperatures 
contain free carbon in excess which weakens their binding power; 
they, also, contain a large amount of anthracine and naphthalene, 
two useless materials from the standpoint of road work. Tars 
produced at low temperatures are to be preferred. Coke tar is low 
temperature tar; gas tar is high temperature tar. 

Refined' Tars. — Much of the road tar is refined tar — that is, it 
has been subjected to fractional distillation to remove the valuable 
volatile compounds. The residuum from this process is a thick 
viscous material known as coal-tar pitch, and if the crude tar from 
which it is obtained was produced at a low temperature it is nearly 
pure bitumen; the dead oils obtained from the distillation are of 
little value and are often run back into the pitch, which makes it 
liquid when cold. The following table gives the approximate com- 
position of water-gas tar, crude coal tar, and refined tar. 



Table 23c. Specific Gravity and Composition of Tar 

Products 
Table from Bulletin No. 34 United States Ofiice of Public Roads 



Kind of Tar 



Water-gas tar . . 
Crude coal tar . 
Refined coal tar 



Specific 
Gravity 



1. 04 1 
1. 210 
1. 177 



Ammo- 
niacal 
Water 



% 
2.4 
2.0 
0.0 



Total 
Light Oils 
to 170° C. 



% 

a2i.6 
^17.2 
612.8 



Total 
Dead Oils 
170° 270° C. 



% 
652.0 
626.0 
^47.6 



Residue 

(by 

Difference) 



% 

C24.O 
/54.8 



a Distillate mostly liquid. 

b Distillate all liquid. 

c Pitch very brittle. 

d Distillate mostly solid. 



e Distillate one-half solid. 
/ Pitch hard and brittle.^ 
g Distillate one-third solid. 



Table 23 J gives a more up-to-date analysis of the coal tars on the 
market. 

The tests and detailed requirements for light, medium, and heavy 
bitumens are given in specifications, page 721. ; 

If the tar is used as a temporary dust-layer only, it should be a , 
low-temperature, dehydrated tar, liquid when cold. If used as a 
more permanent binder and applied hot, it should have a larger 
percentage of pitch, should contain no water, and be free from an 
excessive amount of free carbon. If used as a mastic in butuminous 
macadam, it should contain a high percentage of pitch and be free 
from the defects mentioned. 



BITUMENS 



243 



Natural Bitumens and Artificial Residual Oils and Semi-solids. — 

Mineral oils can be classed as paraffin petroleums, mixed paraffin 
and asphaltic petroleums, and asphaltic petroleums. The relative 
value of oils as a source of supply for road materials depends on 
their percentage of asphaltic residue. The eastern oils found in 
New York, Pennsylvania, West Virginia, etc., are paraffin petro- 
leums; the western oils vary from light to heavy asphaltic petro- 
leums, and the southern oils have a mixed paraffin and asphaltic 
base. 

The crude petroleum is refined by fractional distillation to obtain 
its valuable products, such as kerosene, etc. The character of the 
residue depends, as for the tars, on the crude material and the method 
of manufacture; the operation known as ''cracking," which is used 
to increase the yield of the inflammable oils, produces an excess of 
free carbon. 

The paraffin petroleum residuums are soft and greasy and are not 
suitable for road work; they contain a large amount of the paraffin 
hydrocarbons and paraffin scale (crude paraffin). 

The California petroleum residuums resemble asphalt, and if care- 
fully distilled without cracking should contain little or no free carbon. 
They are suited to road work. 

The Texas, or semi-asphaltic petroleums contain some paraffin 
hydrocarbons and about i per cent, of paraffin scale. Residuums 
from these oils, if containing a relatively small amount of paraffin, 
can be successfully used. 

The tests and required properties of residuum bituminous binders 
used on the New York State roads in 1914 are given in specifications, 
page 721. 

The following tables give a general idea of the relative character- 
istics of the crude petroleums and petroleum residuums. 



Results of Tests of Crude Petroleum 
Tables from Bulletin No. 34 United States Office of Public Roads 



Kinds of Oil 


II 


h 

-So 


Volatility at 
110° C. 
7 Hours 


Volatility at 
160" C. 
7 Hours 


Volatility at 
205° C. 
7 Hours 




Pennsylvania, paraffin 

Texas, semi-asphaltic 

California, asphaltic 


0.801 
.904 
.939 


(a) 
43 
26 


% 
47.3 
20.0 


% 
58.0 
27.0 


% 

68.0 

49.0 

J42.7 


&32.O 
C51.O 
CS7.3 







a Ordinary temperature 
b Soft 



c Quick flow e Soft maltha; sticky 

d Volatility at 200*, 7 hours. 



{Continued on page 248) 



244 



MATERIAI.S 



Table 23(f. Circular No. 97, U. S. OrricE of Public Roads 

Analysis of crude coke-oven tars produced in the United States and Canada- 



Serial 
No. 



S126 
S123 

S124 

S137 

5x21 

512s 

S128 
5200 

5189 

5 160 

5074 

5081 

5095 
5083 

S159 

S107 
S086 
S078 

S087 

S109 

S122 
5188 
5404 

5 108 



S089 



GeDeral Information 



Company and location 



Solvay Process Co., Syracuse, N.Y.. 
Semet-Solvay Co., Pennsylvania Steel 

Co., Steelton, Pa 

Semet-Solvay Co. National Tube Co., 

Benwood, W.Va 

Semet-Solvay Co., Milwaukee Coke & 

Gas Co., Milwaukee, Wis 

Semet-Solvay Co. Pennsylvania Steel 

Co., Lebanon, Pa 

By-Products Coke Corporation, South 

Chicago, 111 

Semet-Solvay Co., Detroit, Mich 

Semet-Solvay Co., Empire Coke Co, 

Geneva, N.Y 

Semet-Solvay Co., Dunbar Furnace Co., 

Dunbar, Pa 

Semet-Solvay Co., Central Iron & Coal 

Co., Tuscaloosa, Ala 

I Philadelphia Suburban Gas & Electric 
[ Co., Chester, Pa 



Semet-Solvay Co., Ensley, Ala , 

The N. E. Gas & Coke Co., Everett,Mass 
I Lackawanna Steel Co., Lackawanna Iron 
( & Steel Co., Lebanon, Pa 

Dominion Tar & Chemical Co., Sydney, 
Nova Scotia 



Hamilton Otto Coke Co., Hamilton, Ohio 
Carnegie Steel Co., South Sharon, Pa.. . 
Maryland Steel Co., Sparrows Point, Md. 
Citizens' Gas Co., Indianapolis, Ind 



\ Pittsburg Gas & Coke Co., The United 
[ Coke & Gas Co., Glassport, Pa 



Zenith Furnace Co., Duluth, Minn. 
Illinois Steel Co., Joliet, HI 



I Illinois Steel Co., Indiana Steel Co., 
^ Gary, Ind 



Camden Coke Co., Camden, N.J. 



Type of 
Oven 



Semet-Solvay 



Otto Hoffman 

}••••■' 



United Otto 



Maximum 

temperature 

of firing 

retorts 



}.,..".... 



.Koppers , 



Cambria Steel Co., Johnstown, Pa.. 



Lackawanna Steel Co., Buffalo, N.Y. 



Otto Hoff. 
man 

United 
Otto 

Otto Hoff- 
man 

United 
Otto 

United 
Otto 

Rotbb erg 



1650-1450° C. 

1050-1450° C. 

1050-1450° C. 

1050-1450° C. 

1050-1450° C. 

1050-1450° C. 
1050-1450° C. 

1050-1450° C. 

1050-1450° C. 

1250° C. 
1050° c. 

1250° c. 

iiioo°C. 
( 1000° C. 
I (1800° F.) 

(2) 
(iiii°C. 
I (2000° F.) 
( 1666° C. 
i(30oo°F.) 

1 1333° c. 

( (2400 F.) 

(I222°C. 

( (2200 F.) 

{ (. 

( I222-I277°C. 
( 2200-2300°F. 

I 1444** C. 
((2600° F.) 

1100° c. 

( 1000° c. 
( (1800° F.) 

I 1222° C. 

( (2200° F.) 
(iiii°C. 

1(2000°F.) 

(iiii°C. 
\ (2000° F.) 
( 1000° C. 
((i8oo°F.) 
( 1000° C. 
l(i8oo°F.) 



BITUMENS 

Table 2^(1. Continued 



245 



Answers to Questions 


Examination 














Per 


Maximum 
temperature 


Specific gravity 


Per cent of 

free carbon 

in tar 


Specific 
gravity 


Per 

cent 


Per 
cent 


cent 
soluble 
in CS2, 
includ- 
ing 


to which coal 


of crude tar 


of tar, 


of free 


of 


is brought 




25° c. 


carbon 


ash 














H2O 


950-1150° C. 


I. 12-1. 21 


3-12 


1.195 


7.76 


0.12 


92.12 


950-1150° C. 


I. 12-1. 21 


3-12 


1.206 


8.77 


.07 


91.16 


950-1150° C. 


I. 12-1. 21 


3-12 


1. 176 


7.14 


.04 


92.82 


950-1150° C. 


I. 12-1. 21 


3-12 


1. 168 


6.10 


.OS 


93.8s 


950-1150° C. 


I. 12-1. 21 


3-12 


1. 173 


4.71 


.06 


95.23 


950-1150° C. 


I. 12-1. 21 


3-12 


1. 191 


7-49 


■03 


92.48 


950-1150° C. 


I. 12-1. 21 


3-12 


1. 169 


6.56 


.11 


93.33 


950-1150° C. 


I. 12-1. 21 


3-12 


1.159 


6.07 


.08 


93.8s 


950-1150° C. 


I. 12-1. 21 


3-12 


1.181 


8.85 


.02 


91.13 


1150° C. 


I. 17 
( 1. 16 

1 (20° C.) 


S.72 


1.159 


5.05 


.02 


94.93 


1000° c. 


— 


1. 141 


3.96 


.05 


95.99 


1150° c. 


{ 1.17 

( (iS°C.) 


8 


1.175 


6.90 


.06 


93.04 


ll200°C. 


1. 17 


8-10 


1. 160 


13.94 


.00 


86.06 


1000° C. ) 
(1800° F.) } 


1. 10 


16-24 


1. 214 


14.05 


•13 


85.82 


(2) 


1. 170 


10-15 


1. 143 


10.81 


.05 


89.14 


1111° C. 
(2000° F.) 


1 1. 14 


616.0 


1. 160 


8.37 


.06 


91-57 


1444° c. 
(2600° F.) 


1 - 


7. 09-10.64 


1. 191 


7.89 


.03 


92.08 


1222° C. 
(2200° F.) 


} ' I.I9 


3 8-10 


1. 179 


8.49 


.03 


91.48 


1222° C. 
(2200° F.) 


1 I. I4-I. IS 
f (50° F.) 


4-5 

1 


1. 133 


S.21 


.07 


94.72 


(2) 


-j 1.207 
I 10° c. 


16.59 


1. 176 


10.53 


.04 


89.43 


(2) 


(2) 


(2) 


1. 195 


12.18 


•OS 


87.77 


1388° C 
(2500° F.) 


1 I. 16-I. 20 


12-15 


1. 171 


3.89 


.06 


96.0s 


{ 880-950° 


*i.i74 
1. 169 


1 4.35 


1. 169 


2.73 


.04 


97.23 


Sas'^C. 














{1500° F.) 
1055° c. 


I. 20-1. 30 
M1.221) 


7-9 


1 1.182 


11.30 


.06 


88.64 


(i900°F.) 














iiiii°C. 














(2000° F.) 














iiiii°C. 


1. 12 


^IS 


1. 211 


12.40 


.16 


87.44 


(2000° F.) 














1000° c. 














(1800° F.) 
1000° c. 


1.16 


16-24 


1. 210 


16.80 


.00 


83.20 


{1800° F.) 


J 













'246 



MATERIALS 



Table 22,d. Continued 



Serial 
No. 



5126 
5123 

S124 

5137 

5I2I 

512s 

5128 
5200 

5189 

SI60 
S074 

S081 
5095 

5083 

5159 

5107 
5086 
5078 
S087 
5109 

5122 

5188 
5404 

5108 
SI27 
5089 



Company and Location 



Solvay Process Co., Syracuse, N.Y. . 
Semet-Solvay Co., Pennsylvania Steel 

Co., Steelton, Pa 

Semet-Solvay Co., National Tube Co., 

Benwood, W.Va 

Semet-Solvay Co., Milwaukee Coke &: 

Gas Co., Milwaukee, Wis 

Semet-Solvay Co., Pennsylvania Steel 

Co., Lebanon, Pa 

By- Products Coke Corporation, South 

Chicago, 111 ., 

Semet-Solvay Co., Detroit, Mich. . .. 
Semet-Solvay Co., Empire Coke Co., 

Geneva, N.Y 

Semet-Solvay Co., Dunbar Furnace Co., 

Dunbar, Pa 

Semet-Solvay Co., Central Iron & Coal 

Co., Tuscaloosa, Ala 

.Philadelphia Suburban Gas & Electric 

Co., Chester, Pa 

Semet-Solvay Co., Ensley, Ala „ . . . 

The New England Gas & Coke Co. 

Everett, Mass 

Lackawanna Steel Co., Lackawanna 

Iron & Steel Co., Lebanon, Pa 

Dominion Tar & Chemical Co., Sydney, 

Nova Scotia 

Hamilton Otto Coke Co., Hamilton, O.. . 
Carnegie Steel Co., South Sharon, Pa.. . . 
Maryland Steel Co., Sparrows Point, Md. 

Citizens' Gas Co., Indianapolis, Ind 

Pittsburg Gas & Coke Co., The United 

Coke & Gas Co., Glassport, Pa 

Zenith Furnace Co., Duluth, Minn 

Illinois Steel Co., Joliet, III 

Illinois Steel Co., Indiana Steel Co., 

Gary, Ind 

Camden Coke Co., Camden, N.J 

Cambria Steel Co,, Johnstown, Pa. . . 
Lackawanna Steel Co., Buffalo, N.Y. . 



Examination, Public Roads 



Distillation results 



Water 






I.O 
I.O 

l.I 

1.8 
.6 

(n 
6.9 

4.0 

2.0 

3.2 

2.3 
3.3 

2.2 
5.4 

3-2 

3-4 

I.O 

1.6 

1.2 
I.I 
3.6 
1.9 
3.5 
2.2 

lO.I 

2.7 






I.O 

1.5 

•5 

5.9 

3.4 

1-7 

2.8 

2.0 
2.8 



2.8 
3-0 

I.O 



I.I 

I.O 

3.0 

1.6 
3.0 
1.9 
8.3 
2.2 



Light oils up 
to 110° C. 






"0.3 
.4 
1.9 
1.4 
1.6 
•4 

92.8 

2.6 

1.7 

2.4 

2.3 
81.4 

2.9 

«i.4 

[1.9 
31 

9 1.6 

1.3 

I.I 
I.I 
1-7 

9 1.7 

^1.3 

1.8 

«3.l 






0.3 

.3 

1.5 

1.2 

1.3 

•3 
2.3 

2.1 

1.4 

1.9 

T^i 
1.0 

2.3 

1.4 

IS 

2.5 
1.2 



.9 
.9 
1-3 
1.2 
1.0 
1.4 
2.3 
.3 



References to Table 23 4 



1 Approximately. 

2 No information. 

3 Varies with coal. Coal with 28 per 
cent of volatile matter used. 

4 With H20. 

5 At present. 

6 Variable. 
1 Trace. 



8 Trace of solids. 

9 Distillate, solid. 

10 Distillate, one-fourth solid. 
" Distillate, nine-tenths solid. 
12 Distillate, three-fourths solid. 
Distillate, eight-ninths solid. 
w Distillate, one-half solid. 



BITUMENS 
Table 2^d, Continued 



247 



Examination, Office of Public Roads 


Distillation results 


Middle oils, 
iio°-i7o C. 


Heavy oils, 
i70°-27o C. 


Heavy oils, 
27o°-3i5° C. 


Pitch 


Serial 
No. 






{1 




^-0 


^.1 




^1 

^1 


0.8 


0.7 


12 13. 1 


11.5 


19 8.2 


7-3 


25 76.6 


79.1 


S126 


82.0 


1.7 


814.0 


12.3 


20 7.9 


6.9 


2674.7 


77.6 


5123 


.7 


.6 


14.9 


13.2 


21 II.9 


10.6 


27 69-5 


73.1 


5124 


.8 


.6 


13 21. 1 


18.9 


2° 5.5 


4.9 


25 69.4 


72.5 


5137 


.8 


.6 


" 17.5 


15.5 


19 9.4 


8.4 


25 70.I 


73.7 


5121 


12 I.I 

' -4 


•9 
.3 


16 23.6 
11 14.6 


20.7 
13.0 


8 9.8 
8 6.9 


8.9 
5-7 


27 65.1 

26 68.4 


68.9 
72.0 


5125 
5128 


.6 


•S 


10 17.6 


15.5 


22 II.4 


10.4 


27 63.8 


67.7 


5200 


.2 


.2 


w 20.0 


17.8 


" 6.5 


5-7 


25 69.6 


73-1 


S189 


.3 


.3 


18.6 


16.3 


^°7.S 


6.8 


27 68.0 


71.5 


5160 


1.2 
.2 


.8 
.2 


22.8 
" 16.S 


19-5 
14.1 


i^i3.6 
" 9-3 


12. 5 

8.2 


57.8 
2^69.3 


62.0 

73.2 


5074 
5081 


.6 


•S 


23.5 


20.4 


17 15-6 


14.4 


2755.2 


59-7 


509s 


9 .1 


.1 


"13.0 


10.9 


21 9.4 


8.1 


25 70.7 


74.6 


5083 


.6 


.5 
.6 
.4 


27.2 

27.9 

W 12. 1 


24.2 
24.4 
10.2 


» 7.3 
1^ 3-8 

19II.O 


6.7 
3-5 
9-7 


2759.8 
27 61. 1 

2573.7 


63.5 
64.9 
77-5 


5159 
5107 
5086 


.6 


•4 


1217.2 


151 


21 9-6 


8.5 


2869.7 


73-2 


5078 


1.4 
■5 
.4 

9 .2 
»2.2 


1-3 
.4 
•3 
.2 
•3 
•5 
.2 

1.7 


23-9 

18 26.9 
" 18.I 
8 20.0 
820.6 
" 20.5 

«7.i 
811.7 


21.4 
23.6 
15.9 
18.0 
18.5 
18.2 
6.1 
9.9 


10 II.6 

14 6.9 

"12.5 
"13.4 
» 7.1 

23 8.5 

12 7-4 

24 II.8 


10.4 
6.3 

II. I 

12.0 
6.5 
7.5 
6.9 

10.2 


27 60.8 

27 63.5 

27 63.7 
26 62.8 
2667.1 

25 66.4 

26 72.0 

27 71. 1 


64.7 
67.6 
67.8 
66.3 
70.2 
70.1 
74.8 
1 75.0 


5087 
5109 
5122 
5188 
5404 
5108 
5127 
5089 



References to Table 23 d 



w Distillate, two-thirds solid. 
" Distillate, four-fifths solid. _ 

17 Distillate, seven-eighths solid. 

18 Distillate, one-ninth solid. 
18 Distillate, one-third solid. 
20 Distillate, one-sixth solid. 
» Distillate, one-fifth solid. 



« Distillate, two-fifths solid. 

23 Distillate, one-seventh solid. 

24 Distillate, three-fifths soHd. 

25 Pitch, soft and sticky. 

26 Pitch, very soft and sticky. 

27 Pitch, hard and brittle. 
» Pitch, plastic. 



248 



MATERIx^S 
Results of Petroleum Residuum 



Kinds of Oil 




1. 


^•2 

?8« 


V 
'in 


-1 


n3 




c/)0 


P4 


1^- 


P^ 


Ph 


^u 


Pennsylvania, paraffin 


0.920 


186 


% 


% 


% 


% 


Texas, semi-asphaltic 


•974 


214 . 


14.2 


085.8 


II.O 


3.0 


California, asphaltic 


1.006 


191 


6.2 


093-8 


1-7 


1-^ 








17.3 


082.7 


0.0 


6.0 



a Soft. 

Tests of Bitumens and Their Significance. — Bitumens for use 
as the cementing material in road construction may, according 
to their source and characteristics, be divided into the two general 
classes of asphalts and tars. 

The asphalts suitable for use as the cementing agent in road con- 
struction are produced either by reducing asphaltic base petroleum 
to a suitable consistency by the distillation process or by softening 
the so-called solid asphalts to a suitable consistency by the addition 
of flux produced by the partial distillation of petroleum. 

The different grades, relative to consistency, of road oils are 
usually produced by the partial reduction of asphaltic base 
petroleum. 

By the destructive distillation of bituminous coals or the "crack- 
ing" of petroleum oils during the carburetting process in the manu- 
facture of water gas, crude tars are produced. These crude tars are 
refined or reduced by distillation to a suitable consistency for use 
in road construction. 

Bitumens are used in road construction for the purpose of water- 
proofing the surface and adding to the mechanical bond of the min- 
eral aggregate by cementing together the finer particles of mineral 
matter, thus preventing their displacement under the action of 
traffic and retaining them in the road surface where they fill the 
interstices between the larger stone and bind them together. 

The desirable characteristics of bituminous material for road 
building purposes are, first, Adhesiveness, second, Non-Susceptibility 
to changes in temperature, and third, Stability or "life.'' The chief 
object of bituminous material specifications is to make imperative 
these desirable qualities of the material. 

In connection with testing bituminous materials the thought 
should be kept in mind that the laboratory results obtained in the 
different tests are largely for comparative purposes. By this means 
new or but little used materials may be compared with materials 
which have proven satisfactory under service tests. Also laboratory 
results furnish an accurate means to specify the exact characteristics 
of the material desired for any given purpose. 

Adhesiveness. — The adhesiveness of the material is provided for 
in specifications by suitable requirements of ductility and toughness. 



TESTS OF BITUMENS 249 

The ductility and toughness tests are made for the purpose of 
determining the adhesive and binding quahties of the material under 
different conditions of temperature. The ductility test is made by 
determining the distance a briquette of the material, having a stand- 
ard cross-section (i sq. cm.) will draw out before breaking. Since 
temperature effects the results, a standard temperature of 77 degrees 
Fahrenheit, has been adopted generally for making this test. Expe- 
rience teaches that the greater the distance that a briquette of the 
material will stretch out before breaking the more sticky and adhesive 
the material. This test may be performed in a rough manner by 
pulling out a small roll of the material between the fingers. 
Material which will not pull out to a long thread before breaking is 
usually spoken of as " short. '* Such materials are not adhesive or 
sticky and it is extremely difficult to bind a road with them, even 
under the most favorable circumstances. 

As stated, the ductility test is usually made at a temperature of 77 
degrees Fahrenheit and thus measures the adhesiveness of the mate- 
rial at a rather high temperature. To obtain an indication of the 
character of the material at a low temperature the Toughness test is 
made at a temperature of 32 degrees Fahrenheit. This test is per- 
formed by dropping a weight of 2 kilograms on a cylinder of the 
material i % inches in diameter by i ^^ inches in height. The first 
height of the drop is usually from a distance of 5 cm. and is gradu- 
ally increased until rupture of the cylinder occurs. A rough field 
test for toughness may be performed by noting whether a piece 
of the material will fracture under a sharp blow. If the temperature 
of the material is about 32 degrees Fahrenheit, the results will be 
more indicative of the character of the material. 

Bitumens which are brittle or which give a low toughness result, 
lose their binding value in cold weather and roads constructed by 
their use are apt to ravel and break up under traflSc. 

Bitumens which give good ductility and toughness results under 
the methods outlined, will give satisfactory results as the cementing 
medium when used in road construction provided the other con- 
struction details have been properly followed out. 

In connection with the stickiness and adhesiveness of bitumens 
the fact should always be kept in mind that their purpose in road 
construction as cementing medium, is most effective when used with 
a hard, clean, dry mineral aggregate. As the departure from these 
qualities of the mineral aggregate increased so also are increased the 
difficulties of getting a satisfactory road surface firmly bound 
together. 

Susceptibility to Changes in Temperature. — The susceptibility 
to changes in temperature is shown by the relative hardness as 
indicated by the penetration tests at different temperatures, as 
32 degrees Fahrenheit, 77 degrees Fahrenheit and 115 degrees 
Fahrenheit. 

The consistency of asphalts is referred to as the "penetration." 
The penetration test is made by measuring the distance in hundredths 
of a centimeter that a standard needle under a stated load, applied 



250 MATERIALS 

for a stated time, will penetrate into it vertically. These variable 
factors are usually as follows : 

Needle — R. J. Roberts' Parabola ''Sharps" No. 2. 
at 32° F. 200 gram weight, i minute, 
at 77^^ F. 100 gram weight, 5 seconds, 
at 115® F. 50 gram weight, 5 seconds. 

The material which is the most susceptible to changes in tempera- 
ture will show the greatest variation in penetration under varying 
conditions of temperature. Roads constructed by the use of mate- 
rials which are extremely susceptible to changes in temperature be- 
come soft in warm weather, mark easily, have a tendency to rut and 
become wavy. In cold weather this material becomes very hard 
and slippery and is apt to be brittle and become chipped from the 
road surface. 

In addition to the general qualities of bitumens which are shown 
by penetration tests, this test is used in specifications to define 
within narrow limits the consistency of the material. The consist- 
ency limits placed in specifications are governed by the climate and 
the type of construction to be followed, also the general size of the 
mineral aggregate to be used. When the penetration method of 
construction is followed it is necessary to use a relatively soft asphalt 
in order that it may be incorporated in the road surface. In the 
mixing types of construction a harder asphalt may be incorporated 
with the mineral aggregate. The use of a hard asphalt together 
with a graded mineral aggregate gives a dense wearing surface that 
does not readily become wavy under traffic. 

The information obtained by the penetration test is not readily 
checked in the field without the aid of laboratory apparatus, but as 
a general rule bitumens which are suitable for binders are plastic 
when ''worked" in the hands. 

Stability.— When the term "Stability'' or "Life" is used in ref- 
erence to bitumens it refers to the quality of the material by which 
it retains its characteristics, usually as defined by the specifications, 
over a long period of time. The laboratory tests which indicate 
this property are the evaporation test, the ratio of the penetration 
after evaporation to the original penetration, and the flash point 

The heating or evaporation test, is made by placing 50 grams of 
the material in a flat bottomed dish 2%6 inches in diameter by 1% 
inches in depth. This is placed in an oven maintained at a specified 
temperature, usually 325 degrees Fahrenheit for a period of 5 hours. 

This test may be considered as an accelerated test on the material. 
In a binder, the percentage lost by weight together with the result- 
ing hardening as shown by the relative penetration, i.e., the ratio of 
the original penetration to the penetration after evaporation, are 
indicative of the "life" of the material. The less the evaporation 
loss and the less the hardening as shown by the relative penetration 
the greater will be the "life" of the material. 

In an oil used for surface application the evaporation test shows 
the presence and quantity of light oils. This is indicative of the 
time required for the oil to "set up" after application to the road 



TESTS OF BITUMENS 251 

surface; the evaporation from the large surface area of the oil as 
applied to the road being roughly comparable with evaporation 
from the smallest surface area of the oil exposed at the higher tem- 
perature at which the test is made. 

The open flash test is made by heating at the rate of about 10 
degrees Fahrenheit per minute, a small quantity of the material, 
approximately 40 grams in a dish of approximately the same size as 
the dish used for the penetration tests, 2^{q inches in diameter by 
I % inches in depth. A small flame from a capillary tube is passed 
over the surface of the oil at each increase of 5 degrees in tem- 
perature. 

A slight ^'puff " or explosion indicates the flash point has been 
reached. The presence of light oils or distillates is indicated by a 
low flash point. The flash point together with the evaporation 
results give an indication as to the methods and materials used in 
the manufacture of the bitumen which is being tested. 

Unless "cut-back" materials are being tested, in which an exceed- 
ingly light distillate as naphtha or benzole has been used as the 
*' cut-back '* agent, considerable " smoke '^ will be given off from the 
sample before the flash point is reached. This feature should be 
kept in mind when material is being heated for application in the 
field. Material should never be heated in the field to a point when 
it smokes profusely, for at such a temperature the material is being 
"burned" or hardened to such an extent that it loses its adhesive- 
ness and becomes brittle when coid, thus failing to become a binding 
or cementing agent which binds the mineral aggregate of the road 
together. 

The same "burning" effect on the material is produced by 
keeping it at a temperature below the "smoking point" for a 
long period (several hours) as would be produced at a higher 
temperature for a shorter period of time. This important feature 
should always be kept in mind when heating material for applica- 
tion in the field. 

Such tests as those for water, specific gravity, purity, par affine, 
etc. are usually placed in specifications in addition to the tests which 
govern adhesiveness, non-susceptibility and stability for the purpose 
of identification of materials used, methods of manufacture, degree 
of refinement and care used in refining. 

The presence of water in bituminous materials causes frothing 
when heated to a temperature of about 212 degrees Fahrenheit. In 
addition to the difficulty experienced in heating material containing 
water, due to the frothing, an even application or distribution to the 
road of such material is extremely difficult, due to the presence of 
the froth which is apt to be applied rather than the liquid bitumen. 

Tests for specific gravity, purity, paraffine, etc. require laboratory 
apparatus to get results which indicate qualities of the material. 
The information obtained by these tests can not be obtained by field 
tests. 

If we assume that a suitable bitumen has been specified and ob- 
tained for construction work in which a bitumen is to serve as the 



252 MATERIALS 

cementing material, the results obtained, relative to the bitumen, 
will depend upon: 

1. Not over-heating (by high temperature or long time) the 
bitumen. 

2. The use of hard, clean, dry stone. 

3. Grading of the mineral aggregate to reduce the voids and obtain 
greater density. 

4. Thorough and uniform incorporation of the bitumen with the 
mineral aggregate. 

5. Maximum consolidation, by rolling when laid. 

When bituminous materials which may be applied cold are to be 
applied to a road surface, that surface should first be put in good 
condition. Surface application treatment is for the purpose of 
preserving a road which is in good condition and not repairing an un- 
even road. We do not repair a house by painting it; rather we 
repair the house and then paint it, in order that it may remain in 
good condition. An attempt to build up a road wearing surface by 
the use of bitumens which may be appied cold usually results in a 
surface which is easily marked, ruts alnd pushes into waves. 

Cement. — There are five different classes of cement, Portland, 
Natural, Pozzolan, Iron Ore, and Magnesia cements. Of these 
the Portland or Natural is usualy spiecified. 

Portland cement is the term lappled to the finely pulverized 
product resulting from the calcination to incipient fusion of an in- 
timate mixture of properly proportioned argillaceous and calcareous 
materials, and to which no addition greater than 3 per cent, has been 
made subsequent to calcination. (Amer. Soc. Testing Materials 
1915— page 353.) 

Natural cement is the term applied to the finely pulverized prod- 
uct resulting from the calcination of an argillaceous limestone at a 
temperature only sufficient to drive off the carbonic acid gas. 
(Amer. Soc. Testing Materials 191 5 — p. 352.) 

Portland cements are usually heavier, stronger, slower setting, 
and more uniform than the natural cements and are generally used 
for road structures, such as culverts, retaining walls, etc. Portland 
cement is practically the only cement used to any extent in the 
United States at the present time. The few manufacturers of 
natural cement who were retaining a hold on the market some few 
years back when the production of Portland cement was expensive, 
are finding it difficult to compete with this latter product at its 
present price and quality. 

The following is the standard specification for Portland cement 
as adopted by the American Society of Civil Engineers and the 
American Society for Testing Materials: 

First: Specific gravity. The specific gravity of cement shall not be less 
than 3.10. Should the test of cement as received fall below this requirement, 
a second test may be made upon a sample ignited at a low red heat. The loss 
in weight of the ignited cement shall not exceed 4 per cent. 

Second: Fineness. It shall leave by weight a residue of not more than 
8 per cent, on the number 100, and not more than 25 per cent, on the number 
200 sieve. 

Third : Time of Setting. It shall not develop initial set in less than thirty 
minutes; and must develop hard set in not less than one hour, nor more than 
ten hours. 



CONCRETE MATERIALS 253 

Fourth: Tensile Strength. The minimum requirements for tensile 
strength for briquettes one square inch in cross section shall be as follows 
and the cement shall show no retrogression in strength within the periods 
specified: 

Age Neat Cement Strength 

24 hours in moist air 175 lbs. 

7 days (i day in moist air, 6 days in water) 500 " 
28 •* (i " " " " 27 " " ** ) 600 " 

One Part Cement — Three Parts Standard Ottawa Sand 
7 days (i day in moist air, 6 days in water) 200 lbs. 
28 " (i " " " •' 27 " " " ) 275 " 

Fifth : Constancy of Volume. Pats of neat cement about three inches in 
diameter, one-half inch thick at the center, and tapering to a thin edge, shall 
be kept in moist air for a period of twenty-four hours. 

(a) A pat is then kept in air at normal temperature and observed at in- 
tervals for at least 28 days. 

(b) _ Another pat is kept in water maintained as near 70 degrees F. as 
practicable, and observed at intervals for at least 28 days. 

(c) A third pat is exposed in any convenient way in an atmosphere of 
steam, above boiling water, in a loosely closed vessel for five hours. 

These pats, to satisfactorily pass the requirements, shall remain firm and 
hard, and show no signs of distortion, checking, cracking or disintegrating. 

Sixth: Chemical Composition. The cement shall not contain more than 
1.75 oer cent, of anhydrous sulphuric acid (SO3), nor more than 4 per cent, 
of magnesia (MgO). 

The methods used in testing cement are standardized in detail 
and can be obtained in the "Year Book'^ of 1913, published by the 
American Society for Testing Materials or Committee report on 
"Uniform Tests of Cement"* of the American Society of Civil 
Engineers 191 2. 

CONCRETE MATERIALS 

Fine Aggregate. — Fine aggregate for use in concrete should con- 
sist of sand free from any deleterious matter. Any sand which 
shows a coating on the grains should not be used until satisfactorily 
cleansed by washing. 

The following tests are made on sand to determine its suitability 
for use in different classes of concrete: 

I St. Gradation. 

2nd. Percentage of voids. 

3rd. Percentage of loam or silt. 

4th. Compressive or tensile strength in cement mortar. 

In order to secure suitable qualities, minimum requirements 
determined from the above tests should be definitely specified. 

The following specifications are now being used by Highway 
Departments in several of the States: 

Sand for use in Portland cement concrete roads shall be of the 
following gradation: 100 per cent, shall pass a }^" screen, not more 
than 20 per cent, shall pass a No. 50 sieve and not more than 6 per 
cent, shall pass a No. 100 sieve. Sand may be rejected for this class 
if it contains more than 5 per cent, of loam and silt. Mortar in the 
proportion of one part of cement to three parts of the sand, shall 
develop a compressive or tensile strength at least equal to the 
strength of a similar mortar of the same age, composed of the 
same cement and standard Ottawa sand. 



254 MATERIALS 

Sand for use in foundations, culverts, retaining walls, etc. shall 
not contain more than 8 per cent, of loam and silt. Mortar in the 
proportion of one part of cement to three parts of the sand, when 
tested shall develop a compressive or tensile strength of at least 80 
per cent, of the strength of a similar mortar of the same age, com- 
posed of the same cement and standard Ottawa sand. 

Screenings if substituted wholly or in part for the above sand, 
should meet the following requirements: 

They shall be free from dust coating or other dirt. 100 per cent, 
shall pass a 34'' screen and not more than 6 per cent, shall pass a No. 
100 sieve. Mortar in the proportions of three parts of the screen- 
ings or mixed screenings and sand, with one part of cement shall 
develop a strength equal to a sand for which it is to be substituted. 

The best and safest way in the selection of a concrete sand is to 
have a fair representative sample from the deposit listed. After this 
is found to meet the requirements, it is necessary to have constant 
and careful field inspections and tests made as the deposit is worked. 

The use of screenings is not advisable on any concrete work, 
except where a good grade of sand is not available. When used the 
product must be constantly inspected and tested as it is likely to 
vary to a considerable degree. Screenings from the softer lime- 
stones should not be used as the fine material is apt to ^'ball" in 
the mixer. 

Sand used for grout in brick and stone block pavement must be 
fine enough to ensure it getting between the joints of the block, but 
an excessively fine sand should be avoided as it weakens the grout. 
Some states and many municipalities require the grout sand to pass 
a No. 20 sieve and not more than 30 per cent, pass a No. 100 sieve. 
Such sand should not contain more than 5 per cent, of loam and silt. 

Coarse Aggregate. — Coarse aggregate for use in structural 
concrete should be of hard durable stone gravel or blast furnace 
slag (see table of tests) free from coating of any kind. For use in 
concrete pavement, stone and gravel should be hard, tough and 
absolutely clean. For use in culverts, retaining walls, etc. stone, 
gravel or slag should be of sound, un weathered material, clean and 
free from coating. It should not contain more than 10 per cent, of 
soft stone or shale. Gravel containing a large percentage of thin 
flat stone should not be used. 

For reinforced concrete the size of the stone is usually }^i" to 
i" in order to facilitate the compacting of the concrete between the 
reinforcing bars or mesh. For plain concrete a mixed size is used 
ranging from 3^'' to 3M''; a scientifically graded stone reduces the 
amount of mortar required, but the structures in road work are so 
small that it does not pay to attempt to reduce the voids in this 
manner and the size that is available is used, varying the propor- 
tions of mortar to get a dense product. For extensive concrete 
pavement of the first class graded sizes are feasible. 

The use of slag in concrete is still a debatable matter but if 
proven to be reasonable will add materially to the source of concrete 
materials. The latest available tests by the Pittsburgh laboratory 
with an up to date discussion is quoted as follows: 



TESTS OF BLAST-FURNACE SLAG 255 

TESTS OF BLAST-FURNACE SLAG AS COARSE 
AGGREGATE IN CONCRETE 

"[In order to secure definite authoritative data on the use of blast- 
furnace slag in concrete, a number of leading interests, which either produce 
or market slag, made a co-operative arrangement with the Pittsburgh Test- 
ing Laboratory of Pittsburgh to conduct a series of experiments and tests 
that would extend ultimately over a period of five years. 

"The reports of these tests will be of more than ordinary value, as the 
care involved in the preparation and testing of the specimens made the tests 
more expensive than would ordinarily be undertaken by a commercial labo- 
ratory, and the results are such as can be obtained only by having a very 
carefully organized research department. 

"Recognizing that these tests are of the utmost value to engineers in ac- 
quainting them with the performance of blast-furnace slag in concrete work, 
the Manufacturers Record publishes herewith extracts from the report com- 
piled by the Pittsburgh Testing Laboratory. — Editor Manufacturers Record.] 

"The purpose of this series of tests v/as to furnish information relative to 
the use of concrete materials, as follows: 

" (i) A comparison of the crushing strengths of air-cooled blast-furnace 
slag, crushed stone and gravel when used as the coarse aggregate in concrete, 
tests to be made at the end of 14, 30, 60 and 180 days, i year, 2 years, 3 years, 
4 years and 5 years. 

" (2) To determine the granulometric analysis of the material as received, 
together with other physical characteristics. 

" (3) Determination of the corrosive tendency of sulphur in slag. 

"(4) Effect of sulphur and other elements on the durability of concrete 
up to the age of five years. 

"(5) Relative strength and durability of concrete made of high magnesia, 
low lime slag and low magnesia high lime slag. 

" The materials used as the coarse aggregates in these tests were secured 
from the following localities: 

P. T. L. Mark 
Slag: Cleveland Macadam Co., Cleveland, Ohio (from 

A. S. & W. Co., Central Fur., Cleveland, Ohio) 87410 

Slag: Duquesne Slag Products Co., Pittsburgh, Pa. (from 

C. S« Co., Duquesne, Pa., slag bank) 87420 

Slag: Carnegie Steel Co., Pittsburgh, Pa. (from Ohio 

Works, Youngstown, Ohio) 87430 

Slag: Northwestern Iron Co., Mayville, Wis 87440 

Slag: Standard Slag Co., Youngstown, Ohio (from S. F. Co., 

Sharpsville, Pa.) 87450 

Slag: Cleveland Macadam Co., Cleveland, Ohio (from C. F. 

Co., Cleveland, Ohio) _. . ._ 87470 

Slag: Birmingham Slag Co., Birmingham, Ala. (from T. C. 

& I. Ry. Co., Ensley, Ala 87480 

Slag: Duquesne Slag Products Co., Pittsburgh, Pa. (from 

E. S. Co., Pottstown, Pa.) 87520 

Slag: The France Slag Co., Toledo, Ohio (from T. F. Co., 

Toledo, Ohio) 87530 

Gravel: Allegheny River, from Pittsburgh, Pa 87460 

Trap Rock: from Birdsboro, Pa 87490 

Gravel: from Akron, Ohio _ 87500 

Crushed granite: from Stockbridge, Ga 87510 

Limestone: from Gates City, Ala 87540 

Dolomitic limestone: Kelly Island, from Cleveland, Ohio.. . 87550 

It did not seem practicable to screen the fine aggregate and recombine 
to conform to Fuller's curve, or to use a combination of two or more sands 
which would make theoretically the best fine aggregate. The material 
selected was reasonably well graded, and the same sand was used throughout 
the series of tests, the whole aniount being secured at one time from the back 
channel of the Ohio River, at Neville Island. 

"The cement used was Alpha Portland, from Manheim, W. Va. This 
brand was selected by lot, being drawn from a list of several standard brands 
of Portland cement. All cement was purchased at the same time and sam- 



2s6 



MATERIALS 



pled and tested before the preparation of concrete test specimens was begun. 
The results of these tests are included in the report. 

"As the various aggregates were received, they were screened through 
sieves consisting of iron plates with circular holes of the following diameters: 
i^i inches, i inch, ^^ inch, 3^ inch and ^^ inch. 

"The portions retained on each of the above sieves were stored separately 
and labeled, to be later recombined to make the coarse aggregate used in 
the tests. 

"In accordance with the specifications, the coarse aggregate was recom- 
bined to conform to Fuller's curve. Since the portion of Fuller's curve 
representing coarse aggregate is a straight line, and since the curve is re- 
ferred to ordinates, of which the vertical ordinate is divided into equal parts, 
showing percentages by weight, and the abscissa is divided into equal parts, 
representing the diameter of the particles in inches, it follows that coarse 
aggregates, when so recombined, will consist of equal percentages of the four 
(4) gradings, which increase in size uniformly from ^^ inch to ij'i inches. 
All aggregates, therefore, were recombined by weighing equal quantities of the 
four gradings and shoveling them fogether, turning them until their appear- 
ance showed them to be thoroughly mixed. 

"In order to accurately proportion the concrete, the weight per cubic foot 
of all materials was determined. Since there is no generally accepted method 
for determining the weight per cubic foot of concrete materials, one was used 
which had been found in the past to give consistent results. A cubic foot 
measure was filled loosely with either sand or the recombined aggregate, 
after which the measure was dropped 10 times on a felt pad one inch thick 
from a height of three inches. The measure was again filled and smoothed 
off with a straight edge and weighed. The average of 10 determinations 
was taken as the weight per cubic foot of the material used. The variation 
of the individual determinations was usually within five-tenths of i per 
cent, and seldom over i per cent. The weight per cubic foot was frequently 
redetermined, to take into account any drying out of the material. The 
weight of the cement per cubic foot was taken at 100 pounds, this being in 
accordance with the generally accepted figures for cement. 

"Void determinations were made on the various aggregates after recom- 
bining. Each coarse aggregate was thoroughly wet, drained and a cubic 
foot measure filled and weighed, as given in the method for determining the 
weight per cubic foot. Water was then slowly added until the measure 
was level full. From the increase in weight the percentage of voids was 
computed. 

"It was not possible to combine the sand and cement with the slag, gravel 
and crushed stone, respectively, to strictly conform to Fuller's curve and 
still have tests which would be comparable with each other on the basis of 
equal proportions of cement. It was, therefore, necessary to determine the 
leanest mixture which would produce a dense concrete when using the coarse 
aggregate having the highest percentage of voids, and then using this mixture 
for all materials. ^ By this method the same quantity of cement was used 
to make each specimen, and the test data shows a comparison of the diffeient 
aggregates under the same conditions. 

"The proportions for the mortar were determined by making trial mortars 
of various proportions of cement and sand and selecting the mixture giving 
the maximum density as shown by increase in volume of the resulting mortar. 
After numerous tests, the proportions of i part cement and 2 parts sand 
were found to most nearly fulfill the tests for maximum density of the 
mortar. 

"The coarse aggregates used for these tests varied in weight per cubic 
foot from 64 to 104.5 pounds, and the percentages of voids from a minimum 
of 31.85 to 49.2 per cent. Since the percentage of voids in one case was 49, 
to obtain the maximum density, using this aggregate, the mixture should 
be almost exactly two parts of mortar and four of coarse aggregate; this pro- 
portion would give some excess mortar in all of the other cases. 

"The fact that a 1-2-4 mixture is one which is very commonly used — and 
a large amount of data may be found for comparison — was an additional 
reason for using it in these tests. , , , . , 

"These proportions by volume having been selected, the equivalent weight 
each of the materials for these proportions was determined, and throughout 
the series of tests all materials were weighed, and greater accuracy in propor- 
tioning thus obtained. The mixture, however, is by volurne, the method of 
weighing being used only to insure more accurate proportions. 



TESTS OF BLAST-FURNACE SLAG 



257 



"A quantity of material sufficient to make 
ten (10) cylinders was mixed at one time, the 
sand being spread in a flat pile and the cement 
placed over this. The two materials were 
turned by two men until the color appeared 
to be uniform, [.three or four turnings being 
required. The coarse aggregate was then 
shoveled on this material and the whole 
turned dry three times. During the fourth 
turn a weighed amount of water was added 
from a sprinkling can and three (3) additional 
turnings given the mixture. During the last 
three turnings small quantities of water were 
added as needed until a * quaking consistency * 
was obtained. In all mixtures an attempt 
was made to secure the same consistency, 
regardless of the amount of water used. For 
this reason, it was not possible to use a me- 
chanical mixer, as the quantity of water is 
very important, and in mechanical mixing the 
material may be made too wet and the whole 
batch spoiled for laboratory purposes. It is 
noteworthy that care must be used to obtain 
the correct consistency, and that the addition 
of I pound of water to a lo-specimen mixture 
would give a consistency too wet, usually de- 
scribed as 'mushy,' and the results of the tests 
would be unsatisfactory. 

*'The specimens were made in steel molds 8 
inches in diameter by 16 inches high. The 
concrete was poured into these molds in layers 
4 inches thick, and each layer tamped thirty 
(30) times with a J-^-inch round rod. After 
the second and fourth layers the sides were 
spaded with a large trowel. These cylinders 
were finally finished at the top by spading 
with a small trowel to form a smooth upper 
rim, and a piece of plate-glass placed on top 
to form a smooth surface. Since the concrete 
would settle slightly after a few hours, it was 
necessary to cap the top of the specimen with 
plaster-of-Paris and cement and again place 
the] plate-glass on the cap to make a smooth 
surface. ; 

"The specimens were kept in the molds for 
forty-eight (48) hours and then stored in damp 
sand for thirty-five (35) days. At the end of 
this time all specimens were removed and 
stored in air. Four (4) short pieces of rein- 
forcing steel were embedded in each of two 
(2) cylinders from every batch. 

"These pieces were 3, 6, 9 and 12 inches 
long, and were cut from }4 inch twisted rein- 
forcing bars furnished by the Carnegie Steel 
Co., Duquesne heat No. 99439. having the 
following chemical analysis: 

Carbon 20.0 per cent. 

Manganese 45-0 per cent. 

Phosphorus 0.018 per cent. 

Sulphur 0.046 per cent. 

"These specimens will be examined at the 
end of the five-year period to determine the 
corrosive action of the aggregates. 

" (i) It will be noted that one-half of the 
tests of the slag concrete were made using 
slag produced by the quick-cooling process^ in 



w 
u 

< 

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(A 
P 



2 
Q 

w 

O 

o 
o 



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00 rO •-• f*5 



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10 t^oo fOt^roO w oj M 
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Ho 5 a S rti^ SPP-o^a-S 
PH(y3<MSHO^c/3(y3c«0 



258 






MATERIALS 


















Table 24.— Results of Physical Tests 










14 


Day Tests 






^ 








u 






A . 


bfl 






>0 


Per Cent. Passing 


^ 
^ 








C . 




o^ 


""^ 


Sieve as Received 


_c 






1^ 


Name of Material 


»-. rt 


..^ 




'>> 


Weight 


-^ S^ 


2s 

A 


Used 


p^S 









of 


^ U 




^^ 


«^^ 
" 




c 


Cylinder 


bo <i> 
C ft 


\^'^ 













lb. 


oz. 


o.S 


rt a=c^ 


iK 


I 


H 


Vz Ya. 


S C w 
<u <u . 


Slag 


























Cleveland 
















9 


62 


8 


1897 




Macadam Co., 


66.5 


49.2 


99.35 


83.70 


48.20 


16.10 


2.40 


18 


62 


10 


1998 


1941 


Central Furnace, 
















29 


63 


3 


1928 




Cleveland, Ohio 


























r. ^^^^ o 


























Duquesne Slag 
















9 


65 


10 


2212 




Products Co. 


78.5 


42.74 


96.70 


83.70 


61.40 


32.80 


3.50 


18 


65 


13 


2318 


2159 


Duquesne, Pa. 
















28 


65 


8 


1946 




Slag 
















9 


65 


4 


2346 




Carnegie Steel Co., 


79.3 


43.15 


97.10 


84.10 


41.30 


11.50 


3.50 


18 


64 


10 


2128 


2134 


Youngstown, Ohio 
















27 


65 


4 


1928 




Slag 
















2 


62 


12 


2238 




Northwestern Iron 


64.5 


45.87 


86.10 


65.20 


37.30 


19.00 


1.60 


12 


62 


12 


2141 


2206 


Co., Mayville, Wis. 
















22 


63 


4 


2238 




Slag 
















2 


65 


14 


2477 




Standard Slag Co., 


75.0 


41.53 


92.40 


69.10 


40.30 


17.80 


3.50 


12 


65 


3 


2380 


2484 


Sharpsville, Pa. 
















28 


64 


14 


2594 




Gravel 
















2 


69 


2 


2045 




Allegheny River, 


104.5 


31.85 


80.28 


68.38 


50.68 


30.21 


9.45 


12 


68 


13 


2093 


2046 


Pittsburgh, Pa. 

Slag 

Cleveland 
















22 


68 


II 


2000 


















2 


62 


4 


2387 




Macadam Co., 


64.0 


46.77 


100. 


88.50 


57.20 


14.50 


4.10 


12 


62 


4 


2237 


2257 


Cleveland Furnace 
















22 


61 


II 


2146 




Cleveland, Ohio 


























Slag 
















2 


66 


13 


2043 




Birmingham Slag 


83.8 


42.00 


98.40 


82.80 


48.70 


15.70 


2.90 


10 


66 


00 


2160 


2109 


Co., Ensley, Ala. 
















21 


66 


10 


2126 




Trap Rock 
















2 


72 


8 


2109 




Birdsboro, Pa. 


98.7 


41.93 


96.80 


87.10 


62.80 


21.10 


2.00 


12 
22 


73 

72 


I 
3 


2053 
2026 


2063 


Gravel 
















2 


68 


00 


1793 




Akron, Ohio 


95.0 


35.9 


99.40 


88.20 


60.30 


25.20 


3.26 


12 
22 


68 
67 


7 
10 


1800 
1792 


1795 


Crushed Granite 
















II 


69 


00 


1980 




Stockbridge, Ga. 


90.0 


42.34 


97.40 


84.30 


53.50 


25.00 


5-00 


21 
22 


68 
69 


00 
8 


2178 
2208 


2122 


Slag 
















I 


63 


00 


2151 




Duquesne Slag 


73.75 


43.55 


98.62 


90.20 


70.02 


36.09 


3.60 


12 


64 


00 


2167 


2187 


Products Co., 
















22 


63 


00 


2244 




Pottstown, Pa. 


























Slag 
















2 


65 


13 


1918 




France Slag Co., 


81.75 


42.5 


90.9 


64.90 


39.50 


29.00 


20.00 


12 


66 


14 


1856 


1942 


East Toledo, Ohio 
















21 


66 


ID 


2051 




Limestone 
















I 


69 


8 


1670 




Gates City, Ala. 


94.87 


40.33 


lOO.O 


98.90 


83.30 


43.40 


6.00 


6 

7 


69 

71 


8 



1750 
1720 


1713 


Dolomitic 
















4 


69 


II 


1830 




Limestone 


94-11 


38.71 


lOO.O 


96.0 


47.00 


11.50 


3.20 


13 


69 


7 


1814 


1804 


Kelly's Island, 
















23 


69 





1769 




Cleveland, Ohio 



























Note. — Above tests carry Pittsburgh Testing Laboratory numbers in consecutive 
87500, 87510, 87520, 87530, 87540, 87550. 

Compression tests made using 8" X 16'' cylinders, 1-2-4 Mix — Alpha cement 



TESTS OF BLAST-FURNACE SLAG 



259 



OF 


Slag, Stone, 


AND Gravel Used in Concrete 








30 Day Tests 


60 Day Tests 


180 Day Tests ] 


1 




■a.s 
1^ 


xn •— ' 


.2 






t. 








l.s 

9 . 


bo 


% 


Weight 


r^ ^ 


■>. 


Weight 




2a 


'>. 


Weight 


^S* 


2c 





of 


^v. 


Average Ci 
Strength ii 
per sq. in. 





of 


C/3 w 


O"" _: 





of 


m ^ 


O"^ _: 


g 


Cylinder 
lb. oz. 


.2 ^ 




■a 

1^ 


Cylinder 
lb. oz. 




Average < 
Strength 
per sq. ir 




■a 


Cylinder 
lb. oz. 




Average < 
Strength 
per sq. ir 


10 


63 


3 


2461 




1 

8 


63 


00 


2815 




7 


62 


10 


3740 




33 


63 


10 


2770 


2525 


13 


62 


15 


2966 


2930 


5 


62 


5 


3958 


3753 


28- 


62 


14 


2343 




26 


62 


13 


3008 




8 


63 





3560 




10 


66 


00 


242s 




4 


65 


6 


3143 




7 


64 


12 


4280 




17 


64 


4 


2983 


2657 


13 


65 


6 


3402 


3117 


16 


65 


10 


4464 


431S 


27 


65 


I 


2562 




22 


65 


4 


2810 




25 


64 


5 


4200 




10 


65 


8 


2642 




7 


66 


4 


3625 




2 


65 


10 


3880 




17 


64 


00 


2568 


2657 


12 


63 


10 


3220 


3306 


16 


65 


00 


4130 


4154 


28 


64 


10 


2761 




22 


65 


12 


3074 




20 


65 


S 


4452 




3 


63 


00 


2640 




5 


62 


5 


3523 




I 


62 


IS 


4146 




13 


62 


12 


2630 


2653 


21 


63 


00 


3363 


3403 


4 


62 


8 


4268 


4309 


23 


63 


4 


2688 




28 


62 


II 


3320 




6 


63 





4512 




3 


65 


00 


3127 




10 


65 


II 


3359 




I 


64 


II 


4906 




13 


65 


00 


2999 


3075 


18 


65 


00 


3468 


3365 


5 


65 


3 


4678 


4803 


27 


65 


00 


3100 




21 


64 


•13 


3268 




9 


64 


II 


4824 




3 


68 


13 


2608 




6 


68 


13 


3427 




7 


68 


14 


4200 




13 


68 


9 


2514 


2510 


21 


69 


2 


3170 


329s 


9 


68 


9 


3816 


3969 


23 


68 


15 


2409 




27 


68 


13 


3289 




19 


69 


I 


3892 




I 


62 


2 


2810 




1 3 


61 


10 


3167 




6 


61 


15 


4588 




II 


61 


8 


3057 


2844 


14 


62 


I 


3126 


3288 


13 


61 


14 


4422 


4394 


21 


62 


5 


2666 




24 


61 


2 


3068 




16 


61 


9 


4172 




I 


66 


9 


2660 




8 


64 


00 


3270 




3 


66 


2 


4432 




II 


66 


00 


2800 


2752 


17 


66 


9 


3354 


3289 


4 


66 


9 


4460 


4451 


20 


67 


2 


2796 




[25 


66 


5 


3244 




7 


66 


7 


4460 




I 


72 


6 


2454 




9 


72 


6 


3411 




3 


72 


15 


4814 




II 


73 


5 


2330 


2386 


ii5 


72 


12 


3416 


3360 


6 


72 


12 


4738 


4819 


21 


72 


9 


2374 




120 


72 


8 


3256 




7 


72 


14 


4906 




I 


66 


13 


2040 




i 8 


67 


12 


2756 




3 


68 


3 


3636 




II. 


67 


9 


2040 


2078 


16 


68 


2 


2378 


2554 


4 


68 


9 


3840 


3627 


21 


67 


8 


2153 




28 


67 


14 


2527 




16 


68 





3404 




I 


69 


00 


2230 




3 


69 


2 


3112 




8 


69 


6 


4190 




12 


68 


4 


2334 


2292 


16 


69 


00 


2760 


3043 


17 


69 





4016 


41SI 


22 


69 


8 


2313 




19 


69 


8 


3258 




23 


69 


5 


4248 




2 


64 


2 


2738 




5 


63 


8 


3245 




27 


63 


5 


4210 




II 


63 


6 


2600 


2650 


14 


63 


00 


3244 


3289 


4 


63 


6 


4203 


4184 


21 


63 


00 


2613 




24 


63 


8 


3378 




3 


63 





4140 




I 


66 


7 


2527 




7 


66 


3 


3251 




3 


66 


4 


4130 




II 


65 


4 


2402 


2536 


16 


66 


5 


2864 


3103 


9 


66 


15 


4333 


4164 


22 


66 


4 


2680 




20 


66 


4 


3195 




13 


65 


6 


4030 




3 


69 


9 


1985 




2 


69 


6 


3149 




4 


70 





3936 




10 


69 


8 


1950 


1988 


15 


68 


13 


3014 


3082 


8 


69 


6 


4636 


4127 


23 


69 


8 


2030 




22 


69 


00 


3072 




9 


68 


12 


3814 




I 


69 


6 


2269 




2 


70 


00 


3503 




3 


70 





4640 




12 


69 


14 


2442 


2360 


17 


69 


12 


3846 


3604 


19 


70 





5011 


4724 


24 


69 


00 


2375 




22 


70 


12 


3462 




27 


69 





4520 





order as follows: 87410, 87420, 87430, 87440, 87450, 87460, 87470, 87480, 87490, 
selected by lot. Ohio River sand. Large aggregates as shown above. 



26o 



MATERIALS 






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TESTS OF BLAST-FURNACE SLAG 



261 



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262 MATERIALS 

pits, in which the slag is shipped within a few days from the time it comes 
from the furnace, and the remainder from slag which had been seasoned in 
banks for a period of six months in some cases and as much as 15 years in 
one case. 

"(2) The length of time during which this series of tests has been con- 
ducted does not warrant the drawing of any definite conclusions, but the 
general uniformity of the results of the crushing tests of the concrete should 
be observed. 

" (3) Slags coming from furnaces many hundred miles apart, varying 
quite widely in chemical analyses, and also varying considerably in the 
weight per cubic foot, do not vary in strength in proportion to either the 
weight or percentage of any chemical constituent. 

Since the following tests were published the one-year test 
has been completed, and in reporting on these the Pittsburgh 
Testing Laboratory states: 

*'In most cases the specimens show a considerable increase in strength 
over those tested at the age of 180 days, but in some cases the increase is 
very slight. Discussion of these tests will be withheld until the end of the 
two or three-year tests, but the discussion of results furnished with the 180- 
day tests^ stili holds trtie for these tests. In some instances, as will be noted, 
an exceptionally high compressive strength has been developed at the age 
of one year. 

Water. — The following quotation from the Concrete Highway 
Magazine of May, 191 8, by Duff A. Abrams shows the effect of 
excessive water on the strength of concrete. It should be borne in 
mind that this represents the laboratory point of view but shows 
very forcibly that excess water is injurious. 

''It is commonly stated that concrete is composed of a mixture 
of cement, sand and pebbles or crushed stones. This conception 
of concrete overlooks one essential element of the mixture; namely, 
water. An exact statement of the ingredients of concrete would be: 
Cement, aggregate, and water. The last-named material has not 
yet received proper consideration in tests of concrete or in specifica- 
tions for concrete work. 

'* Early users of concrete centered their entire attention on the 
quality of the cement, and practically disregarded the characteristics 
of the other ingredients. During the past dozen years some atten- 
tion has been given to the importance of the aggregate, but it 
is only recently that we have learned that the water also requires 
consideration. 

''A great deal has been said and written recently concerning the 
effect of water on the strength and other properties of concrete, 
but the full significance of this ingredient of concrete has not 
heretofore been pointed out. A discussion which appeared in the 
April, 191 7, issue of the Concrete Highway Magazine gave 
a brief review of results of some of the experimental work carried out 
along this line at the Structural Materials Research Laboratory, 
Lewis Institute, Chicago The relation between the water content 
and the compressive strength of the concrete for a wide range of con- 
sistencies was there pointed out and emphasis was placed on the 
injurious effect of too much water. 

** Tests made in studies of the effect of size and grading of ag- 
gregates have shown that the only reason that concrete of higher 
strength and durability can be produced from well-graded aggregate 



WATER 



263 



as compared with a poorly graded aggregate is that the former can 
be mixed with less water. If this is not done no advantage is gained 
from using a coarse, well graded aggregate. The following dis- 
cussion shows that a similar conclusion can now be stated with 
reference to a rich concrete mix as compared with a lean one. 

*' While the injurious effects of too much water in concrete are 
apparent, tests made in this laboratory show that the truly funda- 
mental role played by water in concrete mixtures has been entirely 
overlooked in previous discussions of this subject. The relation 
referred to above is brought out by a series of compression tests 
of about 1600 6 by 12-in. concrete cylinders made up as follows: 



Mix 




Range of Sizes of 




n^^^:^-i- .. 


Cement- Aggregate 


Aggregates | -v......uc....y 


I- 9 
I- 5 
I- 3 
I- 2 
I— I 

Neat , 


> 




' o-14-mesh sieve 
0- 4-mesh sieve 
o-i %-inch 
o-i K-inch 
0-2 -inch 


. 


( 7^ different con- 
1 sistenciesfor 
1 each mix and 
[ aggregate 



*^The mixes used covered a wide range, as did also the grading 
of aggregate and consistency. The aggregates consisted of two 
sizes of sand and mixtures of sand and pebbles graded to the sizes 
shown. The mix is expressed in terms of volumes of dry cement 
and aggregate, regardless of grading; i.e., a i : 5 mix is made up 
of I cu. ft. cement (i sack) and 5 cu. ft. of aggregate as used, 
whether a sand or a coarse concrete mixture. 

" This series gives valuable information on the effect of changing 
the quantity of cement, the size of the aggregate and the quantity 
of water. The effect of many different combinations of these 
variables can be studied. One set of relations gives the effect 
of amount of cement using aggregates of different size and grading; 
another set of relations gives the effect of different quantities of 
water, varying both mix and size of aggregate, etc. In all respects 
these tests bear out the indications of both earlier and later series. 
These tests are of interest in that they reveal for the first time the 
true relation between the strength and the proportions of the con- 
stituent materials in concrete. 

** The figure shows the relation between the compressive strength 
and the water content for the 28-day tests. The water content 
of the concrete has been expressed as a ratio of the volume 
of cement, considering that the cement weighs 94 lb. per cu. ft. 
Distinguishing marks are used for each mix, but no distinction 
is made between aggregates of different size or different consistencies. 

** When the compressive strength is platted against the water in 



264 



MATERIALS 



n' 



this way, a smooth curve is obtained, due to the overlapping 
of the points for different mixes. Values from dry concretes have 
been omitted. If these were used we should obtain a series of 
curves dropping downward and to the left from the curve shown. 
It is seen at once that the size and grading of the aggregate and 
the quantity of cement are no longer of any importance except 
in so far as these factors influence the quantity of water required 



8000 




0.50 



1.00 1.50 e.00 2.50 3.00 3.50 

YVa+er-Rcj-t-jo +o Volume of Cement 



4.oa 



to produce a workable mix. This gives us an entirely new con- 
ception of the function of the constituent materials entering into a 
concrete mix and is the most basic principle which has been dis- 
covered in our studies of concrete. 

** The equation of the curve is of the form, 



5 = A 
■^ B- 



(i) 



where S is the compressive strength of concrete and x is the ratio 
of the volume of water to the volume of cement in the batch. A 
and B are constants whose values depend on the quality of the 
cement used, the age of the concrete, curing conditions, etc. 

** This equation expresses the law of strength of concrete so far as 
the proportions of materials are concerned. It is seen that for 
given concrete materials the strength depends on only one factor — 
the ratio of water to cement. Equations which have been pro- 
posed for this purpose contain terms which take into account such 
factors as quantity of cement, proportions of fine and coarse 
aggregate, voids in aggregate, etc., but they have uniformly omitted 
the only item which is of any importance; that is, the water. 

** For the conditions of these tests, equation (i) becomes, 



14,000 



(2) 



WATER 265 

'' The relation given above holds so long as the concrete is not too 
dry for maximum strength and the aggregate not too coarse for 
a given quantity of cement; in other words, so long as we have a 
workable mix. 

" Other tests made in this laboratory have shown that the charac- 
ter of the aggregate makes little difference so long as it is clean and 
not structurally deficient. The absorption of the aggregate must 
be taken into account if comparison is being made of different 
aggregates. 

*' In certain instances a 1-9 mix is as strong as a 1-2 mix, depending 
only on the water content. The strength of the concrete responds 
to changes in water, regardless of the reason for these changes. 

**It should not be concluded that these tests indicate that lean 
mixes can be substituted for richer ones without limit. We are 
always limited by the necessity of using sufficient water to secure 
a workable mix. So in the case of the grading of aggregates. . The 
workability of the mix will in.all cases dictate the minimum quantity 
of water that can be used. The importance of the workability 
factor in concrete is therefore brought out in its true relation. 

*^The reason a rich mix gives higher strength than a lean one is 
that a workable concrete can be produced by a quantity of water 
which gives a lower ratio of water to cement. If an excess of water 
is used we are simply wasting cement. Rich mixes and coarse, well- 
graded aggregates, are as necessary as ever, but we now know just 
how these factors affect the strength of the concrete. 

*' Practical use may be made of the curve in estimating the rela- 
tive strength of concretes in which the water content is different for 
any reason. For example, a concrete mixed with 7.5 gallons of 
water (i cu. ft.) to one sack of cement (allowance being made for 
absorption of aggregate) gave a strength in this series of 2000 lb. 
per sq. in. (x = i.oo). For x = o.8o (6 gal. of water per sack of 
cement) we have 3000 lb. per sq. in.; for x = o.75 (5.6 gal.) 3300 
lb. per sq. in. Concrete in a 1-4 mix (same as the usual 1-2-3 ^li^ 
with a coarse sand) should be mixed with 5 M to 6 gal. of water per 
sack of cement. 

" The importance of any method of mixing, handling, placing and 
finishing concrete which will enable the work to be done with a mini- 
mum of water is at once apparent. It now seems that practically 
all faulty concrete work can be traced to the use of too much water. 

** Laboratory research performs its true function when it uncovers 
basic principles which have not been revealed by experience in 
construction, or observation of completed work.*' 



PART II 

PRACTICE OF SURVEY, DESIGN AND 
CONSTRUCTION 

CHAPTER X 

PRELIMINARY INVESTIGATIONS 

As stated in the introduction the object of all preliminary in- 
vestigation, either of new locations in unsettled districts or of 
high type pavement improvements in populous sections, is to se- 
cure data on which a reasonable program of work can be based. 
Work of this kind should be done only by experienced highway 
engineers as reliable results depend largely on the judgment of 
engineer which must be based on actual design and construction 
experience under conditions similar to those investigated. As a 
rule this portion of the engineering program is carelessly done due to 
hesitation in spending money before a project is assured but this 
policy is short sighted as there is no part of the work which is more 
important. 

The cost of first-class investigations of this kind range Irom 
$3.00 to $40.00 per mile. A cost of $5.00 to $10.00 per mile is a 
fair average for long mountain road projects similar in character 
to the work being done by the U. S. Office of Public Roads in the 
west and a cost of $5.00 to $15.00 per mile for high type road re- 
ports in the eastern states. Reconnaissance surveys in heavily 
timbered regions may cost as high as $40.00 per mile. 

HIGH TYPE ROAD INVESTIGATIONS IN WELL- 
SETTLED DISTRICTS 

The improvement generally consists of betterments to an existing 
road the location of which is fixed by existing rights-of-way. The 
choice of which road to improve is made by local boards or the 
State Highway Commissioner so that when the problem reaches the 
field engineer his work is confined to a definite engineering report 
on a definite road. 

The field work and report deal with the following main features. 

1. Probable Traffic. — This forms the basis of decision as to general 
type (rigid or flexible) and the width of pavement (single or double 
track). 

2. Local Materials, — This forms the basis for decision as to the 
most economical type of pavement of the general class required. 

3. Cost Estimate. — This forms the basis of appropriations for 
survey, design, and construction and indicates the mileage that 
can be completed with the funds at hand. 

266 



FIELD METHODS 267 

Field Work. — In any district the volume of traffic is entirely 
a matter of judgment. A traffic census can be taken but is of little 
value as the improvement of a road changes the amount and class 
of travel. The most reliable basis for decision is a study of the map 
of the locality and inquires of local residents to determine the 
probable routes of travel for farm traffic to markets or shipping 
points, for long distance truck traffic, and the location of summer re- 
sorts in relation to the improvement, etc. These considerations 
applied in a comparative way to previously built roads of different 
types serving districts of practically the same general character 
form the only reasonable basis for the selection of general type and 
width. See Chapter VI for traffic classification and the principles 
of general selection of type. See sample preliminary report 
page 274 for an example of this part of the work. See page 329 
for traffic notes. 

Local Materials (Field Work). — The investigation for local 
material is very important. Careless work in this particular 
results in specifying impracticable or needlessly expensive sources 
of supply for materials and often in the selection of an unreasonable 
type of construction. A careless estimate of the quantity of avail- 
able local material also causes trouble during construction by a 
shortage in supply. 

It is important not only to determine the amount of local material 
but also its character as for example a local gravel may be suitable 
for a first-class bottom for macadam construction but not suitable 
for a concrete pavement, or it may be suitable for a concrete paving 
base but not for a concrete road taking the traffic directly. A 
local hard sandstone may be suitable when bound with bitumen and 
would not act well if waterbound with its own screenings, etc. 
The necessary properties of stones, gravels, sands, etc., are given in 
the Chapter on Materials, and in Specifications. 

Any preliminary report should cover the sources of supply and 
approx. cost at pit or switch of the following materials : 



t -Gravels. — Suitable for. 



Stone, Slag, Etc. — Suitable for 



Bottom courses. 

Top courses. 

Structural concrete. 

First-class concrete pavement. 

Concrete paving base. 

Sub-base filler. 

Sub-base. 

Bottom course. 

Waterbound macadam top. 

Bituminous macadam pave- 
ment. 

First-class concrete pave- 
ment. 

Concrete paving base. 

Structural concrete. 



268 



PRELIMINARY INVESTIGATIONS 



Sand. — Suitable for. 



Miscellaneous. 



Bottom course filler. 
Cushion sand. 
Structural concrete sand. 
First-class concrete paving 

sand. 
Fine and coarse sand for 

sheet asphalt. 
Bitumens. 
Tars. 

Paving brick. 
Stone block. 
Asphalt block. 
Wood block. 
Stone or brick cubes. 
Location and quality. 

A convenient method of recording the location of materials is 
as follows : 



Water Supply. 



Static Es+. 



/. Oeo.Barber /OOOcu.ycfs. Fence 



Bouiaers 20%6ranite ifo%SandsTorie 
/oxLimesfone 30% son rock 
SO'A of the Granite must he Blasfea 



or 4fcaff9i 



W 



2. Patrick Donlin ZSOO cu.ycfs- same 



€fs apcye 



3. MikeO'Donnell 500 cu VCfs 



/ ya 

Lar^e Qramte Bould erd 7S% must 



'be Blasted 



^, Old Limestone Quarry 20^face 



Samples fakerj'^ looks ^ood for Top Stone 




Pig. 59. 



Unloading Points for Freight. — Provided U. S. geological maps 
are obtainable, the position of sidings may be marked on the 
sheets. The notes for each siding show its car capacity; whether 
or not an elevator plant can be erected, and if hand unloading is 
necessary whether teams can approach from one side or two. 
They should also show any coal trestle that can be utilized in un- 



SAMPLING MATERIALS 269 

loading and the location and probable cost of any new sidings 
that will materially reduce the length of the haul. Canal or river 
unloading points are shown in the same manner. 

Sand, Gravel and Filler Material. — The position of sand and 
gravel pits and filler material are noted with their cost at the pit; 
if no local material is available the cost, f.o.b. at the nearest siding 
is given. Samples are taken and tests made. 

Stone Supply. — Provided imported stone is to be used the work 
is simplified to determining the rate, f.o.b. to the various sidings 
for the product of the nearest commercial stone-crushing plant 
that produces a proper grade of stone. 

In case local stone is available the location of the quarries or 
outcrops is shown; the amount of stripping, if any, and the cost 
of quarry rights. If the estimate will depend upon rock owned 
by a single person an option is obtained to prevent an exorbitant 
raise in price. 

In case of field or fence stone a careful estimate is made of the 
number of yards of boulder stone available, the owners' names, 
what they will charge for it, the position of the fences or piles 
relative to the road, or side roads, and if the fences are not abutting 
on a road or lane the length of haul through fields to the nearest 
road or lane. As fences are usually a mixture of different kinds 
of rock, the engineer estimates the percentage of granite, limestone, 
sandstone, etc., and the percentage that will have to be blasted 
or sledged in order to be crushed by an ordinary portable crusher. 
The amount of field stone required per cubic yard of macadam 
is given in estimates, page 593. If there is a large excess of stone a 
careful estimate need not be made, only enough data being collected 
to determine the probable position of the crusher set-ups and the 
average haul to each set-up. If a sufficient supply is doubtful 
a close estimate is made as outlined above, and options obtained from 
the various owners. 

Samples of the different rocks are tested (see "Materials"). 

Simple field tests can be made but if the department has a testing 
laboratory it is better to take samples and have a careful test made 
and recorded. As these tests are made the location of the sample 
and result of the tests are recorded on a large map of the district 
which in the course of a few years shows at a glance the different 
sources of supply of acceptable materials for the entire county 
or State and saves future duplication of work for reconstruction, 
maintenance and adjacent improvements. 

The method of sampling and the amounts of material required 
for a good test are quoted below from the New York State Instruc- 
tions for Sampling Materials, 

SAMPLING 

Samples of material will be taken by a duly authorized employee of the 
Department, in its place of occurrence or manufacture or delivery by 
carrier. These samples must be taken from different parts of the lot of 
material to be tested, so as to be fairly representative, and must be unmixed 
with foreign substances and placed in clean and safe receptacles; and they 
must conform in all respects to the requirements given under the special 



270 PRELIMINARY INVESTIGATIONS 

headings. They must be carefully and securely packed, enclosing notifica- 
tion slip properly protected from wear and injury, and sent by express 
" collect " to the " Bureau of Tests, State Highway Commission, Albany, 
N. Y.'! a postal card notice being mailed at the same time. Envelopes, 
scoops, cans, thermometers, etc., for use in taking the samples, may be 
had from the Bureau of Finance and Audit at Albany. 

In the case of materials sampled at place of manufacture, check samples 
may be required; these are to be taken and treated the same as ordinary 
samples, except that the packages must be marked "Check Samples," 
and the use of the material needed not be prohibited pending the results of 
the check tests. 

Sand and Gravel. — The character of the supply, whether from stream 
bed, bank, crusher bins, etc., is to be stated; also the use for which it is 
intended, whether for concrete foundations or other structures, binder 
for waterbound macadam, filler or wearing carpet or blotter for bituminous 
macadam, or for aggregate in waterbound or bituminous macadam, etc. 

Material which will all pass through a H in. screen will be considered 
sand. Each sample of sand or screenings shall be H cu. ft. in volume; of 
gravel iH cu. ft. 

A small sample shall be taken from each test sample sent, and be kept 
on the contract as a measure of the quality of material. 

Each sample is to be shipped in a tight box or in a clean, closely woven 
bag from which there will be no leakage; the usual identification slip is to 
be enclosed. ^ In numbering samples, sand and gravel are to be treated 
as one material, not as two. 

Notification of acceptance or rejection may be expected to arrive at the 
Division office twenty days after the submission of the samples and data, 
providing the need of a retest does not cause delay. 

Cement. — One sample is to be taken from at least every ten barrels or 
every forty bags, care being taken to properly distribute the sampling over 
the lot. Each sample shall be not less than 27 cu. in. in volume or enough 
to fill a 3 in. cube. Whenever possible, samples should be forwarded in 
envelopes furnished by the Commission for that purpose, the envelopes 
being filled to the Une marked thereon. 

The individual samples are not to be numbered, but each group or lot 
of these samples representing a single boat load or car load is to be given a 
lot number, and these lot numbers are to run consecutively. Not more 
than one boat load or car load is to be reoresented by one lot number. 

Receipt of notification of acceptance or rejection of cement sampled at 
destination may be expected to arrive at the Division Engineer's office 
twelve days after the submission of the samples and data. ^ If cement is 
held for twenty-eight day tests the Division Engineer will be notified 
accordingly. 

Concrete. — The concrete on each highway must be sampled for testing, 
the samples being taken at rand om from the batches used and being molded 
at the place and time of mixing. The work need not be delayed pending the 
results of the tests. 

Each sample shall be a pair of cubes measuring 6 in. on the edge or of 
cylinders 8 in. in diameter and 16 in. long; the sample is to be made in such 
manner as to fairly represent the concrete going into the structure. ^ At 
least one sample is to be taken, and as many more as seem to be required 
by changes in the character of any ingredient or by any other consideration. 

In concrete pavement work (whether foundation or top course) one pair 
of cubes or cylinders should be sent for every 500 cubic yards. Not less 
than two pairs are to be sent, however small the pavement. 

The sample must remain in the mold two days, then be buried in clean 
sand to age under the same conditions as the material in the structure. 
On the twenty-first day the samples shall be taken out and shipped. 

Each sample is to have its number painted on each piece, and is to be 
shipped in a box, properly protected from breakage and surface chipping, 
accompanied by the usual included identification slip and the postal notifi- 
cation. ^ Especially must the class of concrete, the purpose for which it is 
used (kind of structure and portion), and the date and time of day when 
sample was mixed, be stated. 

Bituminous Material. — When material is shipped in barrels one sample 
is to be taken for every twenty or twenty-five barrels, the sampling being 
properly distributed over the lot. 

When material is shipped in tank cars one sample is to be taken from 



SAMPLING MATERIALS 271 

every 2000 or 2500 gallons, the samples being taken from equally dis- 
tributed levels in the car. 

When mineral bitumen is shipped in loose bulk, one sample is to be taken 
for every five or six tons, the samples being taken from different levels and 
different vocations in the lot and never from the surface of the material. 

Each sample shall be not less than 14 cu. in. in volume, which volume is 
slightly less than one-half pine or about the size of a one pound paint can. 

It should be remembered that the bituminous material will flow at summer 
temperature or thereabouts, and consequently great care should be used in 
sealing cans and doing up packages. Whenever possible, samples should 
be forwarded in the cans furnished by the Commission for the purpose. 

The individual samples are not to be numbered, but each group or lot 
representing a single boat load or car load is to be given a lot numlDer, and 
these lot numbers are to run consecutively; not more than one boat load 
or car load of material is to be represented by one lot number. 

In order to check the weighing and marking of bituminous material 
shipped in barrels, one unopened barrel out of every car load of approxi- 
mately 65 barrels, or a proportionate number of barrels for each boat load, 
is to be selected at random and weighed. The gross weight found, and the 
gross weight marked on the barrel, are to be entered on the Monthly Bitu- 
minous Material Reports or the information rnay be recorded elsewhere 
and submitted to the Bureau of Tests. Any noticeable difference between 
the gallonage marked on a barrel and the gallonage found therein, must be 
reported to the Headquarters office at Albany.^ 

The unit of measure for bituminous material is the gallon measured at 
the temperature of 6o°P. If the volume of material is measured when 
hot, allowance should be made for expansion according to the following 
table, which will apply approximately to all of the different classes of bitu- 
minous material at present used oil the State highways: 

Increase in volume of various classes of bituminous material when heated 
from 6o°F. 

To 400°F. is approximately 12 per cent. 
To 350°F. is approximately 10 per cent. 
To 300°F. is approximately 8 per cent. 
To 250°F. is approximately 6 per cent. 
To 200°F. is approximately 4 per cent. 
To I50°F. is approximately 2 per cent. 

Stone. — Rotten or partially disintegrated stone, or weathered specimens 
from the surface of a quarry or ledge, are not to be submitted. 

Samples ot quarry or ledge stone must be representative of the sound, 
fresh, interior stone of the ledge or quarry. Such samples may be secured 
either by blasting or by breaking up with the sledge. If all material is 
of the same variety, texture, etc., one sample will suffice. If, however, 
there are different varieties, separate samples are to be taken of each and 
report made as to the extent, giving details as to location and position for use. 

All field stone, whether in walls, piles, or scattered over the ground, 
which might be used, must be examined and a representative sample taken. 
When two or more varieties of great difference in quality or texture are 
observed to exist, separate samples are to be taken of each, and report made 
as to the percentage of each kind, the amount of small stone which might 
run through the crusher without action, and the percentage of disintegrated 
or badly weathered rock present. 

In taking samples from the output of crushers, fifteen pounds of crushed 
material not smaller than i}4 in. in size shall be taken, and also one piece 
at least 3 X 4 X S in. shall be procured from the source of supply. 

Each sample shall weigh not less than twenty-five pounds nor more than 
thirty-five pounds. If the entire sample submitted is a single piece of 
stone, it should be remembered that a piece about the size of a man's head 
will weigh twenty-five or thirty pounds. While not less than twenty-five 
pounds are absolutely necessary in each sample, care should be taken to 
see that the samples do not weigh over thirty-five pounds. One piece of 
each sample shall be at least 3X4X5 inches. 

Each sample is to be given a number running consecutively in each 
Division. This number must contain both the Division number and the 
sample number; thus, sample No. 42 from Division No. i would be rnarked 
"1-42." Paint or Higgins drawing ink may be used to mark directly 
on the sample, or a label or tag may be securely fastened thereto. 



272 



PRELIMINARY INVESTIGATIONS 



Samples maj'- be shipped in boxes, burlap, grain bags, cement bags, etc. 
It is preferred that stone be shipped in a strong bag or in a double bag 
which may be formed by placing one bag inside of another. If shipping in 
a single ''>ag which the sample only partially fills, the bag should be securely 
tied just above the sample and the remaining unfilled part of the bag folded 
back so as to completely envelop the stone and the portion of bag contain- 
ing it; this folded back part should then be securely tied on the other side 
of the sample; this makes a tying of the bag on two sides of the stone, 
and permits two thicknesses of the bag to completely surround the stone, 
and if securely tied is as satisfactory as a double bag. 

Receipt of notification of acceptance or rejection of stone may be expected 
to arrive at the Division Engineer's office twelve days after the submission 
of the samples and data, provided acceptance or rejection is not deferred 
awaiting a retest. 

The location of source of supply is to be expressed by an index number 
according to the system used in the Government Office at Washington, 
which is, that each quadrangle of the U. S. Geological Survey Sheet is 
divided into nine sections numbered from i to 9 inclusive, as shown in the 
following plan: 



1 2 3 

4 5 6 

T 8 9 



The north and south sides of each section are then divided into 22 spaces 
designated from A to V and the east and west sides into 32 spaces designated 
I to 32, so that the location of the stone may then be closely defined, as 
for example, Quadrangle Albany, Section 7, Letter J, Number 13, which 
when abbreviated would read " Albany-7-J-i3." 

Paving Brick. — A sufficient number of samples in every case is to be 
taken to insure the use of brick of proper quality, but it should also be borne 
in mind that the charges for transportation and testing of brick are high, 
and only the smallest number of samples necessary for this purpose should 
be submitted. At least one sample is to be taken from every 200,000 brick 
or less. Each sample shall consist of 30 bricks. 

If in a shipment or several shipments of the same make and kind of brick 
there appear to be different classes of brick — such as brick of different de- 
grees of burning, for example — a full sample of each class is to be taken. 

Each brick selected for the sample is to be free from cracks or other 
defects which would prevent its passing inspection at the road, for the sample 
must represent bricks which will not be culled out. Especially is it for- 
bidden that any person financially interested in the manufacture or use of 
brick be present when samples are taken. 

Each sample (consisting of 30 bricks) shall receive a number, the numbers 
to run consecutively for each road. 

The sample shall be shipped in wooden boxes, not more than 10 or 12 
bricks being put in one box on account of weight and strength of package. 

Notification of acceptance or rejection of brick sampled at destination 
may be expected to arrive at the Division Engineer's office nine days after 
submission of samples and data, providing the need of a retest does not 
cause delay. 

Asphalt Block. — A sufficient number of samples in every case is to be 
taken to insure the use of block of proper quality, but it should also be borne 
in mind that transportation and testing costs are high, and only the smallest 



COST ESTIMATES 273 

number of samples necessary should be submitted. At kast one sample is 
to be taken from every 100,000 blocks or less. Each sample shall consist 
of 2 blocks. 

If in a shipment or several shipments of the same make and kind of block 
there appear to be different classes of block, a full sample of each class is 
to be taken. 

Each block selected for the sample is to be free from every defect that 
would prevent its passing inspection at the road, for the sample must 
represent blocks which will not be culled out. 

Each sample (consisting of 2 blocks) shall receive a number, the numbers 
to run consecutively for each road. 

The sample shall be shipped in a wooden box, with usual identification 
card and postal notice. 

Notification of acceptance or rejection of block sampled at destination 
may be expected to reach the Division Engineer's office fourteen days after 
submission of samples and data, providing the need of a retest does not 
cause delay. 

Acceptance 

Upon completion of the testing of any set of samples the Division Engi- 
neer is notified of the acceptance or rejection of the material, and transmits 
the statement to the engineer in charge of the contract. 

Estimates of Cost. — The length of the road can be obtained from 
maps (U. S. G. S. are convenient) or by autometer distances or 
pacing. Maps are generally available and serve as a convenient 
basis for notations. A field inspection by one man preferably 
on foot furnishes the necessary data on required drainage, founda- 
tion soils, approximate amount of excavation, condition of existing 
bridges and all special features. 

Minor drainage features can generally be lumped and assumed 
to run about $700 per mile. (For more detailed cost, estimate each 
culvert separately. See chapter on ''Drainage.") Special bridges 
must be figured in detail. (See chapter on " Drainage for 'Standard 
Design," etc.) 

The amount of excavation per mile for ordinary rolling topog- 
raphy is entirely a matter of judgment which can only |be 
developed by personal experience in similar work. For special 
long hills requiring a cut and fill reduction a rough profile can be 
run with an Abney level. However the item of excavation on 
macadam roads rarely exceeds 20% of total cost and considerable 
error in estimating the yardage will not greatly effect the value of 
the estimate. 

The character of the natural road soil has an important bearing 
on the depths of macadam and must be carefully recorded. This 
can best be done by giving the character of the soil; noting whether 
the improved road will probably be in cut or fill at the points 
recorded and specifying the recommended depths of macadam. 
The depths of macadam for different classes and traffic and dif- 
ferent soils were indicated in Chapter V, page 152. Sample notes 
on foundation soils are shown on page 330. 

Methods of computing pavement costs are given in Chapter XIV. 

The sample preliminary report following illustrates the method 
to be followed for high type roads. A report of this character 
will rarely differ from the final cost of construction by more than 
15%. While photographs increase the value of these reports 



274 PRELIMINARY INVESTIGATIONS 

they are not as essential as for new locations. Notes on photography 
are given in Chapter XII. 

PRELIMINARY DESIGN REPORT, NEW CONSTRUCTION 

December lo, 1914. 
Division Engineer 
Dept. of Highways, 
Dear Sir: 

In accordance with your request on Nov. 25th, find 
enclosed report on a reasonable cost for the Town Line-Manitou 
State-County Highway. 

General Report and Estimate, Town Line-Manitou State -County 

Highway 

With a proper use of local materials a satisfactory 
road can be built at a cost of $94,000 or approx. $11,000 per mile 
including Engineering and Contingencies. An expenditure of 
$1 2,000 per mile would not however be excessive. 

• The Braddocks Bay crossing is the expensive feature 
of this road; it raises the cost of the entire road about $1000 per 
mile. 

Design No. i is recommended (see page 280). 
A detail report follows. 

Signed, 

Designing Engineer. 

DETAIL REPORT AND ESTIMATE, TOWN LINE-MANITOU STATE- 
COUNTY HIGHWAY 

Length. — Eight and fifty-one hundredths miles from the Ridge Road to 
Manitou Beach. 

Foundation SoiL— ;-Heavy soil, not particularly good foundation Sta. 
o to 133; sandy soil balance of distance except across Braddocks Bay, 
A 9 in. thickness of some form of macadam is advisable Sta. o to 133; 7 in. 
or 8 in. the balance of the distance should be satisfactory except across 
Braddocks Bay where it is safe to figure on 12 in. to 15 in. of stone. 

Grade. — The present surface can be followed closely. The excavation 
should not exceed 2800 cu. yd. per mile except across Braddocks Bay; a 
rough estimate of borrow excavation for this fill is 15,000 cubic yards. 

Alignment. — Good; no right-of-way required except possible at Sta. 350 
near the schoolhouse at the turn to Manitou. 

Traffic and_ Section. — There is a heavy volume of automobile pleasure 
traffic and a light volume of heavy hauling traffic on this road. 

The large amount of pleasure travel requires from 16 ft. to 18 ft. of stone 
surface; the heavy hauling does not require over 12 ft. to 14 ft. full depth 
rnetaling. We recommend a graded section 26 ft. to 28 ft. wide between 
ditches in cut with a 12 ft. width of full depth metal with 6 ft. of extra 
width of local crusher run on the shoulders Sta. o to 133; a 14 ft. width with 
4 ft. of stone on shoulders 5ta. 133 to 260; a width of 12 ft. of full depth 
metal with 6 ft. of stone on shoulders the balance of the distance except 
across Braddocks Bay where the entire width of metaling 16 ft. should have 
the full depth. 

This road carries so much high speed traffic that it requires some form 
of bituminous macadam or if Waterbound is selected, it should be treated 
with calcium chloride immediately and have a surface coat of bitumen 
applied early in the next year. 



SAMPLE REPORT 275 

Railroad Crossings. — Sta. 223 R. W. & O. Ry. crossing; no gates or flag- 
man. In the summer time the crossing should have a flagman as the 
orchards cut off the view. The crossing is not particularly dangerous, but 
during the season of the year the traffic on this road is entitled to better 
protection at this point. 

The approach grade from the south should be made easier. 

Drainage. — No special features; approximate cost $3500 exclusive of 
bridges above 5 ft. span to be built by the towns. 

Dangerous Places. — The Braddocks Bay crossing is a dangerous one 
as the fill is high and the swamp is full of semi-fluid muck from 6 ft. to 12 ft. 
deep; a first-class concrete guard rail protection should be provided. 

Materials 

Filler Sand. — In abundance along road and from roadbed excavation. 

Gravel. — The only good gravel is lake gravel; this can be obtained up 
to approximately 6000 cu. yd. i3^ miles north of Sta. 350 and 3000 cu. yd. 
3^^ mile west of Sta. 450. Probably this can be used to advantage (screened 
or selected beach run) as bottom course Sta. 350 to 450 or as filler for sub- 
base bottom and on the shoulders. 

Stone. — Fifteen thousand cubic yards of fence stone are available within 
a mile and a half of the road Sta. o to 133. 

There is practically no local stone Sta. 133 to 350. Four thousand cubic 
yards of fence stone are available within i3^ miles of Sta. 350. 

This material runs about 20 % granite fit for top and the balance soft 
sandstone fit for bottom either as a sub-base bottom or crushed stone bottom. 

There is sufficient stone at the south end of the road to build a sub-base 
bottom with crushed stone filler; a local granite top with crushed stone on 
the shoulders from Sta. o to 133 and a local crushed stone bottom 5 in. 
thick Sta. 133 to about Sta. 200. 

There is sufficient stone at the north end to build about 1% miles of 
crushed stone bottom with stone on shoulders or ij^i miles of sub-base 
bottorn with crushed stone filler and crushed stone on shoulders. I do 
not think there is enough granite to make it worth while to try and use a 
local top on any part of the north end. 

It is probably better to use an imported top from Sta. 133 to 450 and 
imported bottom Sta. 200 to 280. (See detail Stone Statement and Com- 
putations following.) 

Crusher Set up at Sta. 100. — Fifteen thousand cubic yards field stone 
available within 3 miles maximum haul. Average haul 1}^ miles. 

Assume for safety that only 11,000 cu. yd. are available with an average 
haul to crusher of i mile. 

Of this 11,000 cu. yd. field stone. 

3000 cu. yd. used for sub-base bottom average haul 3^^ mile. 

xooo cu. yd. used for crushed stone filler { l^, f^^^^ctle^ « mile. 

,00 cu. yd. used for crushed stone shoulders { h^i ^^.^crushe^^ H^e. 

.500 cu. yd. used for top course { ^-1 t^^-^tYh^ri' mile. 

7200 CU. yd. field stone used for local macadam, from Sta. o-to 133, leaving 
3800 cu. yd. available for crushed bottom and shoulder stone for road north 
of Sta. 133. 

Three thousand eight hundred cubic yards will produce approximately 3000 
cu. yd. of crushed bottom loose measure or about 2300 cu. yd. of rolled 
measure. This will build 10,600 lin. ft. of 5 in. bottom 14 ft. wide. We 
can therefore safely specify local bottom to Sta. 200 which will leave enough 
shoulder stone to use as far north as Sta. 300 if necessary. 

Crusher Set up at Sta. 350. — Four thousand cubic yards available within 
1 3'^ miles say average haul i mile. 

Assumefor safety that 3000 cu. yd. only are available, average haul i 
mile. This will produce about 2400 cu. yd. crushed bottom stone loose 
measure or approximately 1800 cu. yd. rolled measure. One thousand eight 
hundred cubic yards will build approximately 90 Sta. of 12 ft. bottom 5 
in. deep which makes it safe to specify a local bottom using crushed stone 
and lake gravel as far south as Sta. 280 with either gravel or crusher run 
the entire length of road on the shoulders. 

Imported bottom should be used Sta. 200 to 280. 



276 



PRELIMINARY INVESTIGATIONS 



Imported Stone. — One dollar and twenty-five cents per ton f.o.b. switch. 
Switch can be built at Sta. 233 for I300 to $400. 

Water. — Can be obtained at all seasons at intervals from i mile to 11^2 
miles all along the road. 

Cost of Different Types 

Grubbing and clearing $ 300 . 00 

23,000 cu. yd. roadbed excavation @ $0.50 11,500.00 

15,000 cu. yd. brow exc. across Braddocks Bay @, $0.45 6,750.00 

800 cu. yd. sub-base @ $1 .25 1,000.00 

4,000 lin. ft. concrete G. R. across Braddocks Bay @ $1 .00.. . . 4,000.00 

Drainage of system 3,500 . 00 

Minor points @ 400 per mile 3,400 . 00 

Engineering and contingencies ^ 8,000 .00 

Total cost of items other than metaling $38,450 .00 

Schedule of Unit Prices 

Imported waterbound top Sta. 133 to 450 $5 .00 per cu. yd. rolled 

Imported bit. mac. top Sta. 133 to 450 7.30 per cu. yd. rolled 

iLocal granite bit. mac. top Sta. o to 133 6.00 per cu. yd. rolled 

^Imported limestone water mac. Sta. o to 133 5- SO per cu. yd. rolled 

Sub-base bottom crushed stone filler o to 133 i .50 per cu. yd. rolled 

Local crushed bottom Sta. 133 to 200 2 ,50 per cu. yd. rolled 

Imported mac. bottom Sta. 200 to 280 3 .20 per cu. yd. rolled 

Local crushed bottom Sta. 280 to 350 2 .30 per cu. yd. rolled 

Lake gravel bottom Sta. 350 to 450 i .90 per cu. yd. rolled 

Crushed stone or gravel on shotilders i . 50 per cu. yd. loose 

Tarvia B 0.08 per gal. in place 

Table of Comparative Cost 1 



Type 


Approx. Cost Including 
Eng. and Contingencies 


Cost per 
Mile 


Total Cost 


Design No. i (for details see Cost Estimate 
Sheet) 


$11,000 
11,300 
12,000 
12,500 


■■$ 93,500 

96,200 

102,200 

106,000 


Design No. 2 (for details see Cost Estimate 
Sheet) 


Design No. 3 (for details see Cost Estimate 
Sheet) 


Design No. 4 (for details see Cost Estimate 
Sheet) 





Computation of Unit Prices 
Overhead approximately 30c. per cubic yard of bottom and top stone* 
No overhead estimated on other items. 

Sub-base Bottom Course Crushed Stone Filler Sta. to 133 

Cost of stone in fences $0.10 

Loading 0.15 

Hauling 3^^ mile 0.12 

Placing and sledging o . 20 

Rolling 0.05 

Crushed stone filler. (See Filler) 0.35 cu. yd. . : o .40 

$1.02 

20 % profit O . 20 

Overhead . 30 

Estimate ' $1 .52 

Say $1.50 
1 There is no difference in cost Sta. o to 133 between a local granite bit. mac. 
top and an imported limestone waterbound top when treated with Tarvia B, 



SAMPLE REPORT 277 

Crushed Stone Filler (Crusher Run) 

Per Cu. Yd. 

Cost of stone in fences $0.10 

Loading 0.15 

Haul to crusher i mile 0.35 

Crushing o.io 

Cost in bins $0 . 70 

Loading to wagons o. 01 

Haul to road f^ mile 0.22 

Spreading and brooming o. 20 

I1.13 

0.35 cu. yd. per yard of sub-base = $0.40 

Local Crushed Stone Bottom Sta. 133 to 200 

Cost in bins $0.70 

Loading to wagons o.oi 

Hauling to road i^^i miles o .40 

Spreading o. 06 

Rolling 0.05 

$1 .22 
Consolidation 0.3 o .37 

Si. 59 
Filler 0.20 

$1.79 

20 % profit o. 36 

Overhead 0.30 

Say I2.50 I2.45 

Stone on shoulders %i .50 per cu. yd. loose. 

Local Granite Bit. Mac. Top Sta. to 133 

Stone in fences So . i o 

Loading 0.15 

Blasting and sledging 0.15 

Hauling to crusher ^ 0.35 

Crushing 0.15 

$0 . 90 in bins 

Loading to wagons o.oi 

Hauling to road ^^ mile . . 0.22 

Spreading o . 06 

Rolling 0.08 

Si. 27 
Consolidation 0.38 

Si. 65 

Screenings No. 2 and Bit 3 . 10 

Profit o. 90 

Overhead 0.30 

Estimate Ss • 95 

Say S6.00 ^ 

No. 2 Screenings and Bitumen. Note: There should be enough local 
screenings for about ^^3 of the top course. Use imported for the balance. 

Cost o .45 cu. yd. screenings and No. 2 at bin $0.40 

Hauling ^^ mile o . 10 

Spreading 0.12 

Manipulation 21 gal. bitumen @, i^^c 0.32 

Cost 21 gal. bitumen on road @ 8>^c i . 82 

$2 . 74 



278 PRELIMINARY INVESTIGATIONS 

Imported Screenings and No. 2 

Cost o . 45 cu. yd. f.o.b. switch @ $1.25 per ton $0 . 70 

Unloading o . 05 

Hauling 3 miles . 90 

Spreading 0.12 

Manipulation 21 gal. bitumen @ ij'^c o .32 

Cost 21 gal. bitumen on road @ Sj'^c i . 80 



13-89 
Average price $3 ■ 10 

Imported Limestone Waterbound Mac. Sta. o to 133 
Materials: 

4400 lb. of stone @ $1 . 25 per ton I2 . 75 

6 % profit . 0.15 



I2.90 
Labor: 

Unloading |o . 10 

Hauling 3 miles @ |o . 25 o . 75 

Spreading 0.08 

Rolling and puddling o . 10 



$1 .03 
Consolidation 0.3 0.31 



$1.34 

Screenings 0.55 

20 % profit 0.38 

Overhead o . 30 

Materials 2 . 90 



Estimate $5-47 

Screenings: 

Unloading |o . 05 

Hauling 3 miles o . 40 

Spreading and brooming o . 10 



I0.55 



Imported Limestone Waterbound Mac. Sta. 133 to 450 

Materials S2 . 90 

Labor: 

Unloading o.io 

Hauling 90 sta. iH miles 9.55 

Spreading 0.08 

Rolling and puddling o.io 



I0.83 
Consolidation o . 25 



$1.08 

Screenings 0.45 

20 % profit o . 30 

Overhead 0.30 

Materials 2 . 90 



Estimate $5 . 03 

Say S5.00 
Screenings: 

Unloading $0.05 

Hauling i^i miles. 0.30 

Spreading and brooming o.io 

$0.45 



SAMPLE REPORT 279 

Imported Limestone Bituminous Macadam Sta. 133 to 450 

Materials: 

4200 lb. @, $1.25 f.o.b. per ton $2 .62 

6 % profit 0.15 



$2.77 
Labor: 

Unloading $0.10 

Hauling 0.55 

, Spreading 0.08 

Rolling 0.08 

$0.81 
Consolidation 0.3 . 24 

$1.05 

Screenings and bitumen $2 . 52 

20 % profit o . 70 

Overhead 0.30 

Materials 2.77 

Estimate I7 • 34 



Screenings No. 2 and Bitumen 

Unloading $0 . 05 

Hauling * 0.25 

Spreading and brooming 0.12 

21 gal. bitumen A. @ S}r^c i . 78 

Manipulation of bitumen 0.32 

$2.52 



Imported Limestone Bottom Sta. 200 to 280 

Materials: 

3200 lb. stone @ I1.25 per ton $2 .00 

profit o . 10 

Total materials $2.10 

Labor: 

Unloading $0.10 

Hauling average distance, 20 sta 0.15 

Spreading o . 06 

Rolling o . OS 

$0.36 
Consolidation 0.3 o . 1 1 

$0.47 
Filler o . 20 

$0.67 

20% profit . 0.13 

Overhead o . 30 

Materials 2.10 

$3 . 20 



28o PRELIMINARY INVESTIGATIONS 

Local Stone Mac. Bottom Sta. 280 to 350 

Stone in fences $0.10 

Sledging o . 05 

Loading 0.15 

Hauling to crusher i mile o .35 

Crushing 0,12 

Cost in bins $0.77 

Loading to wagons o . 01 

Haul to road o . 7 mile 0.22 

Spreading o. 06 

Rolling 0.05 

$1.11 
Consolidation 0.3 o. 33 

$1.44 
Filler o. 20 

$1.64 

20 % profit 0.33 

Overhead 0.30 

Say $2.30 $2.27 

Lake Gravel Bottom Sta. 350 to 450 
Assume j^i material from Manitou Beach. 
Assume % material from beach 1}^ miles north of Sta.'^^so. 

Selected Beach Run of Gravel 

Cost on beach |o . 10 

Loading 0.15 

Hauling average 2 miles 0. 70 

Spreading 0.05 

Rolling o. 04 

Loam and flushing o. 05 

|i .09 
Consolidation 0.2 0.22 

$1.31 

20 % profit o. 26 

Overhead 0.30 

$1.87 
Say $1.90 

Approximate Cost Estimates 

Design No. i. 

ii2' wide 6'' sub-base 3" bit. mac, local top 6' of stone on 
shoulders. Treated with Tarvia B or No. 4 road oil. Sta. 
o to 133. 
14' wide 5" local mac. bot. 3" waterbound imported lime- 
stone top. Treated with Tarvia B. 4' stone on shoulders. 
I Sta. 133 to 200. 
c, ^ / 14' wide 5" imported bottom; same top as from Sta. 133 to 

£»ec. iNO. 3 ^ 200 Sta. 200 to 260. 4' stone on shoulders, 
c ^ / 12' wide 5" imported bottom 3" water imported top Tarvia B. 

oec. iNO. 4 <, ^, q£ g^Qj^g Qj^ shoulders. Sta. 260 to 280. 
c: M c / 12' wide 5" local mac. bottom 3" water imported top Tarvia 
aec. iNO. 5 \ ^ 5/ stone on shoulders. Sta. 280 to 310. 
q ]ST /- f 16' wide 9" sub-base bottom 3'' water mac. top Tarvia B.- 
vsec. iNO. o j j^Q stone on shoulders. Sta. 310 to 335- 

q ATp, « / 12' wide 5" local mac. bottom 3" water mac. top Tarvia B. 
oec. iNO. 7 <i ^, q£ g^Qj^g ^^ shoulders. Sta. 335 to 350. 
q >^ j> f 12' wide s" lake gravel bottom 3" water mac. top Tarvia B. 
C5ec. iNO. 5 <j^ ^f q£ gj-avel or stone on shoulders. Sta. 350 to 450. 



SAMPLE REPORT 281 

Approximate 

Sec, I. Sia. o to I33 Amount 

3000 cu. yd. 6" sub-base bottom @ $1.50 $4500.00 

1500 cu. yd. 3" bit. mac. (local) top'@ $6.00 9000 .00 

730 cu. yd. stone on shoulders (loose) @ $1.50 1100.00 

3500 gal. Tarvia B on stone shoulders @ $0.08 280 .00 

Sec. 2. Sta. 133 to 200 

1450 cu. yd. 5" local mac. bottom @ $2.50 $3625 .00 

870 cu. yd. 3" imported waterbound top @ $5.00 4350.00 

270 cu. yd. stone on shoulder @ $1.50 405 .00 

5400 gal. Tarvia B @ $0.08 430 . 00 

Sec. 3, Sta. 200 to 260 

1300 cu. yd. 5" imported bottom @ I3.20 $4150.00 

780 cu. yd. 3" imported water mac. top @ $5.00 3900.00 

240 cu. yd. stone on shoulders @- $1.50 36Q .00 

4800 gal. Tarvia B @ $0.08 385 00 

Sec. 4. Sta. 260 to 280 

370 cu. yd. 5" imported bottom @, $3.20 $1185.00 

230 cu. yd. 3" imported water mac. top @ $5.00 1150.00 

no cu. yd. stone on shoulders @ $1.50 165 .00 

1600 gal. Tarvia B @ $0.08 130 . 00 

Sec. 5. Sta. 280 to 310 

560 cu. yd. 5" local bcttiom @ $2.30 $1290.00 

340 cu. yd. 3" water mac. top @ $5-00 1700.00 

170 cu. yd. stone on shoulders @ $1.50 255 .00 

2400 gal. Tarvia B @ $0.08 190 . 00 

Sec. 6. Sta. 310 to 335 

1 130 cu. yd. 9" sub-base bottom @ $i.75 $1980.00 

380 cu. yd. 3" water mac. top @ $5.00 1900 . 00 

1800 gal. Tarvia B @ $0.08 , 145 .00 

Sec. 7. Sta. 335 to 350 

280 cu. yd. 5" local bottom @ $2.30 $ 645 .00 

170 cu. yd. 3" water mac. top @ $5.00 850.00 

80 cu. yd. stone on shoulders @ $1.50 120.00 

1200 gal. Tarvia B @ $0.08 95 00 

Sec. 8, Sta. 3S0 to 450 

1900 cu. yd. 5" lake gravel bottom @ $1 .90 $3,600 .00 

1 150 '• " 3" water mac. top @ $5.00 5,7SO.oo 

550 '* " gravel on shoulders @ $1 .50 825 .00 

8000 gal. Tarvia B. @ $0 . 08 640 . 00 

Totals $55,100 . 00 

Items other than metal 38,450 .00 

Total estimates $93,550 .00 

Design No. 2. Same widths and foundation construction as Design No. i 
except that a 2K" imported limestone bituminous macadam is substituted 
for the 3" waterbound top treated with Tarvia B. 

Cost of 3" water mac. top Design No. i $19,600 .00 

Cost of Tarvia B. on mac. top Design No. i 1,500 .00 

Total $21,100.00 

Cost of 2>^" bit. mac. top 23,800 .00 

Increased cost Design No. 2 over No. i $ 2,700 .00 

Design No. 3. 16' road entire distance local bottom Sta. o to 200 and 
280 to 450 and imported bottom Sta. 200 to 280 with 3" imported water- 
bound macadam treated with 0.4 gal. Tarvia B. or 0.25 gal. No. 4 Road Oil. 

9,200 cu. yd. local bottom 5" thick @ $2 . 25 $20,700 .00 

1,970 " " imported bottom 5" thick @ $3.20 6,300.00 

6,700 " " imported top 3" thick @ $5.10 34,200.00 

32,000 gal. Tarvia B. @ $0.08 2,560.00 

$63,760.00 
Items other than metaling 38,450 .00 

$102,210,00 



282 PRELIMINARY INVESTIGATIONS 

Design No. 4. Substitute a 2J4" bit. mac. top for the 3" waterbound 
top of Design No. 3. This increases the cost approx. $4,000. 

Signed, 

Designing Engineer. 

PRELIMINARY INVESTIGATIONS FOR ROADS IN UN- 
SETTLED DISTRICTS 

Reports of this nature can not be figured as accurately as for 
high type roads but if carefully done should not vary over 25% from 
the final construction cost. The cost of preliminary investigations 
depends very largely on the character of the country, the methods 
employed, and the travel necessary to get to the work and will 
range from $2 to $40 per mile. A fair average cost for work similar 
to that done by the U. S. Office of Public Roads in the mountainous 
districts of the west is $5 per mile for ordinary cases and $30 per 
mile for a plane table sketch survey in difficult country. 

Ordinary Preliminary Investigations. — The improvement to be 
investigated generally consists of a combination of betterments of 
existing roads with a large percentage of relocation of the old road 
or the new location of a highway where no road of any kind traverses 
the territory. The length of these projects range from 5 miles 
to 150 miles. The engineer generally receives orders to report on 
the best general route and approximate cost of a road between 
definite terminals which requires more general investigation than 
called for in the preliminary reports on high type roads previously 
discussed. 

The field work is usually made by one or two men on foot or 
horseback. All possible different routes are examined. As a rule 
this general examination eliminates all but one or two possibilities 
which are examined with care; sufficient notes, photographs, etc., 
being taken to make a reasonably close estimate of cost. 

The selection of general route is based on a comparison of the 
following factors for the different routes. 

1 . Best location for the development of the country. 

2. Longest open season for use. 

3. Least rise and fall. 

4. Feasible ruling grades. 

5. Length and cost. 

The following engineering equipment will cover all requirements 
for obtaining the general data and the detailed information required 
for a reasonably close cost estimate. 

2 Aneroid barometers 2j^"or3''' dial in leather carrying cases. 

Tested for range of altitude needed. 
I Abney level reading to degrees and per cent. 
I Pocket compass 2" floating card dial or, if desired, 
I Prismatic compass (card dial preferred). 
I 4 A Kodak with folding tripod. 
Note books, existing maps, etc. 
In rolling topography it makes no difference in which direction 
the line is traced but where elevation is developed on a ruling grade 
the work should be done from the highest point down hill. 



FIELD METHODS 283 

Where aneroid elevations must be depended on considerable care 
must be exercised. If one aneroid can be left at a stationary point 
and its fluctuations read at intervals during the day very accurate 
results can be obtained when the field aneroid is corrected for the 
fluctuations but this is not feasible for work of this kind as a rule 
and aneroid elevations are to say the least uncertain. Where used 
two instruments should be carried; when reading they should be 
held horizontal and the crystal rapped sharply with the finger nail 
to free the needle if caught which often happens. Any important 
elevations should be determined at least twice and a return trip 
made to the original datum point to check the instrument. 

The general rise and fall can be determined by the aneroids. 

The approximate location of the road for different ruling grades 
can be traced with the Abney level. 

A rough traverse can be run with the pocket compass or pris- 
matic compass. 

Distances can be obtained by pacing (pedometer or hand counter) 
by timing if on horseback; by scaling from reliable maps or by auto- 
meter if on an existing road. 

Cross-sections are determined by the Abney level and are taken 
and recording at sufficient intervals to show the general slope of 
the sidehill. 

Classification of excavation and the cut slopes at which excava- 
tion will stand depends on the judgment of the engineer but must 
be systematically recorded. 

Drainage should be carefully estimated particularly the larger 
structures as this item forms a large percentage of the cost of low 
type roads. 

Clearing and grubbing is recorded by section. 

Each engineer has his own ideas about notes and it makes little 
difference how the data is recorded so long as it is clearly and 
definitely set down in such a way that anyone can retrace the route 
and reestimate the cost without additional field work. 

The main faults of reports and notes are that they are not suffi- 
ciently clear on facts; they generally run strong on generalities 
and judgment and are not worth the paper they are written on if 
the author is not available to explain in detail. 

A well arranged report should either summarize the conclusions 
at the beginning and explain in detail later or be indexed so that 
the conclusions can be readily located. A preliminary estimate 
should be rounded out to even figures as amounts figured to single 
yards or costs figured to odd figures of less amount than 10% of 
the total cost are merely ridiculous and show that the estimator 
has lost track of the relative accuracy of his work. 

The following form of notes serve in a satisfactory way when 
supplemented by photographs, sketches and text descriptions. 

Detail suggestions on photography are given in Chapter XII. 

Table 25 and 26, pages 286 and 296, serve to give a rough ap- 
proximation of the amount of excavation required. 

Drainage costs can be estimated on the standard structures 
required by the State or Government for whom the work is being 



284 



PRELIMINARY INVESTIGATIONS 



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EXCAVATION QUANTITIES 285 

done or can be approximated by reference to the various standard 
structures and costs shown in Chapter III and Table 28, page 298. 
Various miscellaneous information convenient for preliminary 
estimates are given on page 297. A rough approximation of 
magnetic declination can be deterihined from the isogonic charts, 
pages 302 to 308. 

Explanation of Table 25 

Note. — Quantities determined graphically using one way crown 
for single track roads on all cross slopes; the 2 way crown for 
double track roads on cross slopes of 5°, 10° and 15° and the one 
way crown on cross slopes above 15°. 

If for any reason it is desired to use a two way crown on single 
track roads for cross slopes below 15° reduce the quantities shown 
in the table by about 25%. For the use of a two way crown above 
1^5° cross slope, special computations will have to be made. 

To illustrate the use of this table we will figure the approximate 
excavation for the notes shown in Figure 60, page 284. 

From Sta. o to 5 the natural side or cross slope of the ground is 
given as 5°. In this case a turnpike section can be used say T-12. 
Turn to page 286 and under section T-12 for a 5° cross slope we 
find the excavation given as ss cu. yd. per 100' or 165 cu. yd. for 
500 ft. We will increase this 20% according to judgment for profile 
inequalities which gives us 200 cu. yd. earth excavation from Sta. 

to 5. 

From station 5 to 10 we have a 15° cross slope. Suppose we are 
figuring an estimate for a minimum width single track road S-io 
look on page 287 and for a cross slope of 15° and a cut slope of 

1 : I the table gives 46 cu. yd. per 100 ft. or 230 cu. yd. for 500 ft. 
Increase this by say 20% for inequalities in profile which gives us 
276 cu. yd. Estimate the percentage of this classed as rock say 
10% and we have 250 cu. yd. for common exc. and 26 cu. yd. of solid 
rock. 

In a similar way estimate Sta. 10 to Sta. 20. 

From Sta. 20 to Sta. 25 the not€s record a ground cross slope 
of 35°. This calls for a retaining wall section, see page 293, section 
W-8 for a 35° cross slope. The table gives the following quantities 
for 100'. 

55 cu. yd. of wall masonry. 
100 cu. yd. of excavation. 

Multiply this by 5 for 500 feet, add a percentage for inequalities 
of profile and estimate per cent, of solid rock. 

From Sta. 25 to Sta. 30 the notes show a rock ledge with a face 
slope of 50°. This calls for a section benched out of the solid 
ledge. See page 294, use Section S-8 the minimum single track 
section for a cross slope of 50° which gives 350 cu. yd. Rock ex- 
cavation per 100' or 1750 cu. yd. for 500 feet. 

If turnout sections for passing rigs are desired figure the excess 
quantities by referring to the parts of the table dealing with the 
double track widths. 



286 



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QUANTITIES 



293 



-Table 25. — Approximate Quantities Wall Section Minimum 
I Single Track Road Section W-8 

r Double '' '' '' W-12 



1.5 or 2.0 




TYPICAL SECTIONS 
30° & 35° Slopes 

Ditch Excavation Makes 
Fill Back of Wall 



TYPICAL SECTIONS 

40 & 45 Cross Slopes 
Borrow Fill Required 



Note. — Rough rubble masonry walls ,to have outside face batter of 3" to 
i' and a bottom width of 3^ the height. The foundation to be carried to 
a firm strata. 



Natural 

Ground 

Cross 

Slope 


Approximate Quantities per 100' of Road for W-8 SEcnoN 


Wall 
Masonry 


Ditch 
Excavation 
Used in Fill 


Borrow 
Excavation 
for Balance 
^ of Fill 


Wall^ 

Excavation 

Waste 


Total 
Excavation 


•30° 

40° 

45° 


46cu.yd. 
I 55 " ** 
100 *• " 
135 •* " 


55 cu. yd. 
80 " " 
30 " •• 
45 •• " 


None 
None 
90 cu. yd. 
100 " " 


15 cu. yd. 
20 " " 
35 " '• 

45 '* " 


70 cu. yd. 
100 " " 
155 " " 
200 " " 



Table for Minimum Double Track Section W-12 



1 


Approximate Quantities per 100' 


Natural 

Ground 

Cross 

Slope 


Wall 
Masonry 


Ditch 
Excavation 
Used in Fill 

i - 


Borrow 

Excavation 

for Balance 

of Fill 


Wall r^ . 1 


*30° 1 

K 
40° 

45° 


65 cu. yd. 

90 ♦* " 
180 •' " 
250 " •' 

1 


100 cu. yd. 

140 " ** 

30 " " 

45 " " 


None 

None 
200 cu. yd. 
250 " '* 


15 cu. yd. 1 115 cu. yd. 
20 " " 1 160 " *• 

45 " " ; 275 " " 
80 " " 375 *' ** 



Note. — Above 45° ground slope use Rock Bench Sections, except in un- 
usual cases. 

* Retaining wall section on 30° cross slope is not usually economical. 



294 



PRELIMINARY INVESTIGATION 



Table 25. — Table of Approximate Quantities Road 
Benched out of Rock 




TYPICAL BENCH 
SECTION 







Using S-8, S-io, S-12, S-14, 


S-16 




Natural 

Slope of 

Face of 

Rock 

Ledge 


Cut 
Slope 


Approximate Excavation in Cu. Yd. per loo' for 
Different Sections 


*S-8 


S-IO **S-I2 

• 


S-14 


S-16 


50° 
60° 
70° 
80° 


Vertical 

Half 
Tunnel 


350 cu yd 500 cu yd 
600 *• " 850 '• *• 
560 " " 800 " " 
460 " " 550 •' " 


660 cu yd 
1,200 " •* 
1,050 " " 

-680 " " 


870 cu yd 
1,550 " " 
1,400 *' " 


1,100 cu yd 
2,000 ** •* 
1,800 " " 



* Minimum width single track in rock. 
** Minimum width double track in rock. 



Table 26. — Approximate Amounts of Embankment and Ex- 
cavation for Different Center Line Cuts and Fills 
Ground Surface Assumed Level 

(See page 295.) 
Ground Surface Level 




\^-W= 12 to 22— >j 
\<—W^ 14 to 24^' 

' f 

H 
I 



Ground Surface Level 



EXCAVATION' 



295 



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MiOMMCO QO-O lO OMO \Ol-O<N00 M On OsvO t^ 

f*30 O '^00 (N t^ (N t^ CO looo rooo "^ m m \0 O O 

MMM NC^fOfO-^ lOO 00 On M vo Ov rooo ^ 

M M M <N <N ro 


1 


-M 5^ M t^ir)vOO\<N O\t^t>-00P« Tt Tt M o 00 ONoorooo 
jair.. (N looo M lo oo(NvOoio Tf'^irjvooo loiot^ro*-" 
r>J=.M i I-"*-! M(N(Nroro ^t lOO t^oo m -^ t^ m lo 
^C/3 1 M hH M ci CI 

i 


^1? 


l^t^OO-^ vcOO loco MioO'O'^ (NiompoOn 

<NiOO\<NvO OioOn-^On MfOt>i-'t^ (NMiofOiO 

MM (N (N M fO ro »OvO l^ 0\ O ^00 M t^ Ci 

M M M (N cs ro 




5&" 


rooo lo-^Tj- t>Mt^ir>io 0(NNO\"<^ t^oo COO 

CS-'^t^OfO OOfOt^M 00\0\0\M o •^o O t^ 

MM M <N (M OJ ro Tf^^vOoO O r0\O O fO 

M M M <>» « 


(V) M 

m 


-"t O 0» M vO ro '^O <NM l>fOMOO rOMfOOM 

(Nioi^MTt 00<N\OM\O OoOMioO rOMroOM 

MM MtNCsrofO -^lo r^oo O ro l^ M \0 M 

M M M (N (N fO 


Center 1 

Line } D 
Cut J 
in Feet 


looiooio QioOtoO OOOOO OOOOO 
OMM(N<N fOro-^^iO sO 1--00 Oi O (N -^vOoO O 



296 



PRELIMINARY INVESTIGATION 



MO 


0) 










(N 


^ 


o> t^ m 10 


OvnO •'tvO 


00 100 t-00 


vO O PO POOO 


II 


§5 


10 10 t-< r^ 


CO t^ Tl- (N 


t^ -"t N M M 


10 POvO PO 't 


M M W CS 


ro TfTj-iovO 


t- 0\ M po »0 


0> TfOi 10 M 








M M M 


M p< Ci PO Tf 


^ 


§ "^ 










"V 


s 










(^ 


^ " 


100 OvO 


^ro Ci 


PO Tj-t^O -^ 


l>vO -'to 


11 




TtOv ""to 10 


MOO TtMOO 


P0O\vO »o -^ 


vO fO -"to 


M M N 


ro f*5 -^J^ »0 


t^oo Pi "^ 


00 POOO ■^ 








M H M 


M Pi N PO Tt 


^ 


S 










-« 


ft _ 










CS 


r^ 


rJ-M ro t^ 


i/^ t^ OwO ^ 


MOO t^O t^ 


PO rf lOPOO 




§■5 


-^O -^O rf 


<>< o>.o 


MVC PO M 


(N 00 00 PO PI 




M M C» 


ro f*5 "St Tt 10 


t^oo N •^ 


00 CI t^ PO 0\ 










M p« e< PO PO 


& 


fe "" 










*e< 


a. 










N 


^. 


N t^»O»O00 


Tfrl-rJ-OsO 


a N r^po 


00 MvOO C« 


II 




■^00 fOOO CO 


0\ to M l>. Tf 


00 TfOoO t^ 


t^PO N >/^ 


M M OJ 


<N f0"*Tt»O 


OOO M PO 


l^ CI l^ «00 










M M C4 PO PO 


^ 


S "" 










(N 


1- 


rl-O\00 0\ 


ro M N 00 


t^OoO Oi PO 


PO 0\0 t^ 




1—1 "^ 


TtOO <N t^. (N 


00 rtOO N 


M t^rj-po 


PO t^o t^ 




M M N 


N ro '"t'^iO 


vO 00 0\ M PO 


t^ M CI t- 








M M 


M cs N ro PO 


^ 


(^ 













s 










M 


^" 


00 -^o 


r^ao iTixno 


10 000 vOO 


0\ t^ r>.po PO 






rooo <N t^ (N 


i^ cs 00 rfM 


rfON -^M 0\ 


00 Ci POO 


II 


M M CS 


<N r<5 ro "^lO 


sO t^ Oi M (N 


\0 M >0 M t^ 








M M 


M CS CI PO PO 


^ 


g" 










'a 


0*^ 












^ r! 


t^OOO rfO 


M 100 Oi 


p* '^o\ PO 


T^lo t^ t^ o\ 




— < i-N 


fO t^MvO M 


\0 M\0 N 0\ 


MvO MOO 10 


rt t^ TfO CI 




M M (N 


<N fO (r> rl- rj- 


t^ 0\ N 


tOOO 








M M 


M N N ro PO 


& 


S "" 










00 


0) 

04_ 










M 


S - 


10 M C«lO M 


N VC C< C^ 


00 o\ P< 


POOO 10 




_ .-N 


fO t^M 10 


10 »o M r^ 


POOO 10 PI 


cioo >o 




H M CS 


<N PO f*J T '^ 


sO t^OO <N 


-^o »o 








M M 


M N N PO PO 


^ 


s 










M 




rO OnO 0\ <N 


00 fO 


00 <N >0 »0 


10 M 0> PO M 






fOsO "^0\ 


rooo Tf CMo 


t^ M\0 M 00 


10 t^ C« POOO 


II 






CN N roPO -^ 


10 t^OO M 


»o 0\ 'tO\ Tf 










M M M C« PO 


& 


s 










i 


a 










M 




M JO M M ro 


000 10 CMO 


vO t^O P< 00 


M 0\0\>0 t* 






roO ^00 


N l^ CNJ l^PO 


lOOO POOO •^ 


M mOO 


n 




M M M 


c< w PC ro ^ 


lOvO 00 0\ M 


10 0\ rooo Tf 










M M (M PS PO 


^ 












I/) 


0) 

0< 










H 


^. 


0\ M lOTfro 


vO POO NO 


PO M 0\ H 


t^O PO 






fsvO ro t- 


MVO wvO M 


roO rfM 


vOO M PO 


II 


§5 




N N PO PO •^ 


»/5vO 00 0\ M 


tJ-oO POOO PO 










M M C< PI PO 


^ 


fej "^ 










V 














^ 


t^ t^oo •^ 


vo 00 1000 


M 1000 >* 


C« 10 M PO Oi 






<M u^O\ NO 


10 0\ rJ-Os 


M PO t^M t^ 


Ci M 10 PO »>^ 


II 


W\« 


M M 


N M N PO PO 


lovO t^ 0\ 


■^00 « t^ c« 




— < "-f^ 








M M Pi C« PO 


^ 


fe 










6^ 




U^ »0 »>^ 


10 10 


00000 


00000 


M M «N CS 


PO fO't'^iO 


vO t^oO 0\ 


c* Tj-ooo 








M M M M PS 



UNIT PRICES 



297 



Miscellaneous Information of Value in Making Preliminary 
Investigations and Estimates 

Conversion Per Cent, of Grade to Degrees of Vertical 
Angle 
(For use in tracing grade with transit or Abney Level) 
Per cent. Degrees 

1 o°3s' 

2 1° 09' 

3 1:43' 

4 2° 18' 

5 2°S2' 

6 3° 26' 

7 4° 00' 

8 4° 35' 

9 5° 09' 

10 5° 43' 

11 6° 17' 

12 6° si' 

13 7° 24' 

14 7°S8' 

15 .8°32' 



Table 27. — Table or Acres Per Station of 100 Feet and 
Per Mile for Different Widths of Clearing 
OR Right-of-way 





— Acreage 


Width of Strip 












Per 100' 


Per Mile 


30 ft 
40" 
50" 
60" 
70" 
80" 


. 069 acres 
0.092 ** 
0.115 " 
0.138 '' 
0.161 " 
0.184 " 


3 
4 
6 

7 
8 

9 


636 acres 

849 " 
061 ** 

273 '' 
485 " 
697 " 


90" 


0.207 *' 


10 


909 '' 


100 " 


0.230 " 


12 


121 *' 



Range in Unit Estimate Prices 
Clearing and Grubbing. 

Sage brush $ lo to $'50 per mile 

Light clearing $ 20 '* $ 60 per acre 

Medium clearing. . $ 60 " $150 '' " 

Heavy clearing $150" $300 '^ ** 



298 PRELIMINARY INVESTIGATION 

Excavation. 

Common. 

Machine turnpiking $0.15 to $0. 25 per cu. yd. 

Wheel scrapper and machine 

finish $0.25 " $0.35 " '' '' 

Wagon haul and machine 

finish $0.40 '' $0.60 '' '' " 

Side hill plow, scrapper and 

machine $0.35 '' $0.75 " '' '' 

Disintegrated Rock or Dry Hard Clay. 
Considerable hand work or 

shooting $0.75 "• $1.00 '' '' '' 

Solid Rock. 

Blasting open cut, per cu. yd. $0.80 '^ $2.00 '' " " 
Tunnel work $4.00 '' $5.00 '' '* " 

Retaining Walls. 

Rough dry rubber masonry $1.00 '' $3.00 " '* '' 

Mortar rubber $4 . 00 '' $8 . 00 '' " *' 

Concrete $6.00 "$20.00 " '' "■ 

Timber and Lumber S30.00 ''$80.00 '' " '' 

Carpenter Work. 

Simple structures $5.00 " $10.00 " M ft. B.M. 

Truss framing, etc $10.00 '' $20.00 '' " '* 

Table 28. — Approximate Cost Per Foot of Length Small 
Drainage Structures 



Size of Opening 




Kind of Structures 






Corru- 




* 






Vitrified 


gated 


Cas 


t Iron Concrete 


Log 




Pipe 


Metal 
Pipe 


r 


*ipe Boxes 


Culverts 


12" 


$0.60 


$1.25 


$^ 


2.00 




IS-" or 16" 





90 


I 


•50 




2.90 




18" 


I 


10 


I 


.80 




5.40 




24" 


2 


00 


2 


•75 




)-50 




36" 


3 


75 


4 


.00 








48" 






6 


•50 








2' X2' 












3.75 


$1.50 


2;x3' 












4.80 


1.70 


3'X3' 












5.40 


2.30 


3'X4' 












6 . 00 


2.80 


4'X4' 












... 6.75 


3.00 


4'XS' . 












8.00 


3.60 


S'XS' 












8.70 


4.00 



* Based on $50 per ton in place. 
**Based on $10 per cubic yard in place. 



SMALL BRIDGES 



299 



Culvert Data. — ^Local conditions must be considered in prices of 
materials, haul, etc., for a close estimate. 

Table 50, page 559, gives weights of corrugated pipe. 

Table 49, page 558, gives weights of cast iron pipe. 

Quantities of concrete can be figured from standard designs 
given in Chapter III. 

Timber in superstructures can be figured from standard designs 
in Chapter III. 

The summarized data shown in Table 28 will however act as a 
rough guide. 

Amounts of masonry in two abutments and four wings for 
various heights of abutment for small span timber bridge super- 
structures with 16' Roadway. 

H = height from bottom of foundation to bridge seat. 





Cubic 


Yards 


H in Feet 






Concrete 


Masonry 


6 


24 cu. yd. 


29 CU. yd. 


7 


32 \ 




^^\ 






8 


40 




49 






9 


52 




60 ' 






10 


62 ' 




74 ' 


i 




12 


90 ' 




105 ' 






14 


133 




153 






16 
18 


Ti^O * 




200 * 
260 * 






230 ' 








20 


295 '' *' 


325 '' '' 



Compiled from Plate 29, page 119. 

Approximate amoimt of timber in small span stringer bridge su- 
perstructures having 16' roadway and figured to carry a 20 ton 
load. 



(Figured from Plate 21, page 104) 


Clear Span 1 Feet B. M. 


Pounds Hardware 


6 ft. 

8 '' 

10 '' 

14 " 

18 '' 


1000 
1400 
1700 
2500 
3300 


70 pounds 
90 '^ 
no " 

130 " 
150 '' 



Note. — For timber spans 30' to 50', see Plates 22 and 23, 
pages 107 to 108. 

Pile abutments can be figured from Plate 21, page 104. 



300 PRELIMINARY INVESTIGATION 

Net Volume of Logs in Board Measure. — A convenient approxi- 
mate rule for computing the net number of feet board measure of 
sawed timbers in logs is as follows: 

Diameter in inches X radius in inches _ Feet (board measure) 

^ per foot of log. 

Example. 

Suppose you have a log lo' long 12" in diameter. 

Diameter X radius , rr.T^AT e ^ e ^ 

= number of feet B. M. per foot of log. 

12 

11^^ = 6 ft. B. M. per ft. X 10' = 60 ft. B. M. 
12 

Steel Bridges. — The following diagrams taken from various 
sources will serve as a basis for rough estimates on longer span 
steel highway bridges. They are figured for a live load of 100 lb. 
per square foot and presumably for a plank floor. They are of much 
lighter construction than called for on heavy traffic roads where 
solid floors and a heavier loading are gaining favor. 

Magnetic Declination. — The following isogonic charts give the 
approximate magnetic declination for States east and west of the 
Mississippi for January i, 191 5. The yearly change is given. 
These charts will give a value close enough for preliminary investi- 
gation purposes. For meridian determination for location surveys, 
see Chapter XI. ''Polaris" and ''Solar Meridians." 



Explanation of Plates ^7 and 38 (Taken from U. S. Coast 
and Geodetic Chart) 

The solid lines on these charts are lines of equal magnetic de- 
clination. 

The dot and dash lines are lines of equal yearly rate of change in 
the magnetic declination. 

The charts show the magnetic declination for Jan. i, 191 5. 

Lines marked East Declination mean that the north end of the 
magnetic needle points east of true north. 

Lines marked West Declination mean that the north end of the 
needle points west of true north. 

For localities east of the line of no annual change the north end 
of the magnetic needle is moving west. For localities west of this 
line it is moving east at the rate shown by the lines of annual 
change. The location of the line of no annual change is shown on 
Plates 38 and 37G. 



STEEL BRIDGES 



301 



•I 



'11 
>< a. 

- E 

I 



I 



18000 
16000 
14000 
12000 
lOOOO 
8000 
6000 
4000 
2000 






■ 








1 






















- 














































































































/ 




- 












































'< 


'• 


















































































1 > 


;^^ 


> 


/ 








































A 


pO 


V 


M 


/ 












































^ 


/" 










































^ 


^ 


X 






















































































^,15', 




/^ 




Wight of Steel in Bridges, 
exclusive of Joists and 
fznce, Warren yRiveted 
Low Truss, Half Hip, Tee 
Chords, L ive I oad 1600 lb. 
per lin. ft' of Bridge, 
RoadwoL/ 16'0". 












3P' 


LV 


X 


^* 


















.^ 














f 




^ 






















^ 




























































































-J 










1 1 1 1 1 1 1 1 1 1 1 



30 



40 



50 



60 



70 



80 



Span of Bridge inFee-t*. 



















— 


T" 










































' 




















1/ 


' 


/ 














/ 


/ 


/ 














J- 


' , 


/^ 














jVI 


i<^' 


/^ 


' >' 










20' Road,2,e' Sidewalks 
~/8' '^ 2,5' »'. ! 


■^ 


,oof 


y 


.^ 


/ 










l^'- 


.^ 


^ 












le' 9y 2,5' ri ' ~ 


/ , 


y 


'y^ 
















■' ' ' / 




b5^:^ 


> 
















'''.'' 


>' 




















^-^ 




















;i.>^: 






















.JLl^-^ 






















^^. 













































85,000 
80,0 00 
75,000 J) 
70,000 ■§ 
65,000 § 
G0,000 '^- 
55,000 g^ 
50,000 ^ 
45,000 °^ 
40,000 o 
35,0 00 ^ 
30,000 .?^ 
25,000 ^ 
20,000 - 
15,000 -H 



10,000 
5,000 



4-0 50 60 70 80 90 100 110 120 130 140 150 160 



Panele> 



302 



PRELIMINARY INVESTIGATION 



Plate 37A. 




MAGNETIC DECLINATION 



303 



Plate 37B. 




304 PRELIMINARY INVESTIGATION 

Plates 37 C and D. 




I -25« 



— 24° 



/' .^■^2- ,2,0 20, ,9, 



./ ^S: 




MAGNETIC DECLINATION 

Plates 37E and F. 



305 








3o6 PRELIMINARY INVESTIGATION 

Plate 37G. 




Plate 37 H. 




MAGNETIC DECLINATION 
Plate 37I. 



307 




3o8 



PRELIMINARY INVESTIGATION 



Plate 38. 



V .. X'-.,\\X 



3^ 



■•V 



♦ ^'« \\^ 



^ 



i^ 



•k- 



w 



'^•l£\\ 



'5\ 



^^' 



l\%- 0< 



••-1 






I V , 



[Oo 



±s. V, 



■> \ \ N- 

\ \ r-- 

\ \V On 

\ \\ "^ ^^^^- 



W 



j D£C L\//VAT\d(A/ 



\\ 
\\ 



\\ \ ' 

\)s\ 

V\ \ \\ H\ 

\3° \ V \V^ \\.0° 



SAMPLE REPORT 309 

The following sample report shows a form in ordinary use for 
Preliminary Investigations which covers the information required. 

REPORT ON PRELIMINARY INVESTIGATION OF THE 

RED GAP-BIG BEAR RANCH HIGHWAY IN 

PATERSON AND GRANT COUNTIES, 

STATE OF , 1919 

State Commissioner of Highways, 
Dear Sir: 

Complying with your request of May loth, a preliminary investi- 
gation of the proposed Red Gap-Big Bear Ranch Highway was 
made June ist to June loth. 

There is only one feasible route via Clear River Ranch, Coal 
Basin, Stray horse Divide, See Creek and Blackwater river a 
total distance of 30 miles. This route is free from ^now seven 
months in the year. A double track road from Red Gap to Coal 
Basin and a single track road with turnouts and permanent drainage 
structures for the remaining distance will cost approximately 
$175,000. 

In case the entire project can not be undertaken by one appro- 
priation, I recommend the following order of construction of the 
various sections shown on the accompanying map (page 317). 

First in importance G 4, G 5, 

Second '' '' G 7, 

Third '' " G6, 

Fourth " " G 2, G 3, 

Fifth " " G I, P I, P 2, 

Sixth " '' ..^ P3, P4, 

Seventh " '' P 5, 

The report in detail follows. 

Signed, 
Field Engineer. 
Table of Contents 

Page 

1. Introduction 310 

2. Length in Counties and Benefits .... = 310 

3. Metiiods of Investigation 310 

4. Present Condition Roads and Trails 310 

5. General Topography. 311 

6. Proposed General Route 312 

7. Controlling Points 313 

8. Description between Controlling Points 313 

9. Recommendations and General Costs 315 

10. Detail Estimate 315 

{a) Classification of Material 315 

{h) Unit Prices Used 316 

(c) Division into Sections 316 

{d) Estimate by Sections 316 

11. Maps and Photographs 

The field notes on which this report is based can be found in 
Field Book No. 153 Preliminary Investigation file. 



3IO PRELIMINARY INVESTIGATION 

I. Introduction 

It is proposed to build a new road over Stray Horse Divide con- 
necting the valleys of the Clear and Blackwater Rivers and to 
improve the location, grade and width of the existing roads in 
these valleys. The highway will extend from Red Gap in Paterson 
County to Big Bear Ranch in Grant County a distance of approxi- 
mately 30 miles. It will open up a valuable farming section on 
the upper Blackwater River and will afford more direct communi- 
cation between these two counties. 

2. Length in Counties and Benefits 

Paterson County. — Red Gap to Stray Horse Divide 8 miles. 

Grant County. — Big Bear Ranch to Stray Horse Divide 22 
miles. 

Paterson County will be benefited by a better and quicker con- 
nection with communities to the south and by the large amount of 
tourist travel which will undoubtedly use this road. 

Grant County will gain a more direct route to an isolated por- 
tion of its territory and will help the development of a promising 
farming section on the upper Blackwater River. 

While none of this road lies in Socorro County, this county will 
be more directly benefited than Paterson County as the natural 
outlet for trade and produce up the Blackwater lies toward 
Lochiel. 

3. Methods of Investigation 

Field Work.— The entire line was covered twice on foot June 
ist to loth, noting the controlling points (aneroid elevations) the 
general classification of materials, the sidehill slopes and reason- 
able ruling grades. 

Office Work. — The office estimate is based on paced distances 
checked by Forest Service maps and maps of the Clear River 
Railroad. 

The excavation per running foot on sidehill work is based on 
cross slopes taken with an Abney level at frequent intervals and is 
figured on the principle of balanced sidehill sections adding dif- 
ferent percentages for inequalities in profile. 

The classification of excavation is made roughly from notes on 
the general character of the formations. 

The drainage is approximated for the smaller structures. The 
larger bridges are noted in more detail. 

Estimates have been prepared for various widths of roadway. 

4. Present Condition of Roads and Trails 

Paterson County (Red Gap to Stray Horse Divide). — There 
is a fair wagon road from Red Gap to Clear River Ranch about 
2 miles south; a solid but poor wagon road from this point to Coal 
Basin; a fair road from Coal Basin to Stray Horse Station and a well 



SAMPLE REPORT 311 

marked but steep trail from this point to the top of Stray Horse 
Divide. 

Grant Comity (Stray Horse Divide to Big Bear Ranch). — There 
is an easy trail from Stray Horse Divide to Blackwater River ap- 
proximately 8 miles; a very poor wagon road down Blackwater 
River from See Creek to Adams Ranch approximately 9 miles. 
The road between these points crosses the river eight or ten times 
by fords and can not be used at all if the water is much above low 
stage. Under the best conditions a good 'team can not haul over 
I ton. 

From Adams Ranch to Big Bear Ranch (about 5 miles) the road 
is poor and dangerous in many places. It is so steep that one and a 
half tons is about the maximum load for an exceptionally good 
team under the best conditions. 

While this project ends at Big Bear Ranch it should be noted 
that if the road from this point to Lochiel in Socorro County, the 
nearest railroad point, is not improved the value of this project will 
be practically lost. The present road to Lochiel is dangerous, 
limits a team load to about 1 3^ tons and will be an expensive road 
to improve. I estimate roughly that $40,000 will be required to 
put it into reasonably good shape. 

5. General Topography 

Paterson County (Red Gap to Stray Horse Divide) (See photo- 
graphs No. I to No. 10). — From Red Gap south for about 2}/^ miles 
the topography is abrupt. Red sandstone and conglomerate 
clilBfs and dykes hold the road location closely to the Clear River. 
From this point to about one-half mile south of Coal Basin occa- 
sional cliffs occur but a careful location will avoid them and it will 
be possible to gain some elevation along the sides of the valley. 
From the point to Stray Horse Divide and for a couple of miles 
south of the pass there are no cliffs and while the slopes are steep 
averaging 25° to 40° the location can be placed at any desired eleva- 
tion. This strip of country is fortunately favorable to location. 

Grant County (See photos No. 11 to 30). — From Stray Horse 
divide to Thompson's Ranch the formation is favorable for location 
on any desired grade. Few rock outcrops occur. The slopes aver- 
age 20° to 25°. • 

From Thompson's Ranch down See Creek is an ideal road loca- 
tion. No solid rock, very little loose rock, easy water grade. The 
side slopes average 10° for one-half the distance and 20° for the 
balance of the way. 

From the junction of See Creek and Blackwater River down the 
east side of the Valley to Buck Creek the location is easy on a side- 
hill averaging 25° side slope. There are no rock outcrops and very 
little loose rock. An easy grade can be obtained. 

From Buck Creek to Spring Creek along the sidehOl on the east 
side of Blackwater River the following conditions prevail. Average 
sidehill slope 30°; one-half mile of rock ledge slope of face approx. 
60°. Expensive work can not well be avoided but an easy grade 
can be obtained. 



312 



PRELIMINARY INVESTIGATION 



From Spring Creek to Adams^ Ranch the formation on the east 
side of the valley is favorable for location at some distance away 
from the River. A ruling grade of 5 % can be obtained at the worse 
places and ordinarily the grade is light. Benches and sidehill 
slopes are easy averaging 15° for 3^ the distance and 30° for the 
remainder. 

From Adams' Ranch to Big Bear Ranch the best location lies 
on the west side of the valley. Difficult country is encountered, 
heavy scrub oak brush, many large boulders and considerable solid 
rock. The River changes its channel frequently and any permanent 
road location must be placed beyond its reach necessitating ex- 
pensive work. 

The natural soil from Big Bear Ranch to Adams' Ranch is very 
slippery when wet. To get a good safe road Creek Gravel should be 
used as surfacing. Unless the roadbed is sloped toward the hill 
(one way crown) any of this location will be dangerous in wet 
weather. This same condition applies in a less marked degree all 
the way up Blackwater River to See Creek. 

6. Proposed General Route 

Paterson County. — From Red Gap, the proposed road follows 
the present road with some modifications to avoid unnecessary 




WATERFAL'L. 



rise and fall to the first crossing of the Clear River about 1% miles 
south of Red Gap. From this point to the mouth of the Canyon 
about 14 niile the location is open to argument. The existing road 
crossed the river twice (see sketch above). Both of these bridges 
were wrecked by the flood of 19 18 and temporarily the travel is 
using the railroad track between these points. 

With the permission of the railroad, it would be possible to widen 
out the cut on the west side of the track and tunnel or half tunnel 



SAMPLE REPORT 313 

for about 500 feet around the rock bluff point, eliminating the two 
bridges and two railroad crossings. On the other hand the road 
would be very close to the track for 34 mile and would in my opin- 
ion be more dangerous for horse traffic than the old location re- 
quiring two bridges. The bridge location is recommended. 

From the mouth of the gorge the road will follow approximately 
the location of the present highway to the top of canyon hill and 
thence on a new location along the west side of the Clear River Valley 
to Stray Horse Divide. 

Grant County. — Beginning at the County line at Stray Horse 
divide a new location will follow down the north side of See Creek 
to a point about 2j^ miles southwest of Thompson's Ranch and 
thence along the south and east side of See Creek and Blackwater 
River to Adams' Ranch. At Adams' Ranch the road will cross to the 
west side of the valley and remains on this side to Big Bear Ranch 
the end of the proposed improvement varying somewhat from the 
location of the present road to better short sharp grades and to 
avoid Creek flood areas. 

7. Controlling Points (Aneroid Elevations) 

Paterson County. 

Stray Horse Divide 9200 

Bench between CliJBfs at Coal Basin 8200 

Top of Canyon Hill 8100 

Bottom of Canyon Hill 7930 

Red Gap , 7800 

Grant County. 

Stray Horse Divide 9200 

Thompson's Ranch 7900 

23^ miles S. W. of Thompson's 7500 

(See Creek Crossing.) 
Bench between Cliffs between 

Buck and Spring Creek 7150 

Adams Ranch 6780 

Big Bear Ranch 6600 

8. Description of Location Problems Between Controlling Points 

Paterson County 

Stray Horse Divide to Coal Basin. — The difference in elevation 
of these two points is approximately 1000 feet. The direct dis- 
tance is about 1 3-2 miles. In order to get a good grade and come 
somewhere near Coal Basin, which is probably desirable, it will be 
necessary to run south from Stray Horse Divide and then turn 
north. In this way any required ruling grade can be obtained and 
the length of road will depend entirely on the grade selected. The 
switchback can be made without too great cost by a careful loca- 
tion. I recommend a 5 % grade with a length of 4 miles. The road 
in general will follow the corftours. Two pronounced gulleys are 



314 PRELIMINARY INVESTIGATION 

crossed which can be bridged or filled as determined on the location 
survey. 

By the use of a 6% to 7% grade it is possible to run direct from 
Stray Horse Divide to the top of Canyon Hill. This solution should 
be carefully investigated but does not appeal to me to be as good as 
the 5 % location as the topography is not as favorable for location 
and while it is shorter the lighter grade is to be preferred and the 
extra length of road south of the divide will be utilized in the future 
as a part of the road to Stone Quarry. 

Coal Basin to Top of Canyon Hill. — Approximate length 1% 
miles. Along contour of steep sidehill for approx. % mile and then 
along bench cut up by small swales and knolls. No special features. 
Grade any convenient to fit topography. No grade problem on 
this section. Excavation largely earth and loose rock. One lo' 
span bridge required. 

Top of Canyon Hill to Bottom of Canyon Hill at Mouth of Gorge. — 
Approximate length 0.6 mile. Along side of Canyon following 
present highway closely. Largely a question of equalizing grade 
by cut and fill. From Aneroid elevations and Abney level, I judge 
that a 6% grade can be obtained. Certainly a 7% can be built. 
This section of the road will be expensive and will govern the ruling 
grade from Red Gap to Stray Horse Divide. The excavation 
will be approximately 50% solid rock. One 20' span bridge will 
will be required. 

Mouth of Gorge (at Bottom of Hill) to Red Gap. — Approximate 
length 2 miles. From mouth of gorge J^ mile south to wagon 
road on the west side of the river the location is the most expensive 
of the entire project. This strip will require either two bridges 
or heavy rock work as previously discussed. The bridges are 
recommended. From this point to Red Gap there are no difiicult 
problems as the road will follow in general the present location and 
can be cheaply built. Another bridge at Red Gap will better the 
location and increase the convenience of the road. 

Grant County 

Stray Horse Divide to Thompson's Ranch. — The difference 
in elevation is approximately 1300 feet. It is desirable to get down 
to a natural bench at Thompson's ranch. The length of road 
between these points will depend on the ruling grade selected. 
As it is a long climb I recommend 5% with a length of 5 miles 
which can be obtained with one switchback turn. The country 
is favorable for location. Excavation is largely earth and some 
loose rock. 

Thompson's Ranch to See Creek Crossing. — Approximate length 
2 3^i miles. Ideal road location on bench. Easy grade. Excava- 
tion practically all earth. Plow and machine scrapper work. 
No grade problem. One 20' span bridge required. 

See Creek Crossing to Buck Creek. — Easy sidehill location except 
for }/2 mile of rock ledge near Buck Creek. The location should 
keep upon the sidehill to avoid abrupt river banks and slides 
due to freshet scour. 



SAMPLE REPORT 315 

Buck Creek to Adams* Ranch. — Easy sidehill and bench location. 
No difficulty in obtaining grades less than the maximum. Ex- 
cavation earth and loose rock. 

Adams' Ranch to Big Bear Ranch. — ^Location problem one of 
protecting road from River floods, also avoiding ledge and large 
boulder rock work. No hard grade problem. Excavation 50% 
loose rock, boulders and solid ledge. 

9. General Recommendations and Costs 

The cost of construction under present conditions is uncertain. 
The prices used in the following detail estimates should be carefully 
noted in considering the possibility of cheapening the work by the 
use of convict labor. The costs used are for contract work and may 
vary greatly in a short time. 

I recommend for this project a double track sidehill section 
(S-14O from Big Bear Ranch to Coal Creek; a single track. sidehill 
section (S-io) with turnouts from Coal Creek up to Blackwater 
River, See Creek over the Divide and down to the top of Canyon 
hill in Paterson County. A double track road from this point to 
Red Gap. Permanent culverts and bridges. Ruling grades of short 
7% and long 5%. Alignment limited as a rule to a minimum 
curvature of 100' radius with a few 40' radii at exceptionally bad 
places. 

The cost of this type of road is estimated at approximately 
$175,000 divided as follows: 

Clearing and excavation $108,000 

Permanent culverts - • ■ ■ - 20,000 

Permanent bridges over 10' span 35j000 

Engineering . 12,000 

Total $1 75,000 

If it is not possible to construct the entire project by one ap- 
propriation it would be well worth while to build from Big Bear 
Ranch to See Creek at once to open up the new farming section 
on the Upper Blackwater. The cost of this portion of the road 
would be about $70,000. 

For details and various combinations of design see the following 
estimates by sections. 

10. Detail Estimates 

Classification of Materials. — The classification of excavation can 
not be accurately made; it is based on the following assumptions. 

Where the road is located on a bench near the bottom of a slope 
which appears to be slide or wash formation and no rock outcrops 
are visible the excavation is classed as 99 % common and i % rock. 

Where the location is on a steep main mountain slope of 25° 
to 35° covered with loose rock but no solid rock outcrops are visible 
the assumption has been that solid rock will be encountered 6 
feet back of the slope surface. 



3l6 PRELIMINARY INVESTIGATION 

Where occasional outcrops occur rock is assumed 4 feet back 
of the surface. 

Any extended rock ledge has been noted. 

Unit Prices 
Clearing 

Sage brush $ 30 per mile 

Light brush and trees $ 30 '' acre 

Medium brush and trees $100 '* *' 

Excavation 

Solid rock $1 . 00 to $1 . 50 per cu. yd. 

Tunnel rock .....4.00 '* ^' " 

Common Exc. 

Turnpike in earth 0.18" '' " 

Sidehill plow and scrapper o . 30 to 0.40 *' ^' " 

Wagon haul and scrapper 0.40 " " " 

Concrete $12.00 '' " " 

18'' corrugated pipe 2 . 00 " foot 

Rough rubber retaining wall 2 . 00 ** cu. yd. 

Division into Sections. — For the purpose of estimating the road 
is divided into the following sections. 

Paterson County 

Sec. P-i Stray Horse Divide to Coal Basin 4.0 miles 

Sec. P-2 Coal Basin to top of Canyon Hill 1.8 " 

*Sec. P-3 Canyon Hill 0.6 '' 

*Sec. P-4 Canyon Hill to Clear River Ranch 0.25 " 

*Sec. P-5 Clear River Ranch to Red Gap i . 75 " 

Total Paterson Co 8.40 " 

Grant County 

Sec. G-i Stray Horse to Thompson's Ranch 5.0 miles 

Sec. G-2 Thompson's Ranch to See Creek Crossing. ... 2.5 *' 

Sec. G-3 See Creek Crossing to Blackwater River i .0 *' 

*Sec. G-4 See Creek and Blackwater to Buck Creek 2.5 *' 

*Sec. G-5 Buck to Spring Creek 2.0 

*Sec. G-6 Spring Creek to Adams' Ranch 4-5 

*Sec. G-7 Adams' Ranch to Big Bear Ranch 4.3 *' 

Total 21.8 '' 

Note. — See map for location of these sections. The sections 
marked with a * have a poor wagon road at present which however 
can be used. Sections having no star require new construction 
to permit wagon traffic. 
Estimate of Sections. Section P-i. — (Length 4.0 miles.) 
Clearing. — Six acres per mile for 3 miles = 18 acres @ $100 = 
$1800. 



SAMPLE REPORT 



317 



Drainage. — Say 10 culverts per mile for 4 miles @ $700 per 
mile = $2800. 

Excavation for Double Track Road. — Sidehill slope averages 27°. 
Excavation per mile for balanced section S = 14 equals approxi- 
mately 13,000 cu. yd. for a 1:1 cut slope which is considered 









/Big Bear Ranch 








\. :'^^ 






0- 


xV /' 


S+one 







©-6 / Adams "^U^ 


Quarry g 



CO 


8 = 


^^^ -.Ranch /\ ^5 


\-.^ 






PjlCKCMff ..'-'' 


r Y^ 




A5n^ 0^ 


W 




/\ 


, W^ --^©-2 V<. 


1 


J/ 

Its k^' 






y 


^- 




t ptON 









t 1 








f la. 


\ 






10 


\ 




m 


^^ 








M 




Hi 


■- j^> 




K-. 


-_..r^ 




Clear Xv^' 
River .-^ ^ 


•--,.P-4 






Ranch |^ 


P-5 






Red 6a p ^ 


.-' 







safe for this material. Add 25% for inequalities of profile giving 
16,200 cu. yd. per mile or 55,000 cu. yd. for 4 miles. It is estimated 
that 20% of this or 11,000 cu. yd. are rock excavation and the 
balance 44,000 cu. yd. are common. 



3i8 PRELIMINARY INVESTIGATION 

44,000 cu. yd. common @ $0.40 « . $17,600 

11,000 " " rock @ 1.20 13,200 

Total excavation $30,800 

Excavation for Single Track Road S-io. 

Exc. per mile balanced section. . . 7,400 cu. yd. 
Add for profile 25% 1,850 '' " 

9,200 '* " 

Assume 10% rock 900 " '' per mile 

Assume common exc 8,300 '* " " ** 

Cost of Excavation for 4 miles. 

3,600 cu. yd. rock @ $1 . 50 $5,400 

33,000 " '' common @ $0.33 11,000 

Add for turnouts 5 to the mile 

500 cu. yd. rock @ $1 , 20 600 

1,500 " " common @ $0.40 600 



Total $17,600 

Summary of Cost Section P-i. 

Double Track Road Single Track Road 

Clearing $ 1,800 Clearing $ 1,800 

Drainage 2,800 Drainage 2,800 

Excavation 30,800 Excavation 17,600 



$35,400 $22,200 

Contingencies, 

wall, etc 2,600 Contingencies 1,800 



$38,000 $24,000 

Equals $9500 per mile Equals $6000 per mile 

Estimate Section P-2. — (Length 1.8 miles.) 
o . 8 miles similar to section P-i 
1 .0 miles average side slope 15° 

Estimate of the easy mile (side slope 15°) 

Clearing 6 acres @ $50 $300 . 00 

Drainage (ordinary) 500 . 00 

20' span bridge 800 . 00 

Excavation (see S-14) 3300 cu. yd. per mile 

Add for profile 25% 800" " '' " 

4100 " " '^ " 

Rock excavation 100 *' " ©1.50 $150.00 

Common excavation 4,000 '^ " " 0.30..... 1200.00 



$2950.00 
Contingencies 150 . 00 



Total $3100.00 



SAMPLE REPORT 319 

Summary P-2. 

Double Track ^^^^ Single and 

Part Double 

. 8 miles similar to P-i 
@ $9500 per mile = $7,600 

@ $6000 per mile = $4800.00 

1 . o miles as per 

estimate above.... 3,100 , 3100.00 

$10,700 $7900.00 

Say 11,000 Say... 8000.00 

Estimate Section P-3. — (Length 0.6 miles.) Double track road 
based on hand level profile. 

Clearing 3 acres @ $100 $ 300 . 00 

3000 cu. yd. common @ $0.40 1200.00 

3000" " rock® $1.25 3750.00 

Ordinary drainage 500 . 00 

1 20' span bridge 800 . 00 

$6550.00 
Contingencies 150.00 

Total : $6700 . 00 

Estimate Section P-4. — (Length 0.25 miles.) 
Estimate No. i. — Based on location requiring two bridges over the 
Clear River. 

Clearing $ 20 . 00 

1000 cu. yd. common exc. @ $0.40 400.00 

200 " " rock (^$1.50 300.00 

400 " " rip-rap @ $1 . 00 400 . 00 

2 (80' span solid floor steel truss bridges) 16,000.00 

I (20' span concrete bridge) 800.00 

$17,920.00 
Say 18,000 . 00 

Estimate No. 2. — Based on half tunnel west of track. 

Clearing $30 . 00 

5000 cu. yd. of common exc. @ $0.40 2,000.00 

4500 '^ ^' rock tunnel work @ $4.00 18,000.00 

Stone wall between track and road 900.00 

$20,930.00 

Say $21,000.00 

Estimate Section P-5. — (Length i . 75 miles.) Double track road. 
Approximately same cost per mile as Section P-2 on the easy mile. 

1.75 miles @ $3100 per mile $ 5,425.00 

Possible bridge at Rip Gap 8,000.00 

$13,425.00 
Say $14,000 . 00 



320 



PRELIMINARY INVESTIGATION 



Summary of Costs, Paterson County 



Section 


Double Track 


Single 


Track Road 






WITH Turnouts 


P-i 


$38,000 




$24,000 


P-2 


$11,000 




8,000 


»P-3 


7,000 






iP-4 


18,000 






^P-5 


14,000 








$88,000 




Engineering 


4,000 







Total appropriation $92,000 

Estimated total cost for double track road Sec. P-3, P-4 and P-5 
and single track road to the divide Sec. P-i, and P-2 is $75,000. 

Estimated cost of cheap single track road connecting present 
road to the divide Sec. P-i and P-2, with temporary drainage 
structures and 6% ruling grade instead of 5% $25,000. 

Cost Estimate, Grant County 

In a similar manner detail estimates are made for the sections 
in Grant County as summarized below. These estimates can be 
found in computation file F-32. They are not included in this re- 
port as they are bulky. i|L j 

Summary of Costs, Grant County 



Section 


Double Track 
(S-14) 


Single Track (S-io) 
With Turnouts (S-14) 


G-i 


$ 32,000 


$ 22,000 


G-2 


33,000 


3,000 


G-3 


5,000 


3,000 


G-4 


10,000 


7,000 


G-5 


20,000 


12,000 


G-6 


26,000 


20,000 


G-7 


36,000 

— ■ 
$132,300 


25,000 


$ 92,000 


Engineering. . . . 
Appropriation . . 


7,700 


8,000 


$140,000 


$100,000 



Total Summary of Recommended Construction 

Paterson County $ 75,ooo 

Grant County 100,000 

Total $175,000 

1 Sections have usable wagon road at present. 



SAMPLE REPORT 321 

RECONNAISSANCE SURVEYS 

The methods described for ordinary investigations can be used 
for most cases but for heavily wooded country or extremely difficult 
and rough topography a more careful survey is desirable. 

Methods. — For open barren country the transit stadia method is 
preferred by the author using magnetic bearings, stadia distance, 
vertical angle profile and cross slopes and ordinary note book 
sketches and recording. The map is plotted up on a scale 1000 ft. 
to the inch and the profile 100' to the inch. The line is marked in 
the field by tall stakes or lathes with a strip of cloth attached. 

Work of this kind can be done by two men with very simple 
equipment. In remote regions a third man to move and care 
for camp equipment is required (see Chapter XII). 

Engineering Equipment 

Light mountain transit with stadia and verticle circle. 

Light stadia rod, 8' to 10' long. 

Camera. 

Note books, maps, etc. 

100' steel tape. 

2 aneroid barometers. 

For heavily wooded country the U. S. Geological methods are the 
cheapest and most satisfactory using a light 15" sketch plane table 
and tripod oriented with a magnetic needle; 6'' gun sight alidade; 
500' linen tape coated with paraffin for distance. Aneroid inter- 
mediate elevations checked by flying lines of spirit levels or stadia 
levels along trails. 

The main advantage of this method is that it requires no cutting 
as direction is obtained by sighting by ear to a yell or whistle. 
It also gives a complete contour map of all the territory that the 
road can possibly traverse and makes it possible to lay out a better 
final location than any amount of scouting where the engineer 
depends on his memory and sense of direction for his final location. 
The projected line is then followed with a rough plane table traverse, 
slopes, etc., taken and the estimate made. 

Work of this kind can be done by two men with very simple 
equipment for a cost ranging from $10 to $30 per square mile 
mapped. A convenient scale to work on is 2000' to the inch and a 
contour interval ranging from 10' to 50'. 

A third man to move and care for camp is desirable. 

Engineering Equipment 

15'' Plane table with tripod. 

500' Linen tape. 

6" Gun sight alidade in leather case. 

100 Steel tape. 

Plane table map paper. 



322 



PRELIMINARY INVESTIGATION 



2 Aneroid barometers 

Light mountain transit with stadia (for flying levels). 
Stadia rod. 

Conclusion. — It should be borne in mind that if engineering 
is to be of value it must be thorough and that new locations will 
often fix roads for generations. 



% 



Screws to hold 
Double Mourrhed 
Plane Table 
Paper firm I u 
in Place. ^ 



I 




(ah Area Heavilcj Wooded 
; I excepf Portion Harked 
\ \CI earing. 

'^^ i Proposed Locaiion of Road 

\shown in Oo-ffed Lines. 
\^^ i Areas nof Favorable for -^ 
*' \Locafion Hatched ihus ^ 



Pig. 6 1. — Sample plane table map. 



There should be no hesitation in spending what ever is needed 
even if it seems all out of proportion to the cost of the actual con- 
struction work to be performed within a year or so. Government 
programs carry out this principle and they are often criticised for 
high engineering cost but it is well worth while looking to the future. 

The engineering program must be complete or it might just 
as well be discarded entirely. 



CHAPTER XI 



THE SURVEY 

The chapter on survey will be handled under two main divisions : 

(a) Improvement of existing roads. 

(b) Location of new roads. 

(a) FOR THE IMPROVEMENT OF EXISTING ROADS 

As the survey furnishes the information for the design, it must 
be carefully made in regard to the essential features. These are 
alignment, levels and cross-sections, drainage, information con- 
cerning foundation soils, available stone supply, available sand, 
gravel, filler, etc.; direction and amount of traffic, railroad un- 
loading points, the location of possible new sidings, and such 
topography along the road as will have a bearing on the design. 
The survey should be made not more than a year before construc- 
tion starts and during the open season, as a snowfall of any depth 
makes the work unreliable and only fit for a rough estimate. 
When contracts based on winter surveys are awarded it is always 
necessary to take new cross-sections to insure a fair estimate of 
the excavation. 

A party of five men is a well-balanced force for surveys of this 
character. 



Force 
Engineer 
Instrument man 
Three helpers 



Equipment 

Transit 
Level 

2 I go' steel tapes 

3 50' metallic tapes 
3 pickets 

2 level rods 

Pocket compass 

Hatchet 

Sledge 

Axe 

Keel 



Stationery 
Reports 
Pencils 
Notebook 
U. S. G. S. map. 

Stakes 
For preliminary survey 
no stakes per mile 
For construction 
220 stakes per mile 



The Center Line. — The placing of the center-line hubs (transit 
points) requires good judgment and should be done by the chief of 
the party. In locating them he considers the principles of align- 
ment discussed in Chapter I. The hubs are placed at tangent 
intersections and sometimes at the P. C.'s and P. T.'s of curves 
and are referenced to at least three permanent points that will not 
be disturbed during construction. (See sample page of notes. 
Fig. 62.) 

The deflection angles at the tangent intersections are usually 
read to the nearest minute, taking a double angle to avoid mis- 

323 



324 



THE SURVEY 



takes; the magnetic bearing of each course is recorded. For all 
deflection angles over 4° it is good practice to figure and run in 
on the ground the desired curve. Curves with central angles 
of less than 4° can be run in with the eye during construction. 

The center line is marked at intervals of either fifty or one 
hundred feet (see cross-section, page 325) in any convenient 
manner; the alignment of these points should be correct to within 
0.2 and the distance along the line to within o.i per ioo feet of the 
length; any attempt to get more accurate stationing is a waste of 
time. The chaining may be done on the surface of the ground 
up to a grade of 5 % with no objectionable error; beyond that slope, 
however, the tape should be leveled and plumbed. ^ Steel tapes 
should be used for chaining the center line and referencing the hubs 



^ 


Deflection 
Angle 


Curve ^ 



P.l Sta.S-hZdA 


rL-'dW 




I^S Angle 3''Z0'\ J 












P.L 5fu. O-hOO 






V 




J 



I5"0ak 



- Z%^' 



O- 



TeleqraphPole 
^45kz^ 



<*-. 



^^ 



Cor- Post 

i in Fence 

l^ 



'■^^' 



Bam 



^- 



l2"MapleTree 



^^<>. 



^s< 



-'>ol5"0ak 



Fig. 62. — Alignment notes. 

A convenient method of marking the actual center line sta- 
tions is to use a nail and piece of flannel; red flannel for the 100' 
stations and white flannel for the intermediate 50' stations, if 
needed. Where the soil is sandy, or muddy, and these nails would 
be kicked out or covered, a line of stakes can be set outside of the 
traveled way on a specific offset from the center line. However, 
if an offset line is used the chaining of all curves should be done 
on the center line to insure a correct center line distance and the 
stakes placed radially on the desired offset.^ Railroad spikes 
make good permanent transit points and are easily placed. 

At the same time that the line is run it is just as well to paint 
the 100' station numbers on any convenient place where they 
can be readily seen, as stations marked in this manner make it 
much easier to sketch in the topography than if marked in chalk 
on stakes. Also, if the stations are permanently marked it is 



LEVELS 



32s 



easier for the construction engineer to pick up the transit points 
at some future time. 

A party of j&ve men will run from two to four miles of center 
line a day, the speed depending upon the number of curves and 
length of tangents, if the hubs have been previously placed and 
referenced. If the hubs are placed at the same time the line is 
run, the work is greatly delayed. 

Two men can place and reference the transit points at the 
tangent intersections at the rate of from four to ten miles per 
day. 



Sta. 



P.M.^^1 



B.S. 



F. S. 



H.I. 



Elev. 



V" 



Spike m 15" Elm, l^ight of 5fa.5-h6Q 



_/^ 



Fig. 63. — Bench level notes. 

Levels and Cross -Sections. — Bench levels are run in the usual 
manner; the levels will be sufficiently accurate if the rod is read 
to the nearest o.oi'; for such work any good level and a self-read- 
ing rod graduated to hundredths are satisfactory. Benches are 
established at intervals of 1000-1500 feet; they must be substantial, 
well marked, and so situated as not to be disturbed during construc- 
tion. A small railroad spike in the root of a tree, a large boulder, 
or the water table of a building make good benches. 

The bench levels may be referred to some local datum in general 
use or to the U. S. levels, or the datum can be assumed. In run- 
ning bench levels it is better to use each bench as a turning point, 
as side-shot benches may be wrong even if the line of levels is 
correct. 

Cross-sections are taken at either 100' or 50' intervals, at all 
culverts, possible new culvert sites, and any intermediate breaks 
not shown by the normal interval. Enough sections are taken 
to show the constantly changing shape of the road. 

The distance of the shots from the center line of the road is read 
to the nearest 1,0' where the ground has no abrupt change of slope 



326 



THE SURVEY 



and to the nearest 0.5' where there is a well-defined abrupt change. 
The elevations are read to the nearest o.i'. The sections should 
extend from fence line to fence line, or in villages from sidewalk 
to sidewalk, and the position of the pole lines, tree lines, curbs, 
etc., noted. Engineers differ as to whether the sections should be 
taken at a normal interval of 50' or 100'. 

Table 29 gives the difference in the computed quantity of earth- 
work using 50' and 100' sections with intermediate sections at well- 
defined breaks in the grade. 







Table 29 








Name of Road 


Length 
Figured 


Charac- 
ter of 
Road 


Excava- 
tion 50' 
Section 


Excava- 
tion 100' 
Section 


Appro- 
ximate 
Differ- 
ence 


Per cent 
of Differ- 
ence 


Scottsville 

Mumford . . . 
Scottsville 

Mumford . . . 
Leroy 

Caledonia 

*Leroy 

Caledonia 

Clarence 

Center 

Clarence 

Center 

Lockport 
Tonawanda . . . 
*East Henrietta 
Rochester 


I mile 
I " 
I " 

! '' 
I " 
I " 
I " 
I " 


flat 
hilly 
rolling 

flat 
rolling 

eat 

flat 
rolling 


Cu. Ft. 

61,444 
111,109 

57,840 
77,841 
73,727 
38,037 
59,096 
37.275 


Cu. Ft. 

61,995 
111,700 
60,560 
78,659 
73,048 
39,415 
59,470 
36,07s 


Cu. Ft. 

550 
600 

2700 
800 
700 

1400 
400 

1200 


+ I«0% 

+ h% 

+ 4i% 

+ 1 % 
-I % 

+ 3x\% 
+ /tj% 
-3i% 



The following tabulation shows the variation for shorter sections 
of the starred roads. 



Name Station 


Quantities 


Quantities 


Approx- 




of and to 


by 50' Sec- 


by 100' 


imate 


Difference 


road Station 


tions 


Sections 


Difference 




Cu. Ft. 


Cu. Ft. 


Cu. Ft. 




Leroy 










Caledonia, 80- 90 . . . 


19,151 


19,525 


400 


t' Z^ 


*' 90-100 . . . 


21,915 


23,415 


1500 


+ 7 % 


" lOO-IIO . . . 


21,555 


20,689 


900 


-4 % 


" 110-120 . . . 


15,220 


15,030 


200 


- iA% 


Total and averages . 


77,841 


78,659 


800 


+ 1 % 


East Henrietta 










Rochester, 0-19 . . . 


14,625 


14,300 


300 


-2 % 


32-49 . . • 


11,950 


11,575 


350 


-3 % 


49-66 . . . 


10,700 


10,200 


500 


-5 % 


Total and averages . 


37,275 


36,075 


1200 


-3i % 



CROSS SECTIONS 



327 



The question of quantities is not the only factor in determining 
the interval. Where it is important to fit the local conditions, 
as in a village, or to utilize an old hard foundation, the designer 
is helped by 50' sections. 

In taking cross-sections the work becomes mechanical, and un- 
less the engineer in charge is unusually alert to all the inter- 
mediate changes better results will be obtained by the use of 
the shorter interval. For these reasons the author believes that 
a 50' interval is advisable except on long uniform stretches of 
road. 

A party of three men will run from 4000 to 7000 feet of 50' 
cross-sections per day; a party of four men from 5000 to 9000 feet, 
depending on the country. 



Sta. 



lOtOO 



lOtSO 



r.p.tes 

Rock on 
lltOO 



B.S. 



5.41 



I.ZZ 



F.S. 



Z.IO 



H.I. 



esi.75 



3S0.35 



Elev. 



"V 



eze.sz 



eze.6s 



Leff 

< 



^ ^ ^ ^^ >« 
2:4 ^ tvj «M cvj 






0^ CJi 
505Z605ZS\j 



40 14 IZ 5 C 






CVJ 

M <M Ji^ J^ fVJ CM 

0^ 0> C^ C^ C^ (Si 

S£ 6.0 6S 6.5 6.0 



60 



«(i ►O ©J cvi >j. iq 

f\4 PVl CVJ C\j <\4 tVj 

8Z 61 9J 63 6.6 



30 ZO IS & 5 C 10 14 Id 30 



>v. 



Right 



Ki 04 00 ^ CV* 

v£> vo u6 ^ to 

CV4 CM £4 J^ tVi 

Oi C^ C^ 0^ O 

B.4 5.5 S3 S5 6.5 



5 9 II 19 Z4 



>h N N ^ ^v 

If) >*I M^ ^ ►O 

CM r?j cs^ c5i 04 

CT) CXS ^ 0^ ci 

6.5 7.0 7.0 7.6 8.0, 



26 20 14 II 6 O 6 n /2 ZO 23 



dS 



^ N > ^ 

CU ^' CM Ni 

<M CM (M M 

^ C^ cry 'Si 

S.0 93 89 6.0 _ 



Fig. 64. — Cross-section notes. 



DRAINAGE 

The drainage notes show the position and size of all the exist- 
ing culverts; the area of the watersheds draining to them and a 
recommendation of the size culvert to be built; the location, drain- 
age area, and size of desirable new culverts; the necessity for out- 
let ditches and their length, if required; the elevation of flood 
water near streams, and the condition of the abutments and super- 
structure of long-span bridges. The cross-section levels are sup- 
plemented to show these points fully. Where the U. S. geological 
maps are available the areas of watersheds can be easily determined; 



328 



THE SURVEY 



where no such maps have been made the drainage areas can be 
easily mapped with a small 15'' plane table oriented with a magnetic 
needle; the distances can be paced and the divides determined with 
a hand level. One inch to 2000 feet is a convenient scale. 

The drainage scheme should be carefully worked out by the 
Chief of Party, as the possibilities of friction with local people 
are greater on this part of the design than any other. In the 
chapter on Drainage this fact was mentioned and designers were 
cautioned not to use new culverts unless necessary. 



Drainage 
Old Structures 



"V" 



Si-c.if=;-h2S h^resenf I2"V.TP 



Bad ConrJitian 



5ta.24-f 00 P re'sent Concrete 



Culvp.rf- RiiHf hy 



To wn i n 13 U g ^x g ^x -3 0'. C arries 
Water 5(7H.'i-fac.fnrily. 



:^ti7.4-5-hSo~4q-hOo F]o^d~ 



Backwater Covp.rs Present Road 



/. 5 'in Spring of Year, nn Currani-. 

Paise Road 2.S'^nd mnke FHInf 



Boulr/prSfonp arGrnvP.I 



Sta-BS-i-IO PrP'iPnt 24." V.T P does 



not Carry Water in Freshefs 



Notes 
New Structures 



fitaJS-hZS 



Dfninnrgp Arpg 40 AcrfiM 



Hiliy Farm Land. Slope appn 
''Z Q' t n iVa o, U se, WX .t.P 



<^+a. 24-hOn Nq N(>w rulvfift 



.Ne.edeU^. 



5ta. 55-i-IO Drainai^e? Arffa 300 A. 



Q Ro/finq Farm Landj 



'laq. 

^ilopG ahout^O' per 1000 



U.<ik .^ xP^ r.onr.r^tf! Box. 



^& 



y<s^ 



Pig. 65. 



TOPOGRAPHY 



The topography notes show the features of the adjacent terri- 
tory that might affect the design. These include the location 
of buildings, drives, intersecting roads, streams, railroads, poles, 
trees, sidewalks, crosswalks, and property lines. The names 
of property owners are recorded. 

A simple method of locating these points is to refer them di- 
rectly to the previously run center line by right-angle offsets; 
such notes are easily taken and quickly plotted. 

In taking the topography the plus stationing along the center 
line and the offset distances to all points inside of the road fences 
should be measured by tape to the nearest foot; the distances 



TRAFFIC REPORT 



329 



to and the dimensions of buildings, etc., outside of these liniits, 
can be paced or estimated; the bearings of the property lines 
can be read near enough with a pocket compass, except for right- 
of-way surveys which are described on page 333. 

The instruments needed for work of this kind are a pocket 
compass reading to 2°, steel picket, and metallic tape. 

Two experienced men will take from two miles to four miles 
of topography a day except in villages, where from one-half to a 
mile is average speed. 

Direction and amount of traffic is determined by inspection and 
inquiry of the residents along the road. 

To illustrate the information required, an extract from the sur- 
vey report of the Fairport Nine Mile Point Road is given below: 






f50 



Sfa.lZ 



+50 



Sfa.ll 



_±S0 



V Sfa.lO 



■ Sta.lZ+80 



qj field Entruntt 



300' 




% 



I 






I 1 Sta.l&— i^ 2 



I 



jt^DriYevyay < -jp 
150' 



^ta.l2-»l0 



h^mi 



-^ 



24U 



c 



Fig. 66. 



Fairport Nine Mile Point Road Traffic Report 

Heavy Hauling. — The direction of heavy hauling on this road 
is approximately as follows: 

1. Station No. 195 to station o toward Fairport. 

2. " " 19s " " 400 ^' Webster. 

3. '' " 580 " '' 400 '^ 

This divides the road into three sections for the determination 
of the ruling grades. 

The ruling grades for section i will be determined by the hills 
at station 10 and station 48 and probably will be limited to 5 per 
cent. 

The ruling grade for section 2 will be determined by the knolls 
at stations 267, 285, and 300, 



330 



THE SURVEY 



The ruling grade for section 3 will be determined by the hills 
at stations 445 and 494. 

The team traffic is medium heavy station 90 to station o; light, 
station 270 to 90; medium, station 270 to 375; heavy, station 
375 to 386; very heavy, equivalent to city street, station 386 
to 408; medium heavy, station 408 to 450, and light, station 450 
to 580. Macadam construction will not be suitable stations 
386 to 408. 

The automobile pleasure traffic will be largely through traffic 
and probably fairly heavy. 

FOUNDATION SOILS 

The notes on soils show the character, width, and depth of 
the existing surfacing material and the kind of underlying mate- 



Soil Notes ^ 


Foundation Recommendations 


Sta.toSta. 


Surface Mat. 


Sob Surface 







zo 


Sand 8c (b ravel 


Sand 8e Gravel 


Total Ttiickness Macadam 7" 


30 


3/ 


Clay&Orave/ 


Clay 1' down 


11 fi n 12" 


31 


36 


Clay 


Clay 


n V 15" 


36 


40 


Gravel 8"deep 


Wet Clay 


Underdrain On Rt Stone 22" deep 


40 


41 


» 4" „ 


Clay Loam 


Fill at fhib Point »» 9" n 












































































































































-• 


, 






V' 


C 



Pig. 67. 



rial. This feature of the survey is important, as it governs the 
thickness of the bottom course, and, to a certain extent, the posi- 
tion of the grade line where an existing solid foundation can be 
utilized and the thickness of the improved road reduced to a 



minimum. 



Even with a careful soil examination it is impossible to make 
the design of the foundation definite, as mentioned on page 161, 
but the quantity of the material that will be needed can be esti- 
mated very closely. 



LOCATION OF MATERIALS 



33^ 



The sub-soil can be readily examined by driving a ij^" or i" 
steel bar to the required depth, which is usually not over 4.0' 
to 5.0' even in cuts, removing the bar and replacing with a %" 
gas pipe, which is driven a few inches and withdrawn. The core 
will give a fair idea of the material to be encountered. 

Where rock is encountered the elevation of the outcrop is shown, 
and if the rock underlies the road for any distance within two 
or three feet of the surface this depth is determined by driving bars. 
Sample notes below: 



Station 


Left 


Center Line 


Right 


62 
63 


3-5' 
20 

1.5' 

25 


1:1 
00 

1.2' 
00 


0.5' 
20 

i.o' 
22 



The note ^^^means that 20' to the left of the proposed center line 

20 V ^ ^ 

of the improvement, the rock is 3.5' below the present surface; 
from these notes the rock can be readily plotted on the cross- 
sections. Its character can be determined from adjacent out- 
crops, or from test pits, if required. 

LOCATION AND CHARACTER OF MATERIALS 

The selection of materials and the estimate of the construction 
cost depend on a knowledge of the available materials and their 
location relative to the road. 

Provided this data has not been well gathered on the Prelimi- 
nary investigation work it should be obtained at this stage. The 
methods were described in Chapter on Preliminary Investigation 
but will be repeated at this point for convenience. 

Unloading Points for Freight — Provided U. S. geological maps 
are obtainable, the position of sidings may be marked on the 
sheets. The notes for each siding show its car capacity; whether 
or not an elevator unloading plant can be erected, and if hand 
unloading is necessary whether teams can approach from one 
side or two. They should also show any coal trestles that can 
be utilized in unloading, and the location and probable cost of 
any new sidings that will materially reduce the length of the haul. 
Canal or river unloading points are shown in the same manner. 

Sand, Gravel, and Filler Material. — The position of sand and 
gravel pits and filler material are noted with their cost at the 
pit; if no local material is available the cost f.o.b. at the nearest 
siding is given. 

Stone Supply. — Provided imported stone is to be used the work 
is simplified to determining the rate f.o.b. to the various sidings 



332 



THE SURVEY 



for the product of the nearest commercial stone-crushing plant 
that produces a proper grade of stone. 

In case local stone is available the location of the quarries 
or outcrops is shown; the amount of stripping, if any, and the 
cost of quarry rights. If the estimate will depend upon rock 
owned by a single person an option is obtained to prevent an 
exorbitant raise in price. 

In the case of field or fence stone a careful estimate is made of 
the number of yards of boulder stone available, the owners* 
names, what they will charge for it, the position of the fences or 
piles relative to the road, or side roads, and if the fences are not 
abutting on a road or lane the length of haul through fields to 



Stone Est. 



/. Oeo. Barber I OOP cu. yds . fence 
Boulcfers 20 % Oram fe '4o% SanasTone 
lo% Limes for 



lo%Limesfone 30% so-H Rock 
SO'Ao-f -the Granite must he Blasted 
"^ • ed 



' ^(cdge^ 



2. Patrick Don I'm ZSOO cuyds. same 



as ah>o\^e 



3. Mike O'Donnelf 500 cu yds. 



J yd- ^ 

Large Qranite Boulderd 75% must 



he Blasted 



-4-. CId Limestone (Quarry 2o'^ face 



Samples taken- looks good for Top Stone 



Scafe 
l"=IMiIe 




Fig. 68. 



the nearest road or lane. As fences are usually a mixture of 
different kinds of rock, the engineer estimates the percentage of 
granite, limestone, sandstone, etc., and the percentage that will 
have to be blasted or sledged in order to be crushed by an ordi- 
nary portable crusher. The amount of ^ field stone required 
per cubic yard of macadam is given in estimates, page 593. If 
there is a large excess of stone a careful estimate need not be 
made, only enough data being collected to determine the probable 
position of the crusher set-ups and the average haul to each set- 
up. If a sufl&cient supply is doubtful a close estimate is made as 
outlined above and options obtained from the various owners. 
Samples of the different rocks are tested. (See materials.) 



RIGHT OF WAY SURVEYS 333 

Preliminary surveys of the above description should be made 
at a speed of from two to four miles per week at a cost of from 
$35 to $70 per mile, allowing $6 per day for the engineer; $3.50 
for the instrument man; $2 per man for three laborers; $1 per 
day board per man and $4 per day for livery. 

Right-of-way and diversion line surveys are often needed but 
are usually not made at this time; if the, designer believes that 
additional land must be acquired or that a diversion line is necessary, 
he indicates the information desired and the surveys are made. 

RIGHT-OF-WAY SURVEYS 

These surveys are used not only to show the amount of land 
to be acquired but, also, the damage to property from altering 
the shape of a field, cutting a farm in two, changing the position 
of a house or barn relative to the road, etc. 

The acreage to be taken is shown by an ordinary land survey 
in which the road lines, property lines, corners, etc., are located 
in relation to the proposed center line of the improvement, and 
their lengths and bearings carefully determined. It is often 
difficult to locate the road boundaries, as town records are care- 
lessly kept and there is a general tendency to encroach on the 
road. As the amount paid for new right-of-way is rarely settled 
on an acreage basis, it is customary to take the existing fence 
lines as the road line unless it is very evident that the fence has 
been moved. This produces better feeling on the part of the 
property owner and does not affect the price paid. The lines 
between adjoining properties are usually well defined. 

In cases where an orchard is damaged the position and size of 
the trees are noted; where a field or farm is cut the whole field 
is shown, with the shape and acreage of the pieces remaining after 
the land actually appropriated has been taken out. 

As is usually done in all land surveys, the parcel to be bought 
is traversed and the survey figured for closure error to insure 
the description against mistakes. 

The standard form of map and description of the N. Y. State 
Department is shown in the folio mng illustration: 



334 



THE SURVEY 




^ S 



o 
U 



O 



sT . O'O O 0) *> O 









a^ 



^ oil 

I g! 

^ J. J ao" 
^ > <^^ 

^ ^ '" tJ « 






iJ.SP, 



1 « 9 









*Jh k'C 3"^ rtri* p 

g 3 






P =^ S 2 r 



4, =3 U7^ ^,t3 0.J2 



*- .-: i-?^ >» ?^ s o M cj ?^, fl " *^ <u g 4,'S 



•^^^^ 






.g 



S..SJ 






O 

d 



ino-c5.,*««sJ£^da<uS4;*^5 







Xl.S'rO'^ o d^ d 



ffi Si 



STADIA 



335 



Table 30.1 Horizontal Distances and Elevations from 
Stadia Readings 



Minutes 



O 
2 

4 

6 

8 

10 

12 

14 
16 
18 
20 

22 

24 
26 
28 
30 

32 
34 
36 
38 
40 

42 
44 
46 
48 
50 

52 
54 
56 
58 
60 



c = 0.7s 



1.25 



Hor. 
Dist. 



100.00 
100.00 
100.00 
100.00 
100.00 
100.00 

100.00 
100.00 
100.00 
100.00 
100.00 

100.00 

100.00 

99.99 

99.99 

99.99 

99.99 
99.99 
99.99 
99.99 
99.99 

99.99 
99.98 
99.98 
99.98 
99.98 

99.98 
99.98 
99-97 
99-97 
99-97 



Difif. 
Elev. 



0.75 



1. 25 



0.00 
0.06 
0.12 
0.17 
0.23 
0.29 

0.35 
0.41 

0.47 
0.52 
0.58 

0.64 
0.70 
0.76 
0.81 
0.87 

0.93 
0.99 
1.05 
I. II 
1.16 

1.22 
1.28 

1.34 
1.40 

1.45 

1-51 
1.57 
1.63 
1.69 
1.74 



Hor. 
Dist. 



Diff. 
Elev. 



99-97 
99-97 
99-97 
99.96 
99.96 
99.96 

99.96 
99-95 
99-95 
99-95 
99.95 

99-94 
99-94 
99.94 

99-93 
99-93 

99-^3 
99-93 
99.92 

99-92 
99.92 

99.91 
99.91 
99.90 
99.90 
99.90 

99.89 
99.89 
99.89 
99.88 
99.88 



0.75 



1.25 



1.74 
1.80 
1.86 
1.92 
1.98 
2.04 

2.09 

2.15 
2.21 
2.27 
2.33 

2.38 
2.44 
2.50 
2.56 
2.62 

2.67 

2.73 
2.79 
2.85 
2.91 

2.97 
3.02 
3.08 

3-14 
3.20 

3.26 
3-31 
3-37 
3-43 
3-49 



0.03 



Hor. 
Dist. 



99.88 
99.87 
99.87 
99.87 
99.86 
99.86 

99-85 
99-85 
99.84 
99.84 

99-83 

99-83 
99.82 
99.82 
99.81 
99.81 

99.80 
99.80 
99-79 
99-79 
99.78 

99.78 
99.77 
99.77 
99.76 
99.76 

99-75 
99.74 
99.74 
99.73 
99.73 



0.75 



0.03 



i.oo 



1.25 



Diff. 
Elev. 



3-49 
3-55 
3.60 
3.66 
3.72 
3.78 

3-84 
3-90 
3-95 
4.01 
4.07 

4.13 
4.18 
4.24 
4.30 
4-36 

4.42 
4.48 
4-53 
4-59 
4.65 

4.71 
4.76 
4.82 
4.88 
4.94 

4.99 
5-05 
5-11 
5-17 
5.23 



0.03 



0.04 



0.05 



Hor. 
Dist. 



99-73 
99.72 
99.71 
99.71 
99.70 
99.69 

99.69 
99.68 
99.68 
99.67 
99.66 

99.66 

99.65 
99.64 

99-63 
99-63 

99.62 
99.62 
99.61 
99.60 
99.59 

99.59 
99-58 
99-57 
99-56 
99-56 

99.55 
99-54 
99-53 
99-52 
99-51 



0.75 



1-25 



1 From " Theory and Practice of Surveying," by Prof. J. B. Johnson, New York: 
John Wiley & Sons. We are enabled to use this form through the courtesy of Prof. 
J. B. Johnson. 



336 



THE SURVEY 



Table 30. Horizontal Distances and Elevations from 
Stadia READmcs.— Continued 



Minutes 



O 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

52 

54 

56 

S8 

60 

c = 0.75. 



c = 1.25. 



Hor. 
Dist. 



99-51 
99-51 
99-50 
99-49 
99.48 

99-47 

99.46 
99.46 
99-45 
99-44 
99-43 

99.42 
99.41 
99.40 
99-39 
99-38 

99-38 
99-37 
99-36 
99-35 
99-34 

99-33 
99.32 
99-31 
99-30 
99.29 

99.28 
99.27 
99.26 

99-25 
99.24 

0.75 



1.25 



Diff. 
Elev. 



Hor. 
Dist. 



6.96 
7.02 

7.07 

7.13 
7.19 

7.25 

7-30 
7.36 
7.42 
7.48 
7-53 

7.59 
7.65 
7.71 
7.76 
7.82 

7.88 
7-94 
7-99 
8.05 
8.11 

8.17 
8.22 
8.28 

8.34 
8.40 

8.45 
8.51 
8.57 
8.63 
8.68 

0.06 

0.08 



99.24 

99-23 
99.22 
99.21 
99.20 
99.19 

99.18 
99.17 
99.16 

99-15 
99.14 

99-13 
99.11 
99.10 
99.09 
99.08 

99-07 
99.06 

99-05 
99-04 
99-03 

99.01 
99.00 
98.99 
98.98 
98.97 

98.96 
98.94 

98.93 
98.92 

98.91 
0.75 
0.99 
1.24 



Diflf. 
Elev. 



Hor. 
Dist. 



8.68 

8.74 
8.80 
8.85 
8.91 
8.97 

9-03 
9.08 

9.14 
9.20 
9-25 

9-31 
9-37 
9-43 
9.48 

9.54 

9.60 

9-65 
9.71 

9-77 
9-83 

9.88 

9.94 

10.00 

10.05 

lO.II 

10.17 
10.22 
10.28 
10.34 
10.40 

0.07 

0.09 



98.91 
98.90 
98.88 
98.87 
98.86 
98.85 

98.83 
98.82 
98.81 
98.80 
98.78 

98.77 
98.76 
98.74 
98.73 
98.72 

98.71 
98.69 
98.68 
98.67 
98.65 

98.64 
98.63 
98.61 
98.60 
98.58 

98.57 
98.56 
98.54 
98.53 
98.51 

0.75 

0.99 
1.24 



Diff. 
Elev. 



Hor. 
Dist. 



10.40 
10.45 
10.51 

10.57 
10.62 
10.68 

10.74 
10.79 
10.85 
10.91 
10.96 

11.02 
11.08 
II. 13 
II. 19 
11.25 

11.30 
11.36 
11.42 
11.47 
11.53 

11.59 
11.64 
11.70 
11.76 
II.81 

11.87 

11.93 
11.98 
12.04 
12.10 

0.08 



0.14 



98.51 
98.50 
98.48 

98.47 
98.46 

98.44 

98.43 
98.41 
98.40 
98.39 
98.37 

98.36 
98.34 
98.33 
98.31 
98.29 

98.28 
98.27 
98.25 
98.24 
98.22 

98.20 
98.19 

98.17 
98.16 

98.14 

98.13 
98.11 
98.10 
98.08 
98.06 

0.74 

0.99 

1.24 



STADIA 



337 



Table 30. Horizontal Distances and Elevations from 
Stadia Readings. — Continued 



10" 



Minutes 



O 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

52 

54 

56 

58 

60 

= 0.75. 

C = I.OO. 

c = 1.25. 



Hor. 
Dist. 



98.06 
08.05 
98.03 
98.01 
98.00 
97.98 

97-97 
97-95 
97-93 
97-92 
97.90 

97.88 
97.87 
97.85 
97-83 
97.82 

97.80 
97.78 
97.76 
97-75 
97-73 

97.71 
97.69 
97.68 
97.66 
97.64 

97.62 
97.61 
97-59 
97-57 
97.55 

0.74 

0.99 

1.23 



Diff. 
Elev. 



Hor. 
Dist. 



13.78 
13.84 
13.89 

13.95 
14.01 
14.06 

14.12 

14.17 
14.23 
14.28 
14-34 

14.40 

14-45 
14.51 
14.56 
14.62 

14.67 

14.73 
14.79 
14.84 
14.90 

14.95 
15.01 
15.06 
15.12 
15-17 

15-23 
15.28 

15-34 
15.40 

15-45 



0.15 
0.18 



97-55 
97-53 
97-52 
97-50 
97.48 
97.46 

97-44 
97.43 
97.41 
97-39 
97-37 

97.35 
97-33 
97-31 
97.29 
97.28 

97^6 
97.24 
97.22 
97.20 
97.18 

97.16 
97.14 
97.12 
97.10 
97.08 

97.06 
97.04 
97.02 
97.00 
96.98 

0.74 

0.99 
1.23 



Diff. 
Elev. 



Hor. 
Dist. 



15.45 
15.51 
15.56 
15.62 

15-67 
15.73 

15-78 
15-84 
15.89 

15.95 
16.00 

16.06 
16. II 
16.17 
16.22 
16.28 

16.33 
16.39 

16.44 
16.50 
16.55 

16.61 
16.66 
16.72 
16.77 
16.83 

16.88 
16.94 
16.99 

17.05 
17.10 



0.16 



0.21 



96.98 
96.96 
96.94 
96.92 
96.90 
96.88 

96.86 
96.84 
96.82 
96.80 
96.78 

96.76 

96.74 
96.72 
96.70 
96.68 

96.66 
96.64 
96.62 
96.60 
96.57 

96.55 
96.53 
96.51 

96.49 
96.47 

96.45 
96.42 
96.40 
96.38 
96.36 

0.74 

0.98 

1.23 



Diff. 
Elev. 



Hor. 
Dist. 



17.10 
17.16 
17.21 
17.26 
17.32 
17.37 

17.43 
17.48 

17.54 
17.59 
17.65 

17.70 
17.76 
17.81 
17.86 
17.92 

17.97 
18.03 
18.08 
18.14 
18.19 

18.24 
18.30 
18.35 
18.41 
18.46 

18.51 

18.57 
18.62 
18.68 
18.73 

0.14 

0.18 

0.23 



96.36 

96.34 
96.32 
96.29 
96.27 
96.25 

96.23 
96.21 
96.18 
96.16 
96.14 

96.12 
96.09 
96.07 
96.05 
96.03 



95.98 
95-96 
95-93 
95.91 

95-89 
95-86 
95-84 
95-82 
95-79 

95-77 
95-75 
95-72 
95-70 
95-68 

0.73 
0.98 



338 



THE SURVEY 



Table 30. Horizontal Distances and Elevations from 
Stadia Readings. — Continued 



13° 



14" 



15° 



Minutes 



o 

2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 ..... , 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

52 

54 

56 

S8 

60 

c = 0.7s 



c = 1.25. 



Hor. 
Dist. 



95.68 
95.65 
95.63 
95.61 

95.58 
95.56 

95.53 
95.51 
95.49 
95.46 
95.44 

9541 
95.39 
95.36 
95-34 
95.32 

95-29 
95-27 
95-24 
95.22 

95-19 

95.17 
95-14 
95.12 
95.09 
95.07 

95.04 
95.02 
94.99 
94.97 
94-94 

C.73 

0.98 



Diff. 
Elev. 



Hor. 
Dist. 



20.34 
20.39 

20.44 
20.50 

20.55 
20.60 

20.66 
20.71 
20.76 
20.81 
20.87 

20.92 
20.97 
21.03 
21.08 
21.13 

21.18 
21.24 
21.29 

21.34 
21.39 

21.45 
21.50 

21.55 
21.60 
21.66 

21.71 
21.76 
21.81 
21.87 
21.92 

0.16 



0.27 



94.94 
94.91 
94.89 
94.86 
94.84 
94.81 

94-79 
94.76 

94-73 
94.71 
94.68 

94.66 

94.63 
94.60 
94-58 
94-55 

94-52 
94-50 
94-47 
94-44 
94-42 

94-39 
94.36 
94-34 
94-31 
94.28 

94.26 

94-23 
94.20 

94.17 
94.15 

0.73 

0.97 



Diff. 
Elev. 



Hor. 
Dist. 



21.92 
21.97 
22.02 
22.08 
22.13 
22.18 

22.23 
22.28 
22.34 
22.39 
22.44 

22.49 
22.54 
22.60 
22.65 
22.70 

22.75 
22.80 
22.85 
22.91 
22.96 

23.01 
23.06 
23.11 
23.16 
23.22 

23.27 
23.32 
23.37 
23.42 
23.47 

0.17 

0.23 

0.29 



94.15 
94.12 

94.09 
94.07 

94-04 
94.01 

93.98 
93.95 
93.93 
93.90 
93.87 

93.84 
93.81 
93-79 
93.76 
93.73 

93.70 
93.67 
93.65 
93.62 

93-59 

93-56 
93-53 
93.50 
93.47 
93.45 

93.42 
93.39 
93.36 
93.33 
93.30 

0.73 

0.97 



Diff. 
Elev. 



Hor. 
Dist. 



23.47 
23.52 
23.58 
23.63 
23.68 

23.73 

23.78 

23.83 
23.88 

23.93 
23.99 

24.04 
24.09 
24.14 
24.19 
24.24 

24.29 
24.34 
24-39 
24.44 

24.49 

24-55 
24.60 
24.65 
24.70 
24.75 

24.80 

24.85 
24.90 

24.95 
25.00 

0.19 

0.25 

0.31 



93.30 
93.27 
93.24 
93.21 
93.18 
93.16 

93.13 
93.10 

93-07 
93-04 
93.01 

92.98 

92.95 
92.92 
92.89 
92.86 

92.83 
92.80 
92-77 
92.74 
92.71 

92.68 
92.65 
92.62 

92.59 
92.56 

92.53 
92.49 
92.46 

92.43 
92.40 

0.72 

0.96 

1.20 



STADIA 



339 



Table 30. Horizontal Distances and Elevations from 
Stadia Readings. — Contmued 



16° 



17" 



18° 



19" 



Minutes 



O 

2 

4 

6 

8 

10 

12 

14 .... . 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 .... . 

42 

44 

46 

48 

50 

52 

54 

56 

58 

60 

c = 0.75 



1.25 



Hor. 
Dist. 



92.40 
92.37 
92.34 
92.31 
92.28 
92.25 

92.22 
92.19 
92.15 
92.12 
92.09 

92.06 
92.03 
92.00 
91.97 
91-93 

91.90 
91.87 
91.84 
91.81 
91.77 

91.74 
91.71 
91.68 
91.65 
91.61 

91.58 
91-55 
91-52 
91.48 

91-45 
0.72 

0.96 

1.20 



Di£f. 
Elev. 



Hor. 
Dist. 



26.50 

26.55 
26.59 
26.64 
26.69 
26.74 

26.79 
26.84 
26.89 
26.94 
26.99 

27.04 
27.09 

27.13 
27.18 

27.23 

27.28 

27.33 

27.38 

27.43 
27.48 

27-52 
27-57 
27.62 
27.67 
27.72 

27-77 
27.81 
27.86 
27.91 
27.96 



0.28 



0.35 



91-45 
91.42 

91-39 
91-35 
91.32 
91.29 

91.26 
91.22 
91.19 
91.16 
91.12 

91.09 
91.06 
91.02 
90.99 
90.96 

90.92 
90.89 
90.86 
90.82 
90.79 

90.76 
90.72 
90.69 
90.66 
90.62 

90.59 
90.55 
90.52 
90.48 

90.45 
0.72 

0.95 
1. 19 



Diff. 
Elev. 



Hpr. 
Dist 



27.96 
28.01 
28.06 
28.10 
28.15 
28.20 

28.25 
28.30 
28.34 
28.39 
28.44 

28.49 

28.54 
28.58 
28.63 
28.68 

28.73 

28.77 
28.82 
28.87 
28.92 

28.96 
29.01 
29.06 
29.11 
29-15 

29.20 

29-25 
29-30 
29-34 
29-39 

0.23 
0.30 
0.38 



90.45 
90.42 
90.38 

90.35 
90.31 
90.28 

90.24 
90.21 
90.18 
90.14 
90. n 

90.07 
90.04 
90.00 
89.97 
89^93 

89.90 
89.86 
89.83 
89-79 
89.76 

89.72 
89.69 

89.65 
89.61 
89.58 

89-54 
89.51 

89.47 
89-44 
89.40 



0.95 



1.19 



Diff. 
Elev. 



Hor. 
Dist. 



29-39 
29.44 
29.48 

29.53 
29-58 
29.62 

29.67 
29.72 
29.76 
29.81 
29.86 

29.90 

29-95 
30.00 
30.04 
30.09 

30.14 
30.19 
30.23 
30.28 
30.32 

30.37 
30.41 
30.46 

30.51 
30.55 

30.60 
30.65 
30.69 
30.74 
30.78 

0.24 
0.32 
0.40 



89.40 
89.36 

89-33 
89.29 
89.26 
89.22 

89.18 

89.15 
89.11 
89.08 
89.04 

89.00 
88.96 

88.93 
88.89 
88.86 

88.82 
88.78 

88.75 
88.71 
88.67 

88.64 
88.60 
88.56 

88.53 
88.49 

88.45 
88.41 
88.38 
88.34 
88.30 

0.71 

0.94 

1.18 



340 



THE SURVEY 



Table 30. Horizontal Distances and Elevations from 
Stadia Readings. — Continued 



20° 


21° 


22° 


23° 


Minutes. 


Hor. 
Dist. 


Diff. 
Elev. 


Hor. 
Dist. 


Diff. 
Elev. 


Hor. 
Dist. 


Diff. 
Elev. 


Hor. 
Dist. 


Diff. 
Elev. 




2 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

52 

54 

56 

58 

60 


88.30 
88.26 
88.23 
88.19 
88.15 
88.11 

88.08 
88.04 
88.00 
87.96 
87-93 

87.89 
87.85 
87.81 
87.77 
87.74 

87.70 
87.66 
87.62 
87.58 
87.54 

87.51 
87.47 
87.43 
87-39 
87.35 

87.31 
87.27 

87.24 
87.20 
87.16 


32.14 
32.18 

32.23 
32.27 
32.32 
32.36 

32.41 
32.45 
32.49 
32.54 
32.58 

32.63 
32.67 
32.72 
32.76 
32.80 

32.85 
32.89 

32.93 
32.98 
33.02 

33-07 
33-11 
33-15 
33-20 
33.24 

33.28 
33-33 
33-37 
33-41 
33-46 


87.16 
87.12 
87.08 
87.04 
87.00 
86.96 

86.92 
86.88 
86.84 
86.80 
86.77 

86.73 
86.69 

86.65 
86.61 
86.57 

86.53 
86.49 
86.45 
86.41 
86.37 

86.33 
86.29 
86.25 
86.21 
86.17 

86.13 
86.09 
86.05 
86.0I 
85-97 


33-46 
33-50 
33-54 
33-59 
33-63 
33.67 

33.72 
33-76 
33-80 
33-84 
33.89 

33.93 
33-97 
34-01 
34-06 
34.10 

34.14 
34.18 

34.23 
34.27 
34.31 

34-35 
34-40 
34.44 
34-48 
34.52 

34-57 
34-61 
34-65 
34-69 
34-73 


85-97 
85.93 
85.89 
85-85 
85.80 

85-76 

85.72 
85.68 
85.64 
85.60 
85-56 

85-52 
85.48 

85.44 
85.40 
85-36 

85-31 
85-27 
85-23 
85.19 
85-15 

85.11 
85.07 
85.02 
84.98 
84.94 

84.90 
84.86 
84.82 
84.77 
84-73 


34-73 
34-77 
34.82 
34-86 
34-90 
34-94 

34-98 
35-02 
35-07 
35-11 
35.15 

35.19 

35-23 
35.27 
35.31 
35-36 

35-40 
35-44 
35-48 
35-52 
35.56 

35-60 
35-64 
35-68 
35-72 

35-80 
35-85 
35-89 
35-93 
35-97 


84-73 
84.69 

84.65 
84.61 

84-57 
84-52 

84.48 

84-44 
84.40 

84-35 
84.31 

84.27 
84.23 
84.18 
84.14 
84.10 

84.06 
84.01 
83-97 
83-93 
83.89 

83.84 
83.80 
83.76 
83.72 
83.67 

83.63 
83-59 
83-54 
83.50 
83-46 


35-97 
36.01 
36.05 
36.09 

36.13 
36.17 

36.21 

36.25 
36.29 

36.33 
36.37 

36.41 
36.45 
36.49 
36.53 
36.57 

36.61 
36.65 
36.69 
36.73 
36.77 

36.80 
36.84 
36.88 
36.92 
36.96 

37.00 

37.04 
37-08 
37.12 
37.16 


c = 0.75. 


0.70 


0.26 


0.70 


0.27 


0.69 


0.29 


0.69 


0.30 


C = I.OO. 


0.94 


0.35 


0.93 


0.37 


0.92 


0.38 


0.92 


0.40 


c = 1.25. 


1.17 


0.44 


1.16 


0.46 


I-I5 


0.48 


I-15 


0.50 



STADIA 



341 



Table 30. Horizontal Distances and Elevations from 
Stadia Readings. — Continued 



24" 



Minutes 



O , 

2 , 

4 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

52 ...... . 

54 

56. 

58 

60 

c = 0.75, 

c = 1. 00, 

c = 1,25, 



Hor. 
Dist. 



83.46 
83.41 
83.37 
83.33 
83.28 

83.24 

83.20 

83.15 
83.11 
83.07 
83.02 

8-2.98 
82.93 
82.89 
82.85 
82.80 

82.76 
82.72 
82.67 
82.63 
82.58 

82.54 
82.49 
82.45 
82.41 
82.36 

82.32 
82.27 
82.23 
82.18 
82.14 

0.68 

0.91 

I.I4 



Diff. 
Elev. 



37.16 
37.20 
37.23 
37.27 
37.31 
37.35 

37.39 
37.43 
37.47 
37.51 
37.54 

37.58 
37.62 
37.66 
37.70 
37.74 

37.77 
37.81 
37.85 
37.89 
37.93 

37.96 
38.00 
38.04 
38.08 
38.11 

38.15 
38.19 
38.23 
38.26 

38.3Q 
0.31 
0.41 
0.52 



25" 



Hor. 
Dist. 



82.14 
82.09 
82.05 
82.01 
81.96 
81.92 

81.87 
81.83 
81.78 

81.74 
81.69 

81.65 
81.60 
81.56 
81.51 
81.47 

8L42 
81.38 

81.33 
81.28 
81.24 

81.19 
81.15 
81.10 
81.06 
81.01 

80.97 
80.92 
80.87 
80.83 
80.78 



0.90 
I.13 



Diff. 
Elev. 



38-30 
38.34 
38.38 
38.41 
38.45 
38.49 

38.53 
38.56 
38.60 
38.64 
38.67 

38.71 

38.78 
38.82 
38.86 

38.89 
38.93 
38.97 
39.00 

39.04 

39.08 
39.11 
39.15 
39.18 
39.22 

39.26 
39.29 
39.33 
39.36 
39-40 

0.32 

0.43 
0.54 



26° 



Hor. 
Bist. 



80.78 

80.74 
80.69 
80.65 
80.60 
80.55 

80.51 
80.46 
80.41 

80.37 
80.32 

80.28 
80.23 
80.18 
80.14 
80.09 

80.04 
80.00 

79.95 
79.90 
79.86 

79.81 
79.76 
79.72 

79.67 
79.62 

79.58 
79.53 
79.48 

79.44 
79.39 

0.67 
0.89 



Diff 
Elev. 



39.40 
39.44 
39.47 
39.51 
39.54 
39.58 

39.61 
39.65 
39.69 
39.72 
39.76 

39.79 
39.83 
39.86 
39.90 
39-93 

39.97 
40.00 
40.04 
40.07 
4lo.11 

40.14 
40.18 
40.21 
40.24 
40.28 

40.31 

40.35 
40.38 
40.42 
40.45 

0.33 

_o.45 

0.56 



27" 



Hor. 
Dist. 



79.39 
79.34 
79.30 
79.25 
79.20 

79.15 

79.11 
79.06 
79.01 
78.96 
78.92 

78.87 
78.82 
78.77 

78.73 
78.68 

78.63 
78.58 
78.54 
78.49 
78.44 

78.39 
78.34 
78.30 
78.25 
78.20 

78.15 
78.10 
78.06 
78.01 
77.96 

0.66 
0.89 



342 



THE SURVEY 



Table 30. Horizontal Distances and Elevations from 
Stadia Readings. — Concluded 



28° 



29" 



30" 



Minutes 



O , 

2 ...... 

4 

6 

8 

10 

12 

14 ...... 

16 

18 

20 

22 

24 

26 

28 

30 

32 

34 

36 

38 

40 

42 

44 

46 

48 

50 

52 

54 

56 

58 

60 

c = 0.75. 



1.25. 



Hor. 
Dist. 



77.96 
77.91 
77.86 
77.81 
77-77 
77.72 

77.67 
77.62 
77.57 
77.52 
77.48 

77.42 
77.38 
77.33 
77.28 

77.23 

77.18 

77.13 
77.09 

77-04 
76.99 

76.94 
76.89 
76.84 
76.79 
76.74 

76.69 
76.64 
76.59 
76.55 
76.50 

0.66 



Diff. 
Elev. 



Hor. 
Dist. 



41.45 
41.48 
41.52 
41.55 
41.58 
41.61 

41.65 
41.68 
41.71 
41.74 

41.77 

41.81 
41.84 
41.87 
41.90 
41.93 

41.97 
42.00 
42.03 
42.06 
42.09 

42.12 

42.15 
42.19 

42.22 
42.25 

42.28 
42.31 
42.34 
42.37 
42.40 

0.36 

0.48 

0.60 



76.50 
76.45 
76.40 

76.35 
76.30 
76.25 

76.20 

76.15 
76.10 
76.05 
76.00 

75-95 
75.90 

75.85 
75.80 

75-75 

75-70 
75-65 
75.60 

75.55 
75.50 

75.45 
75.40 
75-35 
75-30 
75.25 

75-20 
75-15 
75-10 

75-05 
75.00 

0.65 

0.87 

1.09 



Diff. 
Elev. 



Hor. 
Dist. 



42.40 

42.43 
42.46 

42.49 
42.53 
42.56 

42.59 
42.62 
42.65 
42.68 
42.71 

42.74 
42.77 
42.80 
42.83 
42.86 

42.89 
42.92 

42.95 
42.98 
43.01 

43-04 
43-07 
43.10 

43.13 
43.16 

43.18 
43-21 
43-24 
43-27 
43-30 

0.37 

0.49 

0.62 



75-00 

74-95 
74.90 

74.85 
74-80 

74.7s 

74.70 

74.65 
74.60 

74-55 
74.49 

74-44 
74.39 
74.34 
74.29 
74.24 

74.19 
74.14 

74-09 
74.04 

73-99 

73-93 
73-88 

73-83 
73-78 
73-73 

73.68 

73-58 
73.52 
73-47 

0.65 
0.86 
1.08 



ADJUSTMENT OF INSTRUMENTS 343 

Diversion Line Surveys. — ^Where there is no doubt as to the 
grade to be adopted, or the alignment to be used, the location 
is made directly in the field and the center line is run and the 
cross-sections taken in the same manner as for a preliminary survey. 
If, however, the country is badly cut up and it is difl&cult to make 
a field location direct, a transit stadia survey is made covering the 
territory that will include all the possible locations and from the 
resulting contour map the different locations are projected and 
approximate estimates figured. The adopted line is then run in 
the field, cross-sections taken in the usual manner and an accurate 
estimate made. This method is used so seldom that the author 
does not fed justified in giving much space to the theory of stadia 
measurements or the methods of stadia surveys (see page 416). If 
the reader is not familiar with this class of work he is referred to the 
standard works on surveying. 

A convenient scale for a contour map for the projection work 
mentioned above is i" = 20' with a contour interval of 1' to 5', 
depending on the country. Table 30 is useful for reducing stadia 
notes. For a small number of shots this table and a slide rule will 
answer the purpose; for any extended amount of work a stadia 
reduction diagram or Noble & Casgrain's tables are recommended. 

If the stadia work is well done very satisfactory projections 
can be made. 

ADJUSTMENT OF INSTRUMENTS 

Wye Level. — To Make the Line of Collimation Parallel to the 
Telescope Rings. — Level the instrument roughly. Loosen the Y 
clamps so the telescope can turn freely in them; clamp the hori- 
zontal motion and by means of the leveling screws and tangent 
motion bring the intersection of the cross hairs on some well de- 
fined point. Then, without lifting from the Ys, turn the tele- 
scope over 180° watching to see if the cross wires remain on the 
point during the operation; if they do the adjustment is correct; 
if they do not, correct J^ the apparent error for both vertical and 
horizontal wires by means of the cross hair ring, adjusting screws, 
and repeat until the wires remain on the point for a complete 
revolution. 

To Make the Longitudinal Axis of the Level Bubble Parallel to the 
Plane of the Line of Collimation. — ^Level the machine over either pair 
of leveling screws; unclamp the Ys; rotate the telescope in the Ys 
until the bubble tube is on one side of the bar. If the bubble re- 
mains in the center the adjustment is correct. If it runs from the 
center bring it to its correct position by means of the sidewise ad- 
justing screw at one end of the bubble case. 

To Make the Bubble Parallel to the Rings and Line of Collimation. — 
Level the machine; unclamp the Ys; lift the telescope carefully 
from the Ys and reverse end for end; if the bubble runs to the center 
after the telescope has been reversed the adjustment is correct; 
if not, correct J^ the error by means of the adjusting nuts on the 



344 THE SURVEY 

bubble case and J^ the error with the leveling screws and repeat 
the test until the bubble remains in the center. 

To Adjust the Ys so the Level Bubble Will Be at Right Angles to 
the Axis of the Instrument. — Level the machine approximately over 
both sets of screws; level carefully over one set; rotate on the 
spindle i8o°; if the bubble remains in the center the adjustment 
is correct; if not, correct J^^ the error by means of the adjusting 
nuts on the Ys and J^ by the leveling screws. Repeat until the 
bubble remains in the center when reversed over either pair of 
leveling screws. 

To Test the Horizontal Wire. — Be sure that the pin in the Y clamp 
is in the notch of the telescope ring to keep the telescope from 
rotating; level the machine and compare the horizontal wire 
with any level line; if the wire is not level loosen the cross wire 
ring and turn to the correct position. Adjust again for collimation 
and the level adjustments are complete. 

Dumpy Level. — To Make the Bubble Perpendicular to the Axis 
of the Instrument. — Level the machine roughly over both sets of 
leveling screws and carefully over one set; rotate on the pinion i8o°; 
if the bubble stays in the center the adjustment is correct; if not, 
correct ^i the error by means of the bubble adjusting nut and 3^ by 
the leveling screws, and repeat until correct. 

To Make the Horizontal Line of Collimation Parallel to the Level 
Bubble. — Level the machine; drive a stake about 150' or 200' 
from the instrument and set the level rod target by the horizontal 
wire; rotate the instrument 180° and set another stake at the same 
distance from the machine as the first one; drive it until a rod 
reading taken on it is the same as the reading on the first stake. 
These stakes will then be level even though the machine is out of 
adjustment. Then set the level up near one of the stakes; level 
carefully and take rod readings on both; if these readings are the 
same the level is in adjustment; if not, correct the position of 
the horizontal wire by means of the cross wire ring screws until the 
readings on both stakes are the same. 

Test the horizontal wire on a level line in the same manner as for 
the Y level. 

Transit. — Plate Levels. — ^Level the machine with each plate level 
bubble parallel to one set of leveling screws; rotate on the spindle 
180°; if the bubbles remain in the center the adjustment is correct; 
if not, correct }4 the error with the bubble adjusting screws and 
K with the leveling screws. Repeat until correct. 

Line of Collimation, Ordinary Distances. — ^Level the machine; 
clamp the horizontal motion; with the slow motion screw, set the 
vertical cross wire on some well-defined point 500 or 600 feet away; 
transit the telescope and set a mark the same distance in the op- 
posite direction; then rotate the machine on the spindle, set on 
the first mark and transit the telescope; if the vertical wire strikes 
the second point the adjustment is correct; if not, correct J-l the 
error by means of cross wire ring adjusting screws and repeat 
until correct. 



CURVE FORMULA 



345 



To Make the Standards the Same Height. — ^Level the machine 
carefully; set the vertical wire on some well defined point as 
high as can be seen; bring the telescope down and set a point; 
rotate the machine i8o°; transit the telescope set on the low point 
and raise the telescope; if the wire bisects the original high point 
the adjustment is correct; if not, correct J^ the error by means 
of the standard adjusting screw. 

Test the vertical wire by means of a plumb line to see that it 
is vertical; if not, loosen the cross hair ring and turn to the correct 
position; test again for collimation. 

If the transit is to be used as a level make the level bubble 
parallel to the horizontal wire by the two-peg method in the same 
manner as described for the Dumpy level. 

EXPLANATION OF CURVE TABLES AND DEVELOPMENT 
OF CURVE FORMULA 

Curves for roadwork need not be as carefully worked out as 
in railroad surveying. Except for long curves the external is 
usually measured and the curve run in by the eye, 
and for this reason many of the tables given in the 
railway field manuals are omitted and those used are 
tabulated in a different form. 

Table 31, Radii of Curves, — The curve radii are 
computed on a basis of 5730 feet as the radius of a 
one-degree curve and are inversely proportional to 
the degree of curvature; they are tabulated to the 
nearest o.i'. The usual columns showing logarithm 
of radius, tangent offset and middle ordinate are re- 
placed by the deflection angle per foot of arc, per 
25' of arc, and per 50' of arc, which saves consider- 
able time in the computation of deflections. These 
values are tabulated only for even degree, twenty- 
minute, thirty-minute, and forty-minute curves, as 
there is always sufficient leeway both in the external 
and tangent to select a suitable curve from this list. 

Table 32, Functions of 1° Curve, — Column i gives 
the central angle A for every 10 minutes from 0° to 4° every 
minute 4° to 100°, and every 10 minutes 100° to 120°. 

Column 2 gives the same central angle as in column i expressed 
in decimals of a degree. This simplifies figuring the curve length. 

Columns 3 and 4 give the tangent and external for the central 
angles of column i to the nearest o.i'. By the use of the chord 
lengths recommended at the top of each page of this table no 
correction need be made for tangent length or external distance 
of any desired curve, figured by dividing the. value given in the 
table by the degree of curvature required. 

The error that is introduced by the use of these chords is less 
than 0.1' per 100', which is the allowable limit of error in chaining 
center line. 




346 



THE SURVEY 



For the convenience of readers not familiar with the theory of 
curves and the computation of curve notes, the following brief dem- 
onstration is made : 



RADH OF CURVES AND DEGREE OF CURVATURE 

A one-degree curve is defined as a curve having such a radius that 
loo feet of arc will subtend a one-degree central angle. 

There are 360° of central angle for a complete circle. The circum- 
ference of a circle is expressed by the formula 27r R. Therefore the 
radius of a one-degree curve is determined by the formulae 



2Tr R = 360 X 100 



R = 



36,000 _ 36,000 



27r 2(3.14159) 



= 5729.6 feet 



(i) 



Table 31. Radii and Deflections 
Figured on a basis of R = 5730' for a 1° curve. 



Degree of 
Curve 


Radius of 
Curve 


Deflection 

per foot of 

Arc 


Deflection per 
25' of Arc 


Deflection per 50' 
of Arc 




Feet 


Minutes 


Deg. 


Minutes 


Deg. 


Minutes 


0° 30' . . 
0° 40' . . 
0° 50' . . 
1° 00' . . 
1° 20' . . 

1° 30' . . 
1° 40' . . 
2° 00' . . 
2° 20' . . 

s"* 30' . • 

2** 40' . . 
3^00'.. 


11,460.0 
8.595.0 
6,876.0 
5,730.0 
4,297-5 

3,820.0 
3,438.0 
2,865.0 

2,455.7 
2,292.0 

2,148.8 
1,910.0 


00.15 

00.2 

00.25 

00.3 

00.4 

00.45 

00.5 

00.6 

00.7 

00.75 

00.8 
00.9 


— 


— 


















07.5 

lO.O 

12.5 

I5-0 
20.0 

22.5 
25.0 
30.0 
35.0 
37.5 

40.0 
45.0 



RADII AND DEFLECTIONS 

Table 31. — Continued 



347 



Degree of 


Radius of 


Deflection 

per foot of 

Arc 


Deflection per 


Deflection per 50' 


Curve 


Curve 


25' of Arc 


of Arc 




Feet 


Minutes 


Deg. 


Minutes 


Deg. 


Minutes 


3° 20; . . 


1,719.0 


01. 


— 


— 





50.0 


3>° •• 


1,637.1 


. 01.05 


— 


— 





52.5 


3 40' . . 


1,562.7 


01. 1 


— 


— 





55.0 


4° 00' . . 


1,432.5 


01.2 


— 


— 




00.0 


4° 20' . . 


1,322.3 


01.3 


— 


— 




05.0 


4"" 30' • • 


1,273-3 


01.35 


— 


— 




07.5 


4° 40' . . 


1,227.9 


01.4 


— 


— 




lO.O 


5° 00' . . 


1,146.0 


01.5 


— 


— 




15.0 


5:3°:-- 


1,041.8 


01.65 


— 






22.5 


6° 00' . . 


955.0 


01.8 


— 


— 




30.0 


6° 30' . 


881.5 


01.95 


— 


— 




37.5 


7° 00' . 


818.6 


02.1 


— 


— 




45.0 


7° 30'.. 


764.0 


02.25 


— 






52.5 


8° 00' . . 


716.3 


02.4 


— 


— 


2 


00.0 


8° 30' . . 


674.1 


02.55 


— 


— 


2 


07.5 


9° 00' . . 


636.6 


02.7 


— 


— 


2 


15.0 


9° 30' . . 
10 00 . . 


603.2 
573.0 


02.85 


— 


— 


2 
2 


22.5 
30.0 


03.0 


— 


10° 30' . . 


545.7 


03.15 


— 


— 


2 


37.5 


11° 00' . . 


520.9 


03.3 


— 


— 


2 


45.0 


11° 30' . . 


498.3 


03.45 


— 


— 


2 


52.5 


12° 00' . . 


477-5 


03.6 


— 


— 


3 


00.0 


12° 30' . . 


458.4 


03.75 


— 


— 


3 


07.5 


13° 00' . . 


440.8 


03-9 


— 


— 


3 


15.0 


13° 30' . . 


424.4 


04.05 


— 


— 


3 


22.5 


14° 00' . . 


409.3 


04.2 


— ■ 


— 


3 


30.0 


14° 30' . . 


395.2 


04.35 


— 


— 


3 


37-5 


15° 00' . . 


382.0 


04.5 


— ' 


— 


3 


45.0 


15° 30' . . 


369.6 


04-65 


— 


— 


3 


52.5 


16° 00' . . 


358.1 


04.8 


2 


00.0 


4 


00.0 


16° 30' . . 


347.3 


04.95 


2 


03.8 


4 


07.5 


17° 00' . . 


337.0 


05.1 


2 


07.5 


4 


15.0 


17° 30' . . 


327.4 


05.25 


2 


II. 2 


4 


22.5 


18° 00' . . 


318.3 


05.4 


2 


15.0 


4 


30.0 


18° 30' . . 


309.7 


05.55 


2 


18.7 


4 


37.5 



348 



THE SURVEY 



Table 31. — Continued 



Degree of 


Radius of 


Deflection 

per ft. of 

Arc 


Deflection per 
25' of Arc 


Deflection per 


Curve 


Curve 






so' of Arc 


Minutes 


Degree 


Minutes 


19° 00' 


301.6 


05.7 


2 


22.5 




19° 30' 


293.8 


05.85 


2 


26.2 




20° 00' 


286.5 


06.0 


2 


30.0 




20° 30' 


279.5 


06.15 


2 


33.7 




21° 00' 


272.9 


06.30 


2 


37.5 




21° 30' 


266.5 


06.45 


2 


41.2 




22° 00' 


260.5 


06.6 


2 


45.0 




22° 30' 


254.7 


06.75 


2 


48.7 




23° 00' 


249.1 


06.9 


2 


52.5 




23° 30' 


243.8 


07.05 


2 


56.2 




24° 00' 


238.8 


07.2 


3 


00.0 




24° 30' 


233.9 


07.35 


3 


03.7 




25° 00' 


229.2 


07.5 


3 


07.5 




26° 00' 


220.4 


07.8 


3 


15.0 




27° 00' 


212.2 


08.1 


3 


22.5 




28° 00' 


204.6 


08.4 


3 


30.0 




29° 00' 


197.6 


08.7 


3 


37.5 




30° 00' 


191.O 


09.0 


3 


45.0 


Deflection per 
10' of Arc 


31° 00' 


184.8 


09.3 


3 


52.5 




32° 00' 


179.1 


09.6 


4 


00.0 


1° 


36; 


33° 00' 


173.6 


09.9 


— 


— 


1° 


39 


34° 00' 


168.5 


10.2 


— 


— 


1° 


42' 


35° 00' 


163.7 


10.5 


— 


— 


1° 


45' 


36° 00' 


159.2 


10.8 


— 


— 


1° 


48; 


37° 00' 


154.9 


II. I 


— 


— 


1° 


5^ 


38° 00' 


150.8 


II.4 


— 


— 


1° 


5< 


39° 00' 


146.9 


II. 7 


— 




1° 


57 


40° 00' 


143.2 


12.0 


— 


— 


2° 


00' 


42° 00' 


136.4 


12.6 


— 


— 


2° 


06' 


44° 00' 


130.2 


13.2 


— 


— 


2° 


12' 


46° 00' 


124.6 


13.8 


— 


— 


2° 


18' 


48° 00' 


I19.4 


14.4 


— 


— 


2° 


24' 


50° 00' 


I14.6 


15.0 


— 


— 


2° 


30' 


52° 00' 


II0.2 


15.6 





— 


2° 


36; 


54° 00' 


I06.I 


16.2 


— 


— 


2° 


42' 


56° 00' 


102.3 


16.8 


— ~ 


"~" 


2° 


48' 



CURVE FORMULAE 



349 



For all practical purposes the value of 5730 can be used. 

In the same manner a two-degree curve is one having such a 
radius that 100 feet of arc will subtend two degrees of central 
angle, and its radius is 

27r i^ = ^— X 100 
2 

_ 18,000 



or }4. of the radius of a one-degree curve. 

The radius of a three-degree curve will be J-^ of 5730. 

The radius of a four-degree curve will be J^ of 5730. 

The formula for the radius of any degree of curve is therefore 

(2) 



R = 



5730 
D 



The degree of curvature for any specified radius is therefore 

(3) 

In general the degree of curvature is expressed by the central 
angle subtended by 100 feet of arc, and the radius for that degree 
of curve is found by dividing 5730 feet, the radius of a one-degree 
curve, by the degree of curve desired expressed in degrees and 
decimals of a degree. That is, if the radius of a 3° 30' curve is 
wanted, divide 5730 by :2^.^, which equals 163 7.1'. The radii given 
in Table 31 are computed in this manner. 

Length of Curve. — For a 5° curve a central angle of 5° subtends 

100' of arc; a central angle of 10°, 200' of arc; a central angle of 

12° 30', 250' of arc. That is, for a specified central angle the 

length of any specified curve equals that central angle expressed 

in degrees and decimals of a degree divided by the degree of curve 

expressed in degrees and decimals multiplied by 100; i.e., the length 

20.7^ • 

of a 10° 15' curve for a central angle of 20° 45' = — '■ — X 100' = 

10.25 

202.4' 3-nd is expressed by the formula (continued on page 376) 

Table 32. Functions of a One-Degree Curve Figured on 
A Basis of 1^ = 5730' and Tabulated to Tenths of Feet 

Use 100' chords up to 8° Curves Use 25' chords up to 32" Curves 

Use so' chords up to 16° Curves Use 10' chords above 32° Curves 



5 


0° 


1° 




" 


3° 


g 
5 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





0.0 


0.0. 


0.2 


50.0 


0.9 


lOO.O 


2.0 


. 150-1 





10 


0.0 


8.3 


0.3 


S8.3 


I.O 


108.4 


2.2 


158.4 


10 


20 


0.0 


16.7 


0.4 


66.7 


1.2 


116.7 


2.4 


166.8 


20 


30 


0.1 


25.0 


0.5 


7S.O 


1.4 


125.0 


2.7 


175.1 


30 


40 


0.1 


33.3 


0.6 


83.3 


! 1.6 


1334 


2.9 


183.4 


40 


§° 


0.2 


41.7 


0.7 


91.7 


1.8 


141.7 


3.2 


191.7 


so 


60 


0.2 


50.0 


0.9 


lOO.O 


2.0 


150.1 


3.5 


200.1 


60 



350 



THE SURVEY 



Use loo' chords up to 8" Curves 
Use 50' chords up to 16" Curves 



Use 25' chords up to 32° Curves 
Use 10' chords above 32° Curves 



1 

c 




4 




5 


° 


6 





7 





1 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


3-5 


200.1 


5.5 


250.2 


7.9 


300.3 


10.7 


350.4 





I 


.0167 


3-5 


200.9 


5.5 


251.0 


7-9 


301. 1 


10.8 


351.3 


I 


2 


•0333 


3-6 


201.8 


5-5 


251.8 


8.0 


302.0 


10.8 


352.1 


2 


3 


.0500 


3.6 


202.6 


5.6 


252.7 


8.0 


302.8 


10.9 


352.9 


3 


4 


.0667 


3.6 


203.4 


5.6 


253-5 


8.0 


303.6 


10.9 


353.8 


4 


s 


•0833 


3.6 


204.3 


5.6 


254-3 


8.1 


304.5 


II.O 


354.6 


5 


6 


.1000 


3-7 


205.1 


5.7 


255.2 


8.1 


305.3 


II.O 


355-5 


6 


7 


.1167 


3-7 


205.9 


5.7 


256.0 


8.2 


306.1 


II. I 


356.3 


7 


8 


.1333 


3.7 


206.8 


5.8 


256.8 


8.2 


307.0 


II. I 


357.1 


8 


9 


.1500 


3.8 


207.6 


5.8 


257.7 


8.3 


307-8 


11.2 


358.0 


9 


10 


.1667 


3.8 


208.4 


5-8 


258.5 


8.3 


308.6 


II. 2 


358.8 


10 


II 


.1833 


3.8 


209.3 


5.9 


259.3 


8.4 


309.5 


11.3 


359-6 


II 


12 


.2000 


3.9 


210.1 


5.9 


260.2 


8.4 


310.3 


11.3 


360.5 


12 


13 


.2167 


3-9 


210.9 


5-9 


261.0 


8.4 


3II.I 


11.4 


361.3 


13 


14 


.2333 


3-9 


211.8 


6.0 


261.9 


8.5 


312.0 


11.4 


362.2 


14 


IS 


.2500 


3.9 


212.6 


6.0 


262.7 


8.5 


312.8 


11.5 


363.0 


15 


16 


.2667 


4.0 


213.4 


6.1 


263.5 


8.6 


313.7 


ii.S 


363.8 


16 


17 


•2833 


4.0 


214.3 


6.1 


264.4 


8.6 


314-S 


11.6 


364.7 


17 


18 


.3000 


4.0 


2I5-I 


6.1 


265.2 


8.7 


315-3 


II. 7 


365.5 


18 


19 


.3167 


4.1 


215-9 


6.2 


266.0 


8.7 


316.2 


11.7 


366.3 


19 


20 


.3333 


4.1 


216.8 


6.2 


266.9 


8.8 


317.0 


11.8 


367-2 


20 


21 


•3500 


4.1 


217.6 


6.2 


267.7 


8.8 


317-8 


11.8 


368.0 


21 


22 


.3667 


4.2 


218.4 


6.3 


268.5 


8.9 


318.7 


11.9 


368.8 


22 


23 


.3833 


4.2 


219.3 


6.3 


269.4 


8.9 


319.5 


11.9 


369.7 


23 


24 


.4000 


4.2 


220.1 


6.4 


270.2 


9.0 


320.3 


12.0 


370.5 


24 


^ 


.4167 


4-3 


220.9 


6.4 


271.0 


9.0 


321.2 


12.0 


371.4 


25 


26 


.4333 


4-3 


221.8 


6.4 


271.9 


9.0 


322.0 


12. 1 


372.2 


26 


^l 


.4500 


4-3 


222.6 


6.5 


272.7 


9-1 


322.8 


12. 1 


373.0 


27 


28 


.4667 


4.4 


223.5 


6.5 


273.5 


9-1 


323.7 


12.2 


373.9 


28 


29 


.4833 


4.4 


224.3 


6.5 


274.4 


9.2 


324-5 


12.2 


374.7 


29 


30 


.5000 


4.4 


225.1 


6.6 


275.2 


9.2 


325-4 


12.3 


375.S 


30 


31 


•5167 


4-5 


226.0 


6.6 


276.1 


9-3 


326.2 


12.4 


376.4 


31 


32 


•5333 


4.5 


226.8 


6.7 


276.9 


9-3 


327-0 


12.4 


377.2 


32 


33 


.5500 


4-5 


227.6 


6.7 


277.7 


9-4 


327-9 


12.5 


378.1 


33 


34 


.5667 


4.6 


228.5 


6.8 


278.6 


9.4 


328.7 


12.S 


378.9 


34 


35 


.5833 


4.6 


229.3 


6.8 


279.4 


9.5 


329.5 


12.6 


379.7 


35 


36 


.6000 


4.6 


230.1 


6.8 


280.2 


9-5 


330.4 


12.6 


380.6 


36 


37 


.6167 


4.7 


231.0 


6.9 


281. 1 


9.6 


331.2 


12.7 


381.4 


H 


38 


.6333 


4-7 


231.8 


6.9 


281.9 


9.6 


332.0 


12.7 


382.2 


38 


39 


.6500 


4.7 


232.6 


7.0 


282.7 


9.7 


332.9 


12.8 


383.1 


39 


40 


.6667 


4.8 


233.S 


7.0 


283.6 


9-7 


333.7 


12.9 


383.9 


40 


41 


.6833 


4.8 


234-3 


7.1 


284.4 


9.8 


334.6 


12.9 


384.7 


41 


42 


.7000 


4.8 


235.1 


7-1 


285.2 


9.8 


335.4 


13.0 


385.6 


42 


43 


.7167 


4.9 


236.0 


7.1 


286.1 


9.9 


336.2 


13.0 


386.4 


43 


44 


.7333 


4.9 


236.8 


7.2 


286.9 


9.9 


337.1 


13.1 


387.3 


44 


45 


.7500 


4.9 


237.6 


7.2 


287.7 


lO.O 


337.9 


13.1 


388.1 


45 


46 


.7667 


S.o 


238.5 


7.3 


288.6 


1 0.0 


338.7 


13.2 


388.9 


46 


47 


.7833 


5.0 


239-3 


7.3 


289.4 


lO.I 


339.6 


13.2 


389.8 


4^ 


48 


.8000 


5.0 


240.1 


7.3 


290.3 


lO.I 


340.4 


13.3 


390.6 


48 


49 


.8167 


5.1 


241.0' 


7.4 


291. 1 


10.2 


341.2 


13.4 


391.4 


49 


SO 


.8333 


5-1 


241.8 


7.4 


291.9 


10.2 


342.1 


13.4 


392.3 


SO 


51 


.8500 


5.1 


242.6 


7.5 


292.8 


10.3 


342.9 


13.5 


393-1 


51 


S2 


.8667 


5.2 


243.5 


7.5 


293.6 


10.3 


343.7 


13.5 


394-0 


52 


53 


.8833 


5.2 


244.3 


7.5 


294.4 


10.4 


344.6 


13.6 


394-8 


53 


54 


.9000 


5-2 


245.2 


7.6 


295.3 


10.4 


345.4 


13.7 


395-6 


54 


55 


.9167 


5.3 


246.0 


7.6 


296.1 


lo.s 


346.3 


13.7 


396.5 


55 


56 


.9333 


5.3 


246.8 


7.7 


296.9 


10.5 


347.1 


13.8 


397.3 


56 


57 


.9500 


5.3 


247.7 


7.7 


297.8 


10.6 


347.9 


13.8 


398.1 


57 


58 


.9667 


5.4 


248.5 


7.8 


298.6 


10.6 


348.8 


13-9 


399.0 


58 


59 


.9833 


5.4 


249.3 


7.8 


299.4 


10.7 


349.6 


13.9 


399.8 


59 



FUNCTIONS OF ONE-DEGREE CURVE 

Use loo' Chords up to S° Curves Use 25' Chords up to 32° Curves 
Use 50' Chords up to 16° Curves Use 10' Chords above 32° Curves 



351 



3 




g 


» 


9° 


10° 


11° 


i 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


.i4^o 


400.7 


17.7 


450.9 


21.9 


501.3 


26.5 


551-7 





I 


.0167 


14.0 


401.5 


17.8 


451-8 


21.9 


502.2 


26.6 


552.6 


I 


2 


•0333 


14.1 


402.4 


17.8 


452.6 


22.0 


503. 


26.7 


553.4 


2 


3 


.0500 


14.2 


403.2 


17.9 


453.4 


22.1 


503-8 


26.7 


554-3 


3 


4 


.0667 


14.2 


404.0 


18.0 


454^3 


22.2 


504.7 


26.8 


555.1 


4 


5 


.0833 


14-3 


404.8 


18.0 


455^1 


22.3 


505.5 


26.9 


555-9 


5 


6 


.1000 


14-3 


405.7 


18.1 


456.0 


22.3 


506.4 


27.0 


556.8 


.6 


7 


.1167 


14.4 


406.5 


18.2 


456.8 


22.4 


507-2 


27.1 


557-6 


7 


8 


.1333 


14-5 


407.4 


18.3 


457.7 


22.5 


508.0 


27.2 


558.5 


8 


9 


.1500 


14-5 


408.2 


18.3 


458.5 


22.6 


508.9 


27.2 


559.3 


9 


10 


.1667 


14.6 


409.0 


18.4 


459.3 


22.6 


509.7 


27-3 


560.1 


10 


II 


•1833 


14.6 


409.9 


18.4 


460.2 


22.7 


510.6 


27.4 


561.0 


II 


12 


.2000 


14.7 


410.7 


18.5 


461.0 


22.8 


511-4 


27-5 


561.8 


12 


13 


.2167 


14.8 


4II-5 


18.6 


461.8 


22.9 


512.2 


27.6 


562.7 


13 


14 


.2333 


14.8 


412.4 


18.7 


462.7 


22.9 


513.1 


27.7 


563.5 


14 


15 


.2500 


14.9 


413.2 


i8.r 


463.5 


23.0 


513.9 


27.7 


564-3 


IS 


16 


.2667 


14.9 


414.1 


18.8 


464.4 


23.1 


514.8 


27.8 


565.2 


16 


17 


•2833 


15.0 


414.9 


18.9 


465-2 


23.2 


515.6 


27.9 


566.0 


17 


18 


.3000 


15^1 


415.7 


18.9 


466.0 


23.2 


516.4 


28.0 


566.9 


18 


19 


•3167 


15.I 


416.6 


19.0 


466.9 


23.3 


517.3 


28.1 


567.7 


19 


20 


•3333 


15.2 


417.4 


19.1 


467.7 


23.4 


518.1 


28.1 


568.5 


20 


21 


•3500 


15-2 


418.2 


19.1 


468.5 


23.5 


519.0 


28.2 


569.4 


21 


22 


.3667 


15^3 


419.1 


19.2 


469.4 


23.5 


519-8 


28.3 


570.2 


22 


23 


.3833 


1S.4 


419.9 


19-3 


470.2 


23.6 


520.6 


28.4 


571.1 


23 


24 


.4000 


15-4 


420.8 


19.3 


471. 1 


23.7 


521.5 


28.5 


571.9 


24 


^^ 


.4167 


15^5 


421.6 


19.4 


471.9 


23.8 


522.3 


28.6 


572.8 


25 


26 


.4333 


15.6 


422.4 


19.5 


472.8 


23-8 


523-2 


28.6 


573-6 


26 


27 


.4500 


15.6 


423.3 


19^5 


473-6 


23.9 


524.0 


28.7 


574-4 


27 


28 


.4667 


15.7 


424.1 


19.6 


474-4 


24-0 


524.9 


28.8 


575-3 


28 


29 


.4833 


IS.7 


424.9 


19.7 


475-3 


24.1 


525.7 


28.9 


576.1 


29 


30 


.5000 


I5^8 


425^8 


19.8 


476.1 


24.1 


526.5 


29.0 


577.0 


30 


31 


.5167 


159 


426.6 


19.8 


476.9 


24.2 


527-4 


29.1 


577-8 


31 


32 


•5333 


iS-9 


427.5 


19.9 


477-8 


24-3 


528.2 


29.1 


578.6 


32 


33 


•5500 


16.0 


428.3 


20.0 


478.6 


24.4 


529.0 


29.2 


579.5 


33 


34 


.5667 


16.0 


429.1 


20.0 


479-5 


24-5 


529.9 


29-3 


580.3 


34 


35 


.5833 


16.1 


430.0 


20.1 


480.3 


24.S 


530.7 


29-4 


581.2 


35 


36 


.6000 


16.2 


430.8 


20.2 


481. 1 


24.6 


531.6 


29-5 


582.0 


36 


37 


.6167 


16.2 


431.7 


20.2 


482.0 


24-7 


532.4 


29.6 


582.8 


37 


38 


•6333 


16.3 


432.5 


20.3 


482.8 


24.8 


533-3 


29-7 


583.7 


38 


39 


.6500 


16.4 


433.3 


20.4 


483.6 


24.8 


S34.I 


29.7 


584.5 


39 


40 


.6667 


16.4 


434.2 


20.S 


484.S 


24.9 


534 9 


29.8 


58S-4 


40 


41 


.6833 


16.5 


435.0 


20.S 


485-3 


25.0 


535-8 


29-9 


586.2 


41 


42 


.7000 


16.6 


435-9 


20.6 


486.2 


25.1 


536.6 


30.0 


587.1 


42 


43 


.7167 


16.6 


436.7 


20.7 


487.0 


25.1 


537-5 


30.1 


587.9 


43 


44 


.7333 


16.7 


437^5 


20.7 


487.9 


25.2 


538.3 


30.2 


588.7 


44 


"^1 


.7500 


16.7 


438.4 


20.8 


488.7 


25.3 


S39.I 


30.3 


589.6 


45 


46 


.7667 


16.8 


439-2 


20.9 


489.6 


25-4 


540.0 


30.3 


590.4 


46 


"^l 


.7833 


16.9 


440.0 


21.0 


490.4 


25-5 


540.8 


30.4 


591.3 


47 


48 


.8000 


16.9 


440.9 


21.0 


491.2 


25.5 


541.7 


30.S 


592.1 


48 


49 


.8167. 


17.0 


441.7 


21.1 


492.0 


25.6 


542.5 


30.6 


592.9 


49 


50 


.8333 


17.I 


442.5 


21.2 


492.9 


25-7 


543-3 


30.7 


593.8 


50 


51 


.8500 


17.1 


443.4 


21.2 


493.7 


25.8 


544-2 


30.8 


594-6 


51 


52 


•^^^7 


17.2 


444.2 


21.3 


494-6 


25-9 


545.0 


30.9 


595-5 


52 


S3 


•8833 


17-3 


445-1 


21.4 


495.4 


25-9 


545-9 


3I.O 


596.3 


53 


54 


.9000 


17.3 


445-9 


21.5 


496.3 


26.0 


S46.7 


31.0 


597-2 


54 


55 


.9167 


17^4 


446.7 


21.5 


497-1 


26.1 


547.5 


31.1 


598.0 


55 


56 


•9333 


17.5 


447-6 


21.6 


498.0 


26.2 


548.4 


31.2 


598.8 


56 


57 


.9500 


17.5 


448.4 


21.7 


498.8 


26.3 


549.2 


31.3 


599-7 


57 


58 


.9667 


17.6 


449.3 


21.8 


499-6 


26.3 


550.1 


31-4 


600.5 


58 


59 


.9833 


17.6 


450.1 


21.8 


500.4 


26.4 


550.9 


31-S 


601.4 


59 



352 








THE SUR 


VEY 










Use loo' Chords up to 8 


° Curves 


Use 


25' Chords up to 


sa** Curves 


Use 50 


Chords 


up to 16 


° Curves 


Use 


10' Chords above 32° Curves 


T 

d 




12° 


13° 


i^ 




15° 


1 

3_ 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


31.6 


602.2 


37.1 


652.9 


43.0 


703.5 


49-4 


754.4 





I 


.0167 


31.7 


603.1 


37.2 


653-7 


43-1 


704-4 


49-6 


755.2 


I 


2 


.0333 


31-7 


603.9 


37.3 


654-6 


43-2 


705.2 


49-7 


756.1 


2 


3 


.0500 


31.8 


604.7 


37-4 


655.4 


43-3 


706.1 


49.8 


756.9 


3 


4 


.0667 


31-9 


605.6 


37-5 


656.3 


43.4 


706.9 


49.9 


757.7 


4 


5 


.0833 


32.0 


606.4 


37.6 


657.1 


43.5 


707.8 


50.0 


758.6 


S 


6 


.1000 


32.1 


607.3 


37.7 


657-9 


43-7 


708.6 


50.1 


759-4 


6 


7 


.1167 


32.2 


608.1 


37.7 


658.8 


43-8 


709.5 


50.2 


760.3 


7 


8 


.1333 


32.3 


609.0 


37.8 


659-6 


43-9 


710.3 


50.3 


761.1 


8 


9 


.1500 


32.4 


609.8 


37.9 


660.5 


44.0 


711.2 


50.5 


762.0 


9 


10 


.1667 


32.5 


610.7 


38-0 


661.3 


44.1 


712.0 


S0.6 


762.8 


10 


II 


.1833 


32.S 


611.S 


38.1 


662.2 


44.2 


712.9 


50.7 


763-7 


II 


12 


.2000 


32.6 


612.4 


38.2 


663.0 


44.3 


713-7 


50.8 


764-5 


12 


13 


.2167 


32.7 


613.2 


38.3 


663.8 


44.4 


714.6 


50.9 


765-4 


13 


14 


.2333 


32.8 


614.0 


38.4 


664.7 


44.5 


715.4 


51.0 


766.2 


14 


IS 


.2500 


32.9 


614.9 


38.5 


665.5 


44.6 


716.3 


Si.i 


767.1 


15 


16 


.2667 


33-0 


615-7 


38.6 


666.4 


44.7 


717. 1 


51.2 


767-9 


16 


17 


.2833 


33-1 


616.6 


38.7 


667.2 


44.8 


718.0 


51.3 


768.8 


17 


18 


.3000 


33.2 


617.4 


38.8 


668.1 


44-9 


718.8 


S1.5 


769.6 


18 


19 


.3167 


33.3 


618.3 


•38.9 


668.9 


45.0 


719.6 


S1.6 


770.5 


19 


20 


.3333 


33.4 


619.1 


39.0 


669.8 


45-1 


720.5 


^H 


771.3 


20 


21 


.3500 


33.4 


619.9 


39.1 


670.6 


45.2 


721.3 


51.8 


772.2 


21 


22 


.3667 


33-5 


620.8 


39.2 


671.4 


45.3 


722.2 


51.9 


773.0 


22 


23 


.3833 


33.6 


621.6 


39.3 


672.3 


45.4 


723.1 


j2.0 


773.9 


23 


24 


.4000 


33.7 


622.5 


39.4 


673.1 


45.5 


723.9 


S2.I 


774.7 


24 


25 


.4167 


33.8 


623.3 


39.5 


674-0 


45-6 


724.7 


523 


775.6 


25 


26 


.4333 


33-9 


624.2 


39-6 


674-8 


45-8 


725-6 


52.4 


776.4 


26 


27 


.4500 


34-0 


625.0 


39-7 


675-7 


45-9 


726.5 


52.5 


777-3 


27 


28 


.4667 


34.1 


625.9 


39.8 


676.5 


46.0 


727-3 


52.6 


778.1 


28 


29 


.4833 


34-2 


626.7 


39.9 


677.4 


46.1 


728.1 


52.7 


778.9 


29 


30 


.5000 


34-3 


627.6 


40.0 


678.2 


46.2 


729.0 


52.8 


779.8 


30 


31 


.5167 


34.4 


628.4 


40.1 


679-0 


46.3 


729.8 


52.9 


780.6 


31 


32 


.5333 


34.5 


629.2 


40.2 


679-9 


46.4 


730.7 


53.1 


781.5 


32 


33 


.5500 


34.5 


630.1 


40.3 


680.7 


46.5 


731.5 


53.2 


782.3 


33 


34 


.5667 


34.6 


630.9 


40.4 


681.6 


46.6 


732.4 


53.3 


783.2 


34 


35 


•5833 


34.7 


631.8 


40.5 


682.4 


46.7 


733.2 


53.4 


784.0 


n 


36 


.6000 


34-8 


632.6 


40.6 


683.3 


46.8 


734-0 


53-5 


784.9 


36 


37 


.6167 


34.9 


633-5 


40.7 


684.1 


46-9 


734-9 


53-6 


7?|-7 


H 


38 


.6333 


35-0 


634-3 


40.8 


685-0 


47.0 


735-7 


53-7 


786.6 


38 


39 


.6500 


35.1 


635.1 


40.9 


685.8 


47.2 


736.6 


53.9 


787.4 


39 


40 


.6667 


35.2 


636.0 


41.0 


686.6 


47.3 


737.4 


54.0 


788.3 


40 


41 


.6833 


35.3 


636.8 


41. 1 


687.5 


47.4 


738.3 


54-1 


789.1 


41 


42 


.7000 


35-4 


637-7 


41.2 


688.3 


47.5 


739.1 


54.2 


790.0 


42 


43 


.7167 


35.5 


638.5 


41.3 


689.2 


47.6 


740.0 


54.3 


790.8 


43 


44 


.7333 


35.6 


639.4 


41.4 


690.0 


47.7 


740.8 


54.4 


791.7 


44 


45 


.7500 


35.7 


640.2 


41-5 


690.9 


47.8 


741.7 


54-6 


792.5 


45 


46 


.7667 


35.8 


641. 1 


41.6 


691.7 


47-9 


742.5 


54-7 


793-4 


46 


47 


.7833 


35.8 


641.9 


41.7 


692.5 


48.0 


743-4 


54-8 


794-2 


47 


48 


.8000 


35.9 


642.7 


41.8 


693.4 


48.1 


744-2 


54-9 


795-1 


48 


49 


.8167 


36.0 


643.6 


41.9 


694-2 


48.2 


745.1 


55-0 


795.9 


49 


50 


.8333 


36.1 


644.4 


42.0 


695-1 


48.3 


745.9 


55.1 


796.8 


50 


51 


.8500 


36.2 


645-3 


42.1 


695.9 


48.5 


746.7 


55-3 


797.6 


51 


52 


.8667 


36.3 


646.1 


42.2 


696.8 


48.6 


747.6 


55.4 


798.5 


52 


53 


.8833 


36.4 


647.0 


42.3 


697.6 


48-7 


748.4 


55.5 


799.3 


53 


54 


.9000 


36.S 


647.8 


42.4 


698.5 


48.8 


749.3 


55.6 


800.2 


54 


55 


.9167 


36.6 


648.6 


42.5 


699.3 


48.9 


750.1 


55.7 


801.0 


55 


56 


.9333 


36.7 


649-5 


42.6 


700.1 


49.0 


751.0 


55.8 


801.9 


56 


57 


.9500 


36.8 


650.3 


42.7 


701.0 


49-1 


751.8 


56.0 


802.7 


57 


58 


.9667 


36.9 


651.2 


42.8 


701.8 


49.2 


752.7 


56.1 


803.6 


58 


59 


.9833 


37.0 


652.0 


42.9 


702.7 


49.3 


753.5 


56.2 


804.4 


59 



FUNCTIONS OF ONE-DEGREE CURVE 



353 



Use loo' Chords up to 8° Curves 
Use 50^ Chords up to 16° Curves 



Use 25' Chords up to 32° Curves 
Use 10^ Chords above 32° Curves 



1 




.0000 


I 


e'' 


17° 


I 


8° 


19^ 


1 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


56.3 


805.3 


63.6 


856.4 


71.4 


907.5 


79-7 


958.9 





I 


.0167 


56.4 


806.2 


63.8 


857.2 


71.6 


908.4 


79.8 


959.7 


1 


2 


•0333 


56.5 


807.0 


63.9 


858.1 


71.7 


909.2 


79-9 


960.6 


2 


3 


.0500 


56.7 


807.8 


64.0 


858.9 


71.8 


9ib.i 


80.1 


961.4 


3 


4 


.0667 


56.8 


808.6 


64.2 


859.8 


72.0 


910.9 


80.2 


962.3 


4 


5 


.0833 


56.9 


809.S 


64-3 


860.6 


72.1 


91 1. 8 


80.4 


963.2 


5 


6 


.1000 


57^o 


810.4 


64.4 


861.5 


72.2 


912.7 


80.5 


964.0 


6 


7 


.1167 


57.1 


811. 2 


64-5 


862.3 


72.4 


913.5 


80.7 


964.9 


7 


8 


•1333 


57^3 


812. 1 


64.7 


863.2 


72.5 


914.4 


80.8 


965.7 


8 


9 


.1500 


57.4 


812.9 


64.8 


864.0 


72.6 


915.2 


80.9 


966.6 


9 


10 


.1667 


57^5 


813.8 


64.9 


864.9 


72.8 


916.1 


81.1 


967.4 


10 


II 


.1833 


57.6 


814.6 


65.0 


865.7 


72.9 


916.9 


81.2 


968.3 


II 


12 


.2000 


57^7 


815.5 


65.2 


866.6 


73.0 


917.8 


81.4 


969.2 


12 


13 


.2167 


57.9 


816.3 


65.3 


867.4 


73.2 


918.6 


81.5 


970.0 


13 


14 


.2333 


58.0 


817.2 


65.4 


868.3 


73.3 


919.5 


81.7 


970.9 


14 


IS 


.2500 


58.1 


818.0 


65.6 


869.1 


73.4 


920.3 


81.8 


971.7 


IS 


16 


.2667 


58.2 


818.9 


65.7 


870.0 


73.6 


921.2 


81.9 


972.6 


16 


17 


.2833 


58.3 


819.7 


65.8 


870.8 


73.7 


922.0 


82.1 


973.4 


17 


18 


.3000 


58.5 


820.6 


65.9 


871.7 


73-9 


922.9 


82.2 


974-3 


18 


19 


.3167 


S8.6 


821.4 


66.1 


872.5 


74.0 


923.8 


82.4 


975.1 


19 


20 


•3333 


58.7 


822.3 


66.2 


873.4 


74.1 


924.6 


82.5 


976.0 


20 


21 


.3500 


58.8 


823.1 


66.3 


874.2 


74^3 


925.5 


82.7 


976.9 


21 


22 


.3667 


58.9 


824.0 


66.4 


875.1 


74.4 


926.3 


82.8 


977.7 


23 


23 


.3833 


59-1 


824.8 


66.6 


875.9 


74.5 


927.2 


82.9 


978.6 


23 


24 


.4000 


59.2 


825.7 


66.7 


876.8 


74.7 


928.1 


83.1 


979.4 


24 


^1 


.4167 


59^3 


826.5 


66.8 


877.6 


74.8 


928.9 


83.2 


980.3 


25 


26 


•4333 


59-4 


827.4 


67.0 


878.5 


74.9 


929.8 


83.4 


981.2 


26 


27 


.4500 


59-6 


828.2 


67.1 


879.3 


75.1 


930.6 


83-5 


982.0 


27 


28 


.4667 


59-7 


829.1 


67.2 


880.2 


75.2 


931-5 


83.7 


982.9 


28 


29 


.4833 


59.8 


829.9 


67.3 


88x.o 


75.4 


932.3 


83.8 


983.7 


29 


30 


.5000 


59.9 


830.8 


67.5 


881.9 


75.5 


933.2 


84.0 


984.6 


30 


31 


.5167 


60.0 


831.6 


67.6 


882.7 


75.6 


934-0 


84.1 


985.4 


31 


32 


.5333 


60.2 


832.5 


67.7 


883.6 


75.8 


934-9 


84-3 


986.3 


32 


33 


.5500 


60.3 


833.3 


67.9 


884.5 


75.9 


935-7 


84.4 


987.2 


33 


34 


•5667 


60.4 


834.2 


68.0 


885.3 


76.1 


936.6 


84.6 


988.0 


34 


35 


.5833 


60.S 


835.1 


68.1 


886.2 


76.2 


937.5 


84.7 


988.9 


35 


36 


.6000 


60.7 


835.9 


68.2 


887.0 


76.3 


938.3 


84.8 


989.7 


36 


37 


.6167 


60.8 


836.8 


68.4 


887.9 


76.5 


939-2 


85.0 


990.6 


37 


38 


.6333 


60.9 


837.6 


68.5 


888.7 


76.6 


940-0 


85.1 


991. 5 


38 


39 


.6500 


61.0 


838.5 


68.6 


889.6 


76.7 


940.9 


85.3 


992.3 


39 


40 


.6667 


61.1 


839.3 


68.8 


890.4 


76.9 


941.7 


?5-4 


993-2 


40 


41 


.6833 


61.3 


840.2 


68.9 


891.3 


77.0 


942.6 


85.6 


994.0 


41 


42 


.7000 


61.4 


841.0 


69.0 


892.2 


77^1 


943.5 


85-7 


994.9. 


42 


43 


.7167 


61.S 


841.9 


69.2 


893.0 


77.3 


944-3 


85.9 


995-8 


43 


44 


.7333 


61.6 


842.7 


69-3 


893.9 


77.4 


945.2 


86.0 


996.6 


44 


45 


.7500 


61.8 


843.6 


69.4 


894.7 


77.6 


946.0 


86.2 


997-5 


45 


46 


.7667 


61.9 


844.4 


69.6 


895.6 


77.7 


946.9 


86.3 


998-3 


46 


47 


.7833 


62.0 


845.3 


69.7 


896.4 


77.8 


947-7 


86.5 


999.2 


47 


48 


.8000 


62.1 


846.1 


69.8 


897.3 


78.0 


948.6 


86.6 


1 000.0 


48 


49 


.8167 


62.3 


847.0 


70.0 


898.1 


78.1 


949.4 


86.8 


1000.9 


49 


50 


.8333 


62.4 


847.8 


70.1 


899.0 


78.3 


950.3 


86.9 


1001.8 


50 


51 


.8500 


62.5 


848.7 


70.2 


899.8 


78.4 


951.1 


87.1 


I003.6 


51 


52 


.8667 


62.6 


849.5 


70.4 


900.7 


78.5 


952.0 


87.2 


1003.S 


52 


53 


.8833 


62.8 


850.4 


70.5 


901.5 


7?-7 


952.9 


87.4 


1004.3 


53 


54 


.9000 


62.9 


851.2 


70.6 


902.4 


78.8 


953.7 


87.5 


1005.2 


54 


55 


.9167 


63.0 


852.1 


70.8 


903.3 


79.0 


954-6 


87.7 


1006.0 


55 


56 


•9333 


63.1 


852.9 


70.9 


904.1 


79.1 


955.4 


87.8 


1006.9 


56 


57 


.9500 


63-3 


853.8 


71.0 


905.0 


79.2 


956.3 


88.0 


1007.7 


57 


S8 


.9667 


63.4 


854.7 


71.2 


905.8 


79.4 


957.2 


88.1 


1008.6 


S8 


59 


.9833 


63.S 


855.5 


71.3 


906.7 


79.5 


958.0 


88.2 


1009.5 


59 



354 






THE SURVEY 












Use 100' Chords up to 8 


" Curves Use 25' Chords up to 32° 






Use 50 


' Chords up to 16 


° Curves 


Use 10' Chords above 32 




.a 


QQ 


20° 


21° 


22° 


23'' 


1 


Ext. 


Tan. 


Ext. 


Tan. ^ 


Ext. 


Tan. 


Ext. 


Tan. 


o 


.0000 


88.4 


1010.4 


97.6 


1062.0 


107.2 


1113.8 


117.4 


1165.8 





I 


.0167 


88.5 


1011.2 


97.7 


1062.8 


107.4 


1114.6 


117.6 


1166.6 


I 


2 


.0333 


88.7 


1012.1 


97.9 


1063.7 


107.6 


1115.5 


117.7 


1167.5 


2 


3 


.0500 


88.8 


1012.9 


98.1 


1064.5 


107.7 


1116.4 


117.9 


1 168.3 


3 


4 


.0667 


89.0 


1013.8 


98.2 


1065.4 


107.9 


1117.3 


118.1 


1169.2 


4 


5 


.0833 


89.1 


1014.6 


98.4 


1066.3 


108.0 


1118.1 


118.3 


1170.1 


S 


6 


.1000 


89.3 


IOI5-S 


98.5 


1067.2 


108.2 


1119.0 


118.4 


1171.0 


6 


y 


.1167 


89.4 


1016.3 


98.7 


1068.0 


108.4 


1119.8 


118.6 


1171.8 


7 


8 


.1333 


89.6 


1017.2 


98.8 


1068.9 


108.6 


1120.7 


118.8 


1172.7 


8 


9 


.1500 


89.7 


1018.1 


99.0 


1069.7 


108.7 


1121.5 


118.9 


1173.S 


9 


lO 


.1667 


89.9 


1019.0 


99.2 


1070.6 


108.9 


1122.4 


119.1 


1174.4 


10 


II 


.1833 


90.0 


1019.8 


99.3 


1071.5 


109.0 


1123.3 


119.3 


1175.3 


II 


12 


.2000 


90.2 


1020.7 


99-5 


1072.4 


109.2 


1124.2 


119.5 


1176.2 


12 


13 


.2167 


90.3 


1021.5 


99.6 


1073.2 


109.4 


1125.0 


119.7 


1177.0 


13 


14 


.2333 


90.5 


1022.4 


99.8 


1074.1 


109.6 


1125.9 


119.8 


1177.9 


14 


IS 


.2500 


90.6 


1023.2 


99.9 


1074.9 


109.7 


1126.7 


120.0 


1178.8 


IS 


i6 


.2667 


90.8 


1024.1 


lOO.I 


1075.8 


109.9 


1127.6 


120.2 


1179^7 


16 


17 


.2833 


90.9 


1024.9 


100.2 


1076.6 


IIO.O 


1128.5 


120.4 


1180.S 


17 


i8 


.3000 


91.1 


1025.8 


100.4 


1077.5 


II0.2 


1129.4 


120.5 


1181.4 


18 


19 


.3167 


91.2 


1026.7 


100.5 


1078.4 


1 10.4 


1130.2 


120.7 


I182.2 


19 


20 


•3333 


91.4 


1027.6 


100.7 


1079.3 


II0.6 


1131.1 


120.9 


1183.1 


20 


21 


•3500 


91.6 


1028.4 


100.9 


1080.1 


II0.7 


1131.9 


121.0 


1184.0 


21 


22 


.3667 


91.7 


1029.3 


lOI.I 


1081.0 


II0.9 


1132.8 


121. 2 


1184.9 


22 


23 


.3833 


91.9 


1030.1 


IOI.2 


1081.8 


III.O 


1133.7 


121.4 


1185.7 


23 


24 


.4000 


92.0 


103 1. 


IOI.4 


1082.7 


III. 2 


1134.6 


121.6 


1186.6 


24 


25 


.4167 


92.2 


103 1. 8 


IOI.5 


1083.5 


III.4 


1135.4 


121.7 


1187.5 


25 


26 


•4333 


92.3 


1032.7 


IOI.7 


1084.4 


III.6 


1136.3 


121.9 


1 188.4 


26 


27 


.4500 


92.5 


I033-S 


IOI.8 


1085.3 


III. 7 


1137.1 


122. 1 


1189.2 


27 


28 


.4667 


92,6 


1034.4 


102.0 


1086.2 


111.9 


1138.0 


122.3 


1 1 90. 1 


28 


29 


•4833 


92.8 


1035.2 


102. 1 


1087.0 


112. 1 


1138.8 


122.4 


1 190.9 


29 


30 


.5000 


92.9 


1036.1 


102.3 


1087.9 


112. 3 


1139.7 


122.6 


1191.8 


30 


31 


.5167 


93-1 


1037.0 


102.5 


1088.7 


112.4 


1140.6 


122.8 


1192.7 


31 


32 


•5333 


93-2 


1037.9 


102.7 


1089.6 


112.6 


1141.5 


123.0 


1193.6 


32 


33 


.5500 


93.4 


1038.7 


102.8 


1090.4 


112. 7 


1142.3 


123.2 


1194.4 


33 


34 


.5667 


93-5 


1039.6 


103.0 


1091.3 


112.9 


1143.2 


123.3 


1195.3 


34 


35 


.5833 


93.7 


1040.4 


103. 1 


1092.2 


113.1 


1 144.0 


123.5 


1196.2 


35 


36 


.6000 


93.9 


1041.3 


103.3 


1093. 1 


113.3 


1 144.9 


123.7 


1197.1 


36 


3t 


.6167 


94.0 


1042. 1 


103.4 


1093.9 


113.4 


1145.8 


123.9 


1197.9 


37 


38 


.6333 


94.2 


1043.0 


103.6 


1094.8 


113.6 


1146.7 


124.1 


1 1 98.8 


38 


39 


.6500 


94-3 


1043.9 


103.8 


1095.6 


II3-7 


1147.S 


124.3 


1199.6 


39 


40 


.6667 


94-5 


1044.8 


104.0 


1096.5 


113.9 


1 148.4 


124.4 


1200.5 


40 


41 


.6833 


94.6 


1045.6 


104. 1 


1097^4 


114.1 


1149.2 


124.6 


1201.4 


41 


42 


.7000 


94.8 


1046.5 


104.3 


1098.3 


114.3 


1150.1 


124.8 


1202.3 


42 


43 


.7167 


94.9 


1047.3 


104.4 


1099.1 


114.4 


1151.0 


124.9 


1203. 1 


43 


44 


.7333 


9S.I 


1048.2 


104.6 


1 1 00.0 


114.6 


1151.9 


125.1 


1204.0 


44 


^1 


•^12° 


95^2 


1049.0 


104.7 


1 100.8 


114.8 


1152.7 


125^3 


1204.9 


45 


46 


.7667 


95.4 


1049.9 


104.9 


1101.7 


115.0 


1153.6 


125.5 


1205.8 


46 


^J 


.7833 


95^6 


1050.8 


105. 1 


1102.5 


115. 2 


1154.5 


125.7 


1206.7 


47 


48 


.8000 


95.7 


1051.7 


105.3 


1103.4 


115.3 


1155.4 


125.8 


1207.5 


48 


49 


.8167 


95-9 


1052.5 


105.4 


1 104.3 


115.5 


1156.2 


126.0 


1208.3 


49 


SO 


•8333 


96.0 


1053.4 


105.6 


1105.2 


115.7 


1157.1 


126.2 


1209.2 


50 


51 


•55^° 


96.2 


1054.2 


105.7 


1106.0 


115.8 


1157.9 


126.4 


•1210.1 


51 


52 


.8667 


96.3 


1055.1 


105.9 


1106.9 


116.0 


1158.8 


126.6 


1211.0 


52 


53 


•8833 


96.5 


1055.9 


106. 1 


1107.8 


116.1 


1159.7 


126.7 


1211.8 


53 


54 


.9000 


96.7 


1056.8 


106.3 


1108.6 


116.3 


1160.6 


126.9 


1212.7 


54 


55 


.9167 


96.8 


1057.7 


106.4 


1 109.4 


116.5 


1161.4 


127.1 


1213.6 


55 


S6 


.9333 


97.0 


1058.6 


106.6 


1 1 10.3 


"5-7 


1162.3 


127.3 


1214.5 


56 


57 


.9500 


97.1 


1059.4 


106.7 


mi. 2 


116.8 


1163.1 


127.5 


1215.3 


57 


S8 


.9667 


97^3 


1060.3 


106.9 


1112.1 


117.0 


1164.0 


127.6 


1216.2 


58 


59 


.9833 


97.4 


1061.1 


107.0 


1112.9 


117. 2 


1164.9 


127.8 


1217.1 


59 



FUNCTIONS OF ONE-DEGREE CURVE 

Use loo' Chords up to 8° Curves Use 25' Chords up to 32° Cui-ves 
Use so' Chords up to 16° Curves Use 10' Chords above 32" Curves 



355 



to 

Si 

g 




24° 


25" 


26"* 


27"* 


1 

.2 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


128.0 


1218.0 


139.1 


1270.3 


150.7 


1322.9 


162.8 


1375.6 





I 


.0167 


128.2 


1218.8 


139-3 


1271.1 


150.9 


1323.7 


163.0 


1376.5 


I 


2 


•0333 


128.4 


1219.7 


139-5 


1272.0 


151.1 


1324.6 


163.2 


1377.4 


2 


3 


.0500 


128.5 


1220.5 


139-7 


1272.9 


151-3 


132^-5 


163.5 


1378.3 


3 


4 


.0667 


128.7 


I22I.4 


139.9 


1273.8 


iSi-5 


1326.4 


163.7 


1379.2 


4 


5 


.0833 


128.9 


1222.3 


140.1 


1274.6 


151.7 


1327.3 


163.9 


1380.0 


5 


6 


.1000 


129.1 


1223.2 


140.3 


1275.5 


151.9 


1328.1 


164.1 


1380.9 


6 


7 


.1167 


129.3 


1224.0 


140.4 


1276.4 


152.1 


13290 


164-3 


1381.8 


7 


8 


.1333 


129.5 


1224.9 


140.6 


1277.3 


152.3 


1329.9 


164.5 


1382.7 


8 


9 


.1500 


129.7 


1225.8 


140.8 


1278.2 


152.5 


1330.7 


164.7 


1383.6 


9 


10 


.1667 


129.8 


1226.7 


141.0 


1279.1 


152.7 


1331.6 


164.9 


1384.5 


10 


II 


.1833 


130-0 


1227.5 


141.2 


1279-9 


152.9 


1332.5 


165.1 


1385.3 


11 


12 


.2000 


130.2 


1228.4 


141-4 


1280.8 


153.1 


1333-4 


165-3 


1386.2 


12 


13 


.2167 


130.4 


1229.3 


141.6 


1281.6 


153.3 


1334.3 


165-5 


'^^^' 


13 


14 


.2333 


130.6 


1230.2 


141.8 


1282.5 


153.5 


1335-2 


165.7 


1388.0 


14 


15 


.2500 


130.7 


1231.0 


142.0 


1283.4 


153.7 


1336.0 


'?|-^ 


1388.9 


15 


16 


.2667 


130.9 


I23I.9 


142.2 


1284.3 


153.9 


1336.9 


166.1 


1389-8 


16 


17 


.2833 


13I.I 


1232.7 


142.3 


1285.2 


154.1 


1337.8 


'^<'3 


1390.6 


17 


18 


.3000 


I3i^3 


1233-6 


142.5 


1286.1 


154-3 


1338.7 


166.5 


1391.5 


18 


19 


.3167 


131.S 


1234-5 


142.7 


1286.9 


154-5 


1339.5 


166.7 


1392.4 


19 


20 


.3333 


131-7 


1235-4 


142.9 


1287.8 


154.7 


1340.4 


167.0 


1393-3 


20 


21 


.3500 


131-9 


1236.2 


143.1 


1288.7 


154-9 


1341.3 


167.2 


1394-1 


21 


22 


.3667 


132.0 


1237.1 


143.3 


1289.6 


155.1 


1342.2 


167.4 


1395-0 


22 


23 


.3833 


132.2 


1238.0 


143-5 


1290.4 


155.3 


1343.0 


167.6 


1395-9 


23 


24 


.4000 


132.4 


1238.9 


143.7 


1291.3 


155-5 


1343.9 


167.8 


1396.8 


24 


25 


.4167 


132.6 


1239.7 


143.9 


1292.2 


155-7 


1344-8 


168.0 


1397-7 


25 
26 


26 


•4333 


132.8 


1240.6 


144.1 


1293.1 


1SS.9 


1345-7 


168.2 


1398.6 


27 


.4500 


I33-0 


1241.5 


144.3 


1293.9 


156.1 


1346.5 


168.4 


1399-4 


27 


28 


.4667 


I33^i 


1242.4 


144-5 


1294.8 


156.3 


1347.4 


168.6 


1400.3 


28 


29 


.4833 


I33^3 


1243.2 


144-7 


1295.7 


156.5 


1348.3 


168,9 


1401.2 


29 


30 


.5000 


133-5 


1244.1 


144.9 


1296.6 


156.7 


1349.2 


169.1 
169.3 
169.5 
169.7 
169.9 


1402.1 


30 


31 


.5167 


133.7 


1244.9 


145-1 


1297.4 


15^-9 


1350.1 


1403-0 


31 


32 


•5333 


133-9 


1245.8 


145-3 


1298.3 


157-1 


1351.0 


1403-9 


32 


33 


.5500 


134.0 


1246.7 


145-5 


1299.2 


157.3 


1351.8 


1404-7 


33 


34 


.5667 


134-2 


1247.6 


145-6 


1300.1 


157.5 


1352.7 


1405.6 


34 


35 


.5833 


134-4 


1248.4 


145.8 


1300.9 


157-7 


1353.6 


170.1 


1406.5 


35 


36 


.6000 


134.6 


1249.3 


146.0 


1301.8 


157.9 


1354.5 


170.3 


1407-4 


36 


37 


.6167 


134-9 


1250.2 


146.2 


1302.7 


158.1 


1355.3 


170.5 


1408.3 


37 


38 


•6333 


135-0 


1251-1 


146.4 


1303.6 


158.3 


1356.2 


170.8 


1409.2 


\^l 


39 


.6500 


135.2 


1251.9 


146.6 


1304.4 


158.5 


1357.1 


171.0 


1410.0 


39 


40 


.6667 


135-4 


1252.8 


146.8 


1305.3 


158.7 


1358.0 


171.2 


1410.9 
1411.8 


40 


41 


.6833 


135.6 


1253-7 


147-0 


1306.2 


158.9 


1358.9 


171.4 


41 


42 


.7000 


135-7 


1254.6 


147-2 


1307.1 


159.1 


^^IPi 


171.6 


1412.7 
1413-6 


42 


43 


.7167 


135.9 


1255.4 


147-4 


1307.9 


159-3 


1360.6 


171.8 


43 


44 


.7333 


136.1 


1256.3 


147-6 


1308.8 


159.5 


1361.5 


172.0 


1414-5 


44 


45 


.7500 


136.3 


1257.2 


147.8 


1309.7 


159.7 


1362.4 


172.2 


1415-4 


45 
146 


46 


.7667 


136.5 


1258.1 


148.0 


1310.6 


160.0 


^S^S'S 


172.5 


1416.3 


47 


.7833 


136.7 


1258.9 


148.2 


1311-5 


160.2 


1364.2 


172.7 


1417.1 


47 
'48 


48 


.8000 


136.9 


1259.8 


148.4 


1312.4 


160.4 


1365.1 


172.9 


1418.0 


49 


.8167 


137.1 


1260.7 


148.6 


1313-2 


160.6 


1365-9 


173-1 


1418.9 


49 


50 


•8333 


137.2 


1261.5 


148.8 


1314-1 


160.8 


1366.8 


173.3 


1419.8 


50 


51 


.8500 


137.4 


1262.4 


149.0 


1315-0 


161.0 


1367-7 


173-5 


1420.7 


51 


52 


.8667 


137.6 


1263.3 


149.2 


1315-9 


161. 2 


1368.6 


173-7 


1421.6 


52 


53 


•8833 


137.8 


1264.1 


149.4 


1316.7 


161.4 


1369-5 


173-9 


1422.4 


;53 


54 


.9000 


138.0 


1265.0 


149-5 


1317-6 


161.6 


1370.4 


174-1 


1423-3 


|54 


55 


.9167 


138.2 


1265.9 


149-7 


1318.5 


161.8 


1371-2 


174.4 


1424.2 


55 
'56 


56 


•9333 


138.4 


1266.8 


149-9 


1319.4 


162.0 


1372.1 


174-6 


1425-1 


57 


.9500 


138.6 


1267.6 


150.1 


1320.3 


162.2 


1373-0 


174-8 


1426.0 
1426.9 


57 
58 


58 


.9667 


138.7 


1268.5 


150.3 
150.5 


1321.1 


162.4 


1373.9 


175.0 


59 


.9833 


138.9 


1269.4 


1322.0 


162.6 


1374.7 


175.2 


1427.7 


59 



356 




THE SURVEY 










Use loo' Chords up to 8" Curves Use 25' Chords up 


to 32" Curves 1 


Usesc 


' Chords up to 16° Curves Use 10 ' Chords above 32"* Curves | 


1 



6 S) 

^0 


28° 


29° 


30« 


31° 


1 

a 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


175-4 


1428.6 


188.S 


1481.9 


202.1 


1535.3 


216.3 


1589.0 





1' 


.0167 


175.6 


1429.5 


188.7 


1482.8 


202.3 


1536.2 


216.5 


1589-9 


I 


2 


.0333 


175.8 


1430.4 


189.0 


1483.7 


202.6 


1537.1 


216.8 


1590.8 


2 


3 


.0500 


176.0 


1431.3 


189.2 


1484.5 


202.8 


1538.0 


217.0 


1591.7 


3 


4 


.0667 


176.3 


1432.2 


189.4 


1485.4 


203.1 


1538.9 


217.2 


1592.6 


4 


S 


.0833 


176.S 


1433.1 


189.6 


1486.3 


203.3 


1539.8 


217.4 


1593.5 


5 


6 


.1000 


176.7 


1434.0 


189.9 


1487.2 


203.5 


1540.7 


217.7 


1594.4 


6 


7 


.1167 


176.9 


1434-8 


190.1 


1488.1 


203.7 


1S41.6 


217.9 


1595.3 


7 


8 


.1333 


177.1 


1435.7 


190.3 


1489.0 


204.0 


1542.5 


218.2 


1596.2 


8 


9 


.1500 


177.3 


1436.6 


190.5 


1489.9 


204.2 


1543.4 


218.4 


1597.1 


9 


10 


.1667 


177.6 


1437.5 


190.8 


1490.8 


204.5 


1544.3 


218.7 


1598.0 


10 


II 


.1833 


177.8 


1438.4 


191.0 


1491.7 


204.7 


1545.2 


218.9 


1598.9 


11 


12 


.2000 


178.0 


1439.3 


191.2 


1492.6 


204.9 


1546.0 


219.2 


1599.8 


12 


13 


.2167 


178.2 


1440.2 


191.5 


1493.4 


205.1 


1546.9 


219.4 


1600.7 


13 


14 


.2333 


178.4 


1441.1 


191.7 


1494.3 


205.4 


1547.8 


219.6 


1601.6 


14 


IS 


.2500 


178.6 


1441.9 


191.9 


1495.2 


205.6 


1548.7 


219.8 


1602.5 


IS 


16 


.2667 


178.9 


1442.8 


192.1 


1496.1 


205.9 


1549.6 


220.1 


1603.4 


16 


17 


.2833 


179.1 


1443-7 


192.3 


1497.0 


206.1 


1550.5 


220.3 


1604.3 


17 


18 


.3000 


179.3 


1444.6 


192.5 


1497.9 


206.3 


1551.4 


220.6 


1605.2 


18 


19 


.3167 


179.5 


1445.5 


192.7 


1498.8 


206.5 


1552.3 


220.8 


1606.1 


19 


20 


.3333 


179.7 


1446.4 


193.0 


1499.7 


206.8 


1553.2 


221.1 


1607.0 


20 


21 


.3500 


179.9 


1447.3 


193-2 


1500.6 


207.0 


1554.1 


221.3 


1607.9 


21 


22 


.3667 


180.2 


1448.2 


193-5 


1501.S 


207.3 


1555.0 


221.6 


1608.8 


22 


23 


.3833 


180.4 


1449.0 


193-7 


1502.3 


207.5 


1555.9 


221.8 


1609.7 


23 


24 


.4000 


180.6 


1449.9 


193.9 


1503.2 


207.7 


1556.8 


222.1 


1610.6 


24 


25 


.4167 


180.8 


1450.8 


194.1 


1504.1 


207.9 


1557.7 


222.3 


1611.5 


25 


26 


.4333 


181.0 


1451.7 


194.4 


1505.0 


208.2 


1558.6 


222.6 


1612.4 


26 


27 


.4500 


181.2 


1452.6 


194-6 


1505.9 


208.4 


1559.5 


222.8 


1613.3 


27 


28 


.4667 


181.S 


1453.5 


194.8 


1506.8 


208.7 


1560.4 


223.0 


1614.2 


28 


29 


•4833 


181.7 


1454.3 


195.0 


1507.7 


208.9 


1561.3 


223.2 


1615.1 


29 


30 


.5000 


181.9 


1455.2 


195.3 


1508.6 


209.1 


1562.2 


223.S 


1616.0 


30 


31 


.5167 


182.1 


1456.1 


195.5 


1509-5 


209.3 


1563.1 


223.7 


1616.9 


31 


32 


.5333 


182.3 


1457.0 


195.7 


1510.4 


209.6 


1564.0 


224.0 


1617.8 


32 


33 


.5500 


182.S 


1457-9 


195-9 


1511-2 


209.8 


1564.9 


224.2 


1618.7 


33 


34 


.5667 


182.8 


1458.8 


196.2 


1512.1 


210.1 


1565.7 


224.5 


1619.6 


34 


35 


.5833 


183.0 


1459.7 


196.4 


1513.0 


210.3 


1566.6 


224.7 


1620.5 


35 


36 


.6000 


183.2 


1460.6 


196.7 


1513.9 


210.5 


1567.5 


225.0 


1621.4 


36 


37 


.6167 


183.4 


1461.4 


196.9 


1514.8 


210.7 


1568.4 


225.2 


1622.3 


H 


38 


•6333 


183.6 


1462.3 


197.1 


1515.7 


211.0 


1569.3 


225.5 


1623.2 


38 


39 


.6500 


183.8 


1463.2 


197.3 


1516.6 


211.2 


1570.2 


225.7 


1624.1 


39 


40 


.6667 


184.1 


1464.1 


197.6 


1517.5 


211.5 


1571.1 


226.0 


1625.0 


40 


41 


.6833 


184.3 


1465.0 


197.8 


1518.4 


211.7 


1572.0 


226,2 


1625.9 


41 


42 


.7000 


184.5 


1465.9 


198.0 


1519-3 


212.0 


1572.9 


226.5 


1626.8 


42 


43 


.7167 


184.7 


1466.8 


198.2 


1520.1 


212.2 


1573.8 


226.7 


1627.7 


43 


44 


.7333 


185.0 


1467.7 


I98.S 


1521.0 


212.4 


1574.7 


227.0 


1628.6 


44 


4| 


.7500 


185.2 


1468.6 


198.7 


1521-9 


212.6 


1575.6 


227.2 


1629.5 


45 


46 


.7667 


185.4 


1469-5 


198.9 


1522.8 


212.9 


1576.5 


227.5 


1630.5 


46 


47 


.7833 


185.6 


1470.3 


199.1 


1523-7 


213.1 


1577.4 


227.7 


1631.4 


47 


48 


.8000 


185.9 


1471.2 


199.4 


1524-6 


213.4 


1578.3 


228.0 


1632.3 


48 


49 


,8167 


186.1 


1472.1 


199.6 


1525.5 


213.6 


1579.2 


228.2 


1633.2 


49 


50 


.8333 


186.3 


1473.0 


199.8 


1526.4 


213.9 


1580.1 


228.4 


1634.1 


50 


SI 


.8500 


186.5 


1473.9 


200.0 


1527.3 


214.1 


1581.0 


228.6 


1635.0 


51 


52 


.8667 


186.8 


1474.8 


200.3 


1528.2 


214-4 


1581.9 


228.9 


1635-9 


52 


53 


.8833 


187.0 


1475.7 


200.5 


1529.1 


214.6 


1582.8 


229.1 


1636.8 


53 


54 


.9000 


187.2 


1476.6 


200.8 


1530.0 


214-8 


1583.7 


229.4 


1637.7 


54 


55 


.9167 


187.4 


1477.4 


201.0 


1530.9 


215.0 


1584.6 


229.6 


1638.6 


H 


56 


•9333 


187.6 


1478.3 


201.2 


1531.7 


215-3 


1585.5 


229.9 


1639.5 


56 


57 


.9500 


187.8 


1479.2 


201.4 


1532.6 


215.5 


1586.3 


230.1 


1640.4 


H 


58 


.9667 


188.1 


1 480. 1 


201.7 


1533.5 


215.8 


^S?7.2 


230.4 


1641.3 


S8 


59 


.9833 


188.3 


1481.0 


201.9 


1534.4 


216.0 


1588.1 


230.6 


1642.2 


59 



FUNCTIONS OF ONE-DEGREE CURVE 



357 



Use loo' Chords up to 8° Curves 
Use 50' Chords up to 16" Curves 



Use 25' Chords up to 32° Curves 
Use 10' Chords above 32° Curves 



1 

.a 





32** 1 


33" 


34° [ 


sf 1 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


230.9 


1643.1 


246.1 


1697-3 


261.8 


1751.8 


278.1 


1806.7 





I 


.0167 


231.1 


1644.0 


246.3 


1698.2 


262.0 


1752.7 


278.4 


1807.6 


I 


2 


•0333 


231.4 


1644.9 


246.6 


1699. 1 


262.3 


1753-7 


278.6 


1808.5 


2 


3 


.0500 


231.6 


1645.8 


246.8 


1700.0 


262.6 


1754-6 


278.9 


1809.4 


3 


4 


.0667 


231-9 


1646.7 


247.1 


1700.9 


262.9 


1755.5 


279.2 


1810.3 


4 


5 


.0833 


232.1 


1647.6 


247.4 


1701.8 


263.1 


1756.4 


279.4 


1811.2 


5 


6 


.1000 


232.4 


1648.5 


247.7 


1702.7 


263.4 


1757.3 


279.7 


1812.2 


6 


7 


.1167 


232.6 


1649.4 


247.9 


1703.6 


263.7 


1758.2 


280.0 


1813.1 


7 


8 


•1333 


232.9 


1650.3 


248.2 


1704.5 


264.0 


I759-I 


280.3 


18140 


8 


9 


.1500 


233.1 


1651.2 


248.4 


1705.4 


264.2 


1760.0 


280.6 


1814.9 


9 


10 


.1667 


233-4 


1652.1 


248.7 


1706.4 


264.5 


1761.0 


280.8 


1815.8 


10 


II 


.1833 


233-6 


1653.0 


248.9 


1707.3 


264.7 


1761.9 


281.1 


1816.7 


II 


12 


.2000 


233.9 


1653.9 


249.2 


1708.2 


265.0 


1762.8 


281.4 


1817.7 


12 


13 


.2167 


234-1 


1654-8 


249.4 


1709.1 


265.3 


1763.7 


281.6 


1818.6 


13 


14 


.2333 


234.4 


1655.7 


249-7 


1710.0 


265.6 


1764.6 


281.9 


1819.5 


14 


IS 


.2500 


234-6 


1656.6 


249.9 


1710.9 


265.9 


1765-S 


282.2 


1820.4 


IS 


16 


.2667 


234.9 


1657-5 


250.2 


1711.8 


266.1 


1766.4 


282.5 


1821.3 


16 


17 


.2833 


235.1 


1658.4 


250.5 


1712.7 


266.4 


1767.3 


282.7 


1822.2 


17 


18 


.3000 


235.4 


1659-3 


250.8 


1713-6 


266.7 


1768.3 


283.0 


1823.2 


18 


19 


.3167 


235-6 


1660.2 


251.0 


1714.5 


266.9 


1769.2 


283.3 


1824.1 


19 


20 


.3333 


235-9 


1661.1 


251-3 


1715.5 


267.2 


1770.1 


283.6 


1825.0 


20 


21 


.3500 


236.1 


1662.0 


251.5 


1716.4 


267.4 


1771-0 


283.9 


1825.9 


21 


22 


.3667 


236.4 


1662.9 


251.8 


1717.3 


267.7 


1771-9 


284.2 


1826.8 


22 


23 


.3833 


236.6 


1663.8 


252.0 


1718.2 


268.0 


1772.8 


284.4 


1827.7 


23 


24 


.4000 


236.9 


1664.7 


252.3 


1719.1 


268.3 


1773.7 


284.7 


1828.7 


24 


25 


.4167 


237-1 


1665.6 


252.6 


1720.0 


268.6 


1774.6 


285.0 


1829.6 


25 


26 


.4333 


237-4 


1666.5 


252.9 


1720.9 


268.8 


1775.6 


285.3 


1830.5 


26 


27 


.4500 


237-6 


1667.4! 


253.1 


1721.8 


269.1 


1776.5 


285.6 


1831.4 


27 


28 


.4667 


237.9 


1668.3 


253.4 


1722.7 


269.3 


1777.4 


285.9 


1832.3 


28 


29 


.4833 


238.1 


1669.2 


253-6 


1723.6 


269.6 


1778.3 


286.1 


1833.2 


29 


30 


.5000 


238.4 


1670.1 1 


253-9 


1724.6 


269.9 


1779.2 


286.4 


1834.2 


30 


31 


.5167 


238.7 


1671.0 


254.1 


1725.5 


270.1 


1780.1 


286.7 


1835.1 


31 


32 


.5333 


239.0 


1671.9 


254-4 


1726.4 


270.4 


1781.0 


287.0 


1836.0 


32 


33 


.5500 


239.2 


1672.8 


254.7 


1727.3 


270.7 


1781.9 


287.2 


1836.9 


33 


34 


.5667 


239-5 


1673.7 


255.0 


1728.2 


271.0 


1782.9 


287.5 


1837.8 


34 


35 


.5833 


239.7 


1674.6 


255-2 


1729-1 


271.2 


1783.8 


287.8 


1838.7 


35 


36 


.6000 


240.0 


1675.5 


255.5 


1730.0 


271.5 


1784.7 


288.1 


1839.7 


36 


37 


.6167 


240.2 


1676.4 


255.7 


1730.9 


271.7 


1785.6 


288.4 


1840.6 


37 


38 


.6333 


240.S 


1677.4 


256.0 


1731.8 


272.0 


1786.5 


288.7 


1841.5 


38 


39 


.6500 


240.7 


1678.3 


256.2 


1732.7 


272.3 


1787.4 


289.0 


1842.4 


39 


40 


.6667 


241.0 


1679-2 


256.5 


1733.6 


272.6 


1788.4 


289.2 


1843.4 


40 


41 


.6833 


241.2 


1680.1 


256.8 


1734-5 


272.9 


1789-3 


289.5 


1844.3 


41 


42 


.7000 


241.5 


1681.0 


257.1 


1735.5 


273.1 


1790.2 


289.8 


1845.2 


42 


43 


.7167 


241.7 


1681.9 


257-3 


1736.4 


273-4 


1791.1 


290.1 


1846.1 


43 


44 


.7333 


242.0 


1682.8 


257-6 


1737.3 


273-7 


1792.0 


290.4 


1847.1 


44 


45 


.7500 


242.2 


1683.7 


257.8 


1738.2 


274-0 


1792.9 


290.6 


1848.0 


45 


46 


.7667 


242.5 


1684.6 


258.1 


1739.1 


274-2 


1793-9 


290.9 


1848.9 


46 


47 


.7833 


242.7 


1685.5 


"5?-| 


1740.0 


274-5 


1794.8 


291.2 


1849.8 


^? 


48 


.8000 


243.0 


1686.4 


258.6 


1740.9 


274.8 


1795.7 


291.5 


1850.7 


48 


49 


.8167 


243-2 


1687.3 


258.9 


1741.8 


275.0 


1796.6 


291.8 


1851.6 


49 


50 


.8333 


243-5 


1688.2 


259.2 


1742.7 


275.3 


1797.5 


292.0 


1852.6 


50 


51 


•?i5° 


243-8 


1689.1 


259.4 


1743-6 


275.6 


1798.4 


292.3 


1853.5 


51 


52 


.8667 


244.1 


1690.0 


259.7 


1744.6 


275.9 


1799.3 


292.6 


1854.4 


52 


53 


.8833 


244-3 


1690.9 


259.9 


1745.5 


276.1 


1800.2 


292.9 


1855.3 


53 


54 


.9000 


244.6 


1691.8 


260.2 


1746.4 


276.4 


1801.2 


293-2 


1856.3 


54 


55 


.9167 


244.8 


1692.7 


260.5 


1747-3 


276.7 


1802.1 


293-4 


1857.2 


55 


56 


•9333 


245.1 


1693.7 


260.8 


1748-2 


277-0 


1803.0 


293.7 


1858.1 


56 


57 


.9500 


245-3 


1694.6 


261.0 


1749-1 


277-3 


1803.9 


294.0 


1859.0 


57 


58 


.9667 


245.6 


1695.5 


261.3 


1750.0 


277.5 


1804.8 


294.3 


1859.9 


58 


59 


.9833 


245.8 


1696.4 


261.5 


1750.9 


277-8 


1805.7 


294.6 


1860.8 


59 



558 



THE SURVEY 





Use 100' Chords up to 8 


° Curves 


Use 


25' Chords up to 32® Curves 




Use so' 


Chords 


up to 16 


° Curves 


Use 


10' Chords above 32" Curves 


o 


^1 


36^ 


37** 


38'' 


39** 


i 

i 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


294-9 


1861.8 


312.3 


1917.3 


330.2 


1973.0 


348.7 


2029.1 





I 


.0167 


295-2 


1862.7 


312.5 


1918.2 


330.5 


1973.9 


349.0 


2030.0 


I 


2 


.0333 


295.4 


1863.6 


312.8 


1919.1 


330.8 


1974.9 


349.3 


2031.0 


2 


3 


.0500 


295.7 


1864.5 


313-1 


1920.0 


331. 1 


1975.8 


349.6 


2031.9 


3 


4 


.0667 


296.0 


1865.5 


313.4 


1921.0 


331.4 


1976.7 


349.9 


2032.9 


4 


5 


.0833 


296.3 


1866.4 


313-7 


1921.9 


331.7 


1977.6 


350.3 


2033.8 


5 


6 


.1000 


296.6 


1867.3 


314.0 


1922.8 


332.0 


1978.6 


350.6 


2034.7 


6 


7 


,1167 


296.9 


1868.2 


314-3 


1923.7 


332.3 


1979.5 


350.9 


2035.6 


7 


8 


•1333 


297.2 


1869.2 


314.6 


1924.7 


332.6 


1980.5 


351.2 


2036.6 


8 


9 


.1500 


297-5 


1870.1 


314.9 


1925.6 


332.9 


1981.4 


351.5 


2037.S 


9 


lO 


.1667 


297-7 


1871.0 


315.2 


1926.S 


333.2 


1982.3 


351.8 


2038.5 


10 


II 


.1833 


298.0 


1871.9 


315.5 


1927.4 


333.S 


1983.2 


352.1 


2039.4 


II 


12 


.2000 


298.3 


1872.9 


315.8 


1928.4 


333.8 


1984.2 


352.4 


2040.4 


12 


13 


.2167 


298.6 


1873.8 


316. 1 


1929.3 


334.2 


1985.1 


352.8 


2041.3 


13 


14 


.2333 


298.9 


1874-7 


316.4 


1930.2 


334.S 


1986.1 


3S3.I 


2042.3 


14 


IS 


.2500 


299.2 


1875-6 


316.7 


1931.1 


334.8 


1987.0 


353.4 


2043.2 


IS 


i6 


.2667 


299.5 


1876.5 


317.0 


1932. 1 


335.1 


1987.9 


353-7 


2044.1 


16 


17 


.2833 


299.7 


1877.4 


317.2 


1933.0 


335.4 


1988.8 


354.0 


2045.0 


17 


i8 


^000 


300.0 


1878.4 


317.5 


1933.9 


335.7 


1989.8 


354.3 


2046.0 


18 


19 


.3167 


300.3 


1879.3 


317.8 


1934.8 


336.0 


1990.7 


354.6 


2046.9 


19 


20 


.3333 


300.6 


1880.2 


318.1 


1935.8 


336.3 


1991.7 


354.9 


2047.9 


20 


21 


.3500 


300.9 


1881.1 


318.4 


1936.7 


336.6 


1992.6 


355.3 


2048.8 


21 


22 


.3667 


301.2 


1882. 1 


318.7 


1937.6 


336.9 


1993-6 


355.6 


2049.8 


22 


23 


.3833 


301.5 


1883.0 


319.0 


1938.5 


337.2 


1994.5 


355.9 


2050.7 


23 


24 


.4CK)0 


301.8 


1883.9 


319.3 


1939.5 


337.S 


1995.4 


356.2 


2051.7 


24 


25 


.4167 


302.0 


1884.8 


319.6 


1940.4 


337.8 


1996.3 


356.6 


2052.6 


25 


26 


•4333 


302.3 


1885.8 


319-9 


1941.3 


338.1 


1997.3 


356.9 


2053.5 


26 


27 


.4500 


302.6 


1886.7 


320.2 


1942.2 


338.4 


1998.2 


357.2 


2054.4 


27 


28 


.4667 


302.9 


1887.6 


320.5 


1943.2 


338.7 


1999.2 


357.5 


2055.4 


28 


29 


.4833 


303.2 


1888.S j 


320.8 


1944.1 


339.1 


2000.1 


357.8 


2056.3 


29 


30 


.5000 


303.5 


1889.5 


321.1 


I94S-0 


339.4 


2001.0 


358.1 


2057.3 


30 


31 


.5167 


303.8 


1890.4 


321.4 


1945-9 


339.7 


2001.9 


25^4 


2058.2 


31 


32 


.5333 


304.1 


1891.3 j 


321.7 


1946.9 


340.0 


2002.9 


358.8 


2059.2 


32 


33 


.5500 


304.3 


1892.2 


322.0 


1947.8 


340.3 


2003.8 


359.1 


2 060. 1 


33 


34 


.5667 


304.6 


1893.2 


322.3 


1948.8 


340.6 


2004.8 


359.4 


2061. 1 


34 


35 


.5833 


304.9 


1894.1 


322.6 


1949.7 


340.9 


2005.7 


359.8 


2062.0 


35 


36 


.6000 


305.2 


1895.0 


322.9 


1950.6 


341.2 


2006.6 


360.1 


2063.0 


36 


37 


.6167 


305.5 


1895-9 


323.2 


1951.5 


341.5 


2007.5 


360.4 


2063.9 


37 


38 


•6333 


305.8 


1896.9 


323.5 


1952.5 


341.8 


2008.5 


360.7 


2064.8 


38 


39 


.6500 


306.1 


1897.8 


323.8 


1953.4 


342.1 


2009.4 


361.0 


2065.7 


39 


40 


.6667 


306.4 


1898.7 


324.2 


1954.4 


342.4 


2010.4 


361.3 


2066.7 


(40 


41 


.6833 


306.7 


1899.6 


324.5 


1955.3 


342.8 


201 1. 3 


361.6 


2067.6 


41 


42 


.7000 


307.0 


1900.6 


324-8 


1956.2 


343.1 


2012.3 


362.0 


2068.6 


42 


43 


.7167 


307.2 


1901.5 


325.1 


1957.1 


343.4 


2013.2 


362.3 


2069.5 


43 


44 


.7333 


307.5 


1902.4 


325.4 


1958.1 


343-7 


2014.1 


362.6 


2070.5 


44 


45 


.7500 


307.8 


1903-3 


325.7 


1959.0 


344-0 


2015.0 


363.0 


2071.4 


45 


46 


.7667 


308.1 


1904.3 


326.0 


1960.0 


344-3 


2016.0 


363.3 


2072.4 


46 


47 


.7833 


308.4 


1905.2 


326.3 


1960.9 


344-6 


2016.9 


363.6 


2073.3 


47 


48 


.8000 


308.7 


1906. 1 


326.6 


1961.8 


344-9 


2017.9 


363.9 


2074.2 


48 


49 


.8167 


309.0 


1907.0 


326.9 


1962.7 


345-3 


2018.8 


364.2 


2075.1 


49 


50 


•8333 


309.3 


1908.0 


327.2 


1963.7 


345-6 


2019.7 


364.S 


2076.1 


50 


51 


.8500 


309.6 


1908.9 


327.5 


1964.6 


345-9* 


2020.6 


364.9 


2077.0 


51 


52 


.8667 


309.9 


1909.8 


327.8 


1965-5 


346.2 


2021.6 


365.2 


2078.0 


52 


53 


.8833 


310.2 


1910.7 


328.1 


1966.4 


346.5 


2022.5 


365.5 


2078.9 


53 


54 


.9000 


310.5 


1911.7 


328.4 


1967.4 


346.8 


2023.5 


365.8 


2079.9 


54 


55 


.9167 


310.8 


1912.6 


328.7 


1968.3 


347-1 


2024.4 


366.2 


2080.8 


55 


56 


.9333 


311.1 


1913.5 


329.0 


1969.3 


347-4 


2025.4 


366.5 


2081.8 


S6 


57 


.9500 


311.4 


1914.4 


329.3 


1970.2 


347.8 


2026.3 


366.8 


2082.7 


57 


58 


.9667 


311.7 


1915.4 


329.6 


1971.1 


348.1 


2027.2 


367.1 


2083.7 


58 


59 


.9833 


312.0 


1916.3 


329.9 


1972.0 


348.4 


2028.1 


367.4 


2084.6 


59 



FUNCTIONS OF ONE-DEGRFE CURVE 



359 



Use loo' Chords up to 8° Curves 
Use so' Chords up to 16" Curves 



Use 25' Chords up to 32° Curves 
Use 10' Chords above 32° Curves 



a 


^1 


40'' 



41 


42" 


43° ^ 


.s 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


367-7 


2085.5 


387.4 


2142.3 


407.7 


2199.5 


428.6 


2257.1 


I 


.0167 


368.0 


2086.4 


2?Z-^ 


2143.2 


408.0 


2200.4 


429.0 


2258.0 


I 


2 


.0333 


368.4 


2087.4 


388.1 


2144.2 


408.3 


2201.4 


429-3 


2259.0 


2 


3 


.0500 


368.7 


2088.3 


2??-5 


2145.1 


408.7 


2^2.3 


429.7 


2260.0 


3 


4 


.0667 


369-0 


2089.3 


388.8 


2146.1 


409.0 


2203.3 


430.0 


2261.0 


4 


5 


•0833 


369-4 


2090.2 


389.1 


2147.0 


409.4 


2204.3 


430.4 


2261.9 


5 


6 


.1000 


369-7 


2091.2 


389-4 


2148.0 


409.7 


2205.3 


430.7 


2262.9 


6 


7 


.1167 


370.0 


2092.1 


389.8 


2148.9 


410.1 


2206.2 


431. 1 


2263.8 


7 


8 


.1333 


370.3 


2093.1 


390.1 


2149.9 


410.4 


2207.2 


431.4 


2264.8 


8 


Q 


.1500 


370.7 


2094.0 


390.4 


2150.9 


410.8 


2208.1 


431.8 


2265.7 


9 


ro 


.1667 


371.0 


2095.0 


390.7 


2151.9 


411.1 


2209.1 


432.1 


2266.7 


10 


II 


•1833 


371.3 


2095.9 


391.1 


2152.8 


411.5 


2210.0 


432.4 


2267.7 


ii 


12 


.2000 


371.6 


2096.9 


391-4 


2153.8 


411.8 


2211.0 


432.8 


2268.7 


12 


13 


.2167 


372.0 


2097.8 


391-8 


2154.7 


412.2 


2211.9 


433.2 


2269.6 


13 


14 


.2333 


372.3 


2098.8 


392.1 


2155.7 


412.5 


2212.9 


433.5 


2270.6 


14 


15 


.2500 


372.6 


2099.7 


392.4 


2156.6 


412.9 


2213.9 


433.9 


2271.5 


15 


16 


.2667 


372.9 


2100.7 


392.7 


2157.6 


413.2 


2214.9 


434.2 


2272.5 


16 


17 


.2833 


373-3 


2101.6 


393-1 


2158.5 


413.6 


2215.8 


434.6 


2273.5 


^l 


18 


.3000 


373.6 


2102.6 


393.4 


2159.5 


413.9 


2216.8 


434-9 


2274.5 


18 


19 


.3167 


374.0 


2 103. 5 


393.7 


2160.4 


414.3 


2217.7 


435.3 


2275.4 


19 


20 


•3333 


374-3 


2104.5 


394-1 


2161.4 


414.6 


2218.7 


435-6 


2276.4 


20 


21 


•3500 


374.6 


2105.4 


394-4 


2162.3 


415-0 


2219.6 


436.0 


2277.3 


21 


22 


.3667 


374.9 


2106.3 


394.7 


2163.3 


415.3 


2220.6 


436.3 


2278.3 


22 


23 


.3833 


375-3 


2107.2 


395-1 


2164.2 


415-7 


2221.5 


436.7 


2279.2 


23 


24 


.4000 


375-6 


2108.2 


395.4 


2165.2 


416.0 


2222.5 


437.0 


2280.2 


24 


25 


.4167 


375.9 


2109. 1 


395.8 


2166.1 


416.3 


2223.4 


437-4 


2281.2 


25 


26 


•4333 


376.2 


2110.1 


396.1 


2167. 1 


416.6 


2224.4 


437.8 


2282.2 


26 


27 


.4500 


376.6 


2111.0 


396.5 


2168.0 


417.0 


22254 


438.2 


2283.1 


27 


28 


.4667 


376.9 


2 II 2.0 


396.8 


2169.0 


417.3 


2226.4 


438.5 


2284.1 


28 


29 


.4833 


377.2 


2112.9 


397-2 


21^9.9 


417.7 


2227.3 


438-9 


2285.0 


29 


30 


.5000 


'377^5 


2113.9 


397.5 


2170.9 


418.0 


2228.3 


439-2 


2286.0 


30 


31 


•5167 


377.9 


2114.8 


397-8 


2171.8 


418.4 


2229.2 


439-6 


2287.0 


31 


32 


•5333 


378.2 


2115.8 


398.1 


2172.8 


418.7 


2230.2 


439-9 


2288.0 


32 


33 


.5500 


378.S 


2116.7 


398.5 


2173.7 


419.1 


2231. I 


440-3 


2288.9 


33 


34 


•5667 


378.8 


2117.7 


398.8 


2174.7 


419.4 


2232.1 


440.6 


2289.9 


34 


35 


•5833 


379.2 


2118.6 


399.2 


2175.6 


419.8 


2233.0 


441 -o 


2290.8 


35 


36 


.6000 


379.5 


2119.6 


399.5 


2176.6 


420.1 


2234.0 


441-4 


2291.8 


36 


37 


.6167 


379-8 


2120.5 


399-9 


2177.5 


420.5 


2235.0 


441.8 


2292.8 


37 


38 


•6333 


380.1 


2121.5 


400.2 


2178.5 


420.8 


2236.0 


442-1 


2293.8 


38 


39 


.6500 


380.5 


2122.4 


400.6 


2179.4 


421.2 


2236.9 


442.5 


2294.7 


39 


40 


.6667 


380.8 


2123.4 


400.9 


2180.4 


421.5 


2237.9 


442.8 


2295.7 


40 


41 


.6833 


381. 1 


2124.3 


401.2 


2181.4 


421.9 


2238.8 


443-2 


2296.7 


41 


42 


.7000 


381.4 


2125.3 


401.5 


2182.4 


422.2 


2239-8 


443.5 


2297.7 


42 


43 


.7167 


381.8 


2126.2 


401.9 


2183.3 


422.6 


2240.7 


443.9 


2298.6 


43 


44 


•7333 


382.1 


2127.2 


402.2 


2184.3 


422.9 


2241.7 


444.2 


2299.6 


44 


45 


.7500 


382.5 


2128.1 


402.6 


2185.2 


423.3 


2242.6 


444.6 


2300.5 


45 


46 


.7667 


382.8 


2129.1 


402.9 


2186.2 


423.6 


2243.6 


445.0 


2301.5 


46 


47 


•7833 


383-1 


2130.0 


403.3 


2187.1 


424.0 


2244.6 


445.4 


2302.5 


47 
48 


48 


.8000 


383.4 


2131.0 


403.6 


2188.1 


424.3 


2245-6 


445-7 


2303.5 


49 


.8167 


383.8 


2131.9 


404.0 


2189.0 


424-7 


2246.5 


446.1 


2304.4 


49 


SO 


•8333 


384.1 


2132.9 


404.3 


2190.0 


425-0 


2247-5 


446.4 


2305.4 


50 


SI 


.8500 


384.5 


2133.8 


404.6 


2190.9 


425-4 


2248.4 


446.8 


2306.3 


51 


52 


.8667 


384.8 


2134-7 


404.9 


2191.9 


425-7 


2249-4 


447.1 


2307.3 


52 


53 


.8833 


385.1 


2135^6 


405.3 


2192.8 


426.1 


2250.3 


447-5 


2308.3 


53 


54 


.9000 


385.4 


2136.6 


405.6 


2193.8 


426.4 


2251.3 


447.8 


2309.3 


54 


55 


.9167 


385.8 


2137.5 


406.0 


2194.7 


426.8 


2252.3 


448.2 


2310.2 


55 
56 


•56 


.9333 


386.1 


2138.5 


406.3 


2195.7 


427.1 


2253.3 


448.6 


2311.2 


57 


.9500 


386.5 


2139.4 


406.7 


2196.6 


427.5 


2254.2 


449.0 


2312. 1 


^l 


58 


.9667 


386.8 


2140.4 


407.0 


2197.6 


427.8 


2255.2 


449.3 


2313.1 


58 


59 


•9833 


387.1 


2141.3 


407-4 


2198.5 


428.2 


2256.1 


449.7 


2314.1 


59 



360 



THE SURVEY 



Use 100' Chords up to S" 
Use so' Chords up to 16° 



Curves 
Curves 



Use 25' Chords up to 32° Curves 
Use 10' Chords above 32* Curves 



G 

s 






44" 



45 


46 V 


47** 


1 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


450.0 


2315-1 


472.1 


2373.4 


494.8 


2432.2 


518.3 


2491.S 





I 


.0167 


450.4 


2316.0 


472.5 


2374-4 


495.2 


2433.2 


S18.7 


2492.4 


I 


2 


•0333 


450.7 


2317.0 


472.9 


2375-4 


495.6 


2434.2 


519.0 


2493-4 


2 


3 


.0500 


45I-I 


2318.0 


473.3 


2376.3 


496.0 


2435.1 


519.4 


2494-4 


3 


4 


.0667 


451.5 


2319.0 


473.6 


2377-3 


496.4 


2436.1 


519.8 


2495.4 


4 


5 


.0833 


451-9 


2319.9 


474.0 


2378.3 


496.7 


2437.1 


520.2 


2496.4 


5 


6 


.1000 


452.2 


2320.9 


474.4 


2379-3 


497.2 


2438.1 


520.6 


2497.4 


6 


7 


.1167 


452.6 


2321.8 


474.8 


2380.2 


497.6 


2439.1 


521.0 


2498.4 


7 


8 


.1333 


452.9 


2322.8 


475.1 


2381.2 


497-9 


2440.1 


521.4 


2499.4 


8 


9 


.1500 


453.3 


2323.8 


475.5 


2382.2 


498-3 


2441.1 


521.8 


2500.4 


9 


10 


.1667 


453.7 


2324.8 


475-9 


2383-2 


498.7 


2442.1 


522.2 


2501.4 


10 


II 


.1833 


454.1- 


2325.7 


476.3 


2384.2 


499-1 


2443.0 


522.6 


2502.4 


II 


12 


.2000 


454.4 


2326.7 


476.6 


2385.2 


499-5 


2444.0 


523.0 


2503.4 


12 


13 


.2167 


454-8 


2327.7 


477-0 


2386.1 


499-9 


2445.0 


523-4 


2504.4 


13 


14 


•2333 


455.1 


2328.7 


477-4 


2387.1 


500.3 


2446.0 


523.8 


2505.4 


14 


IS 


.2500 


455.5 


2329.6 


477-8 


2388.1 


500.7 


2447.0 


524.2 


2506.3 


IS 


16 


.2667 


455-9 


2330.6 


478.1 


2389.1 


501.0 


2448.0 


524.6 


2507.3 


16 


17 


.2833 


456.3 


2331.6 


478.5 


2390.0 


501.4 


2449.0 


525.0 


2508.3 


17 


18 


.3000 


456.6 


2332.6 


478.9 


2391-0 


501.8 


2449.9 


525.4 


2509.3 


18 


19 


•3167 


457-0 


2333-5 


479-3 


2392.0 


502.2 


2450.9 


525.8 


2510.3 


19 


20 


•3333 


457-3 


2334-5 


479-6 


2393-0 


502.6 


2451.9 


526.2 


2511.3 


20 


21 


.3500 


457-7 


2335-4 


480.0 


2393-9 


503.0 


2452.9 


526.6 


2512.3 


21 


22 


.3667 


458.1 


2336.4 


480.4 


2394.9 


503-4 


2453.9 


527.0 


2513.3 


22 


23 


.3833 


458.5 


2337-4 


480.8 


2395.9 


503.8 


2454.9 


527.4 


2514.3 


23 


24 


.4000 


458.8 


2338.4 


481. 1 


2396.9 


504. 1 


2455.9 


527.8 


2515.3 


24 


25 


.4167 


459-2 


2339-3 


481.S 


^397.8 


S04-5 


2456.8 


528.2 


2516.3 


25 


26 


.4333 


459-5 


2340.3 


481.9 


2398.8 


504-9 


^457-8 


528.6 


2517.3 


26 


27 


.4500 


459-9 


2341-3 


482.3 


2399-8 


505.3 


2458.8 


529.0 


2518.3 


27 


28 


.4667 


460.3 


2342.3 


482.6 


2400.8 


505-7 


2459.8 


529-4 


2519.3 


28 


29 


.4833 


460.7 


2343-2 


483-0 


2401.8 


506.1 


2460.8 


529-8 


2520.2 


29 


30 


.5000 


461.0 


2344-2 


483-4 


2402.8 


506.5 


2461.8 


530.2 


2521.2 


30 


31 


•5167 


461.4 


2345 -X 


483.8 


2403.7 


506.9 


2462.8 


530.6 


2522.2 


31 


32 


.5333 


461.7 


2346.1 


484.2 


2404-7 


507-3 


2463.8 


531.0 


2523.2 


32 


33 


•5500 


462.1 


2347.1 


484-6 


2405.7 


507-7 


2464.7 


531.4 


2524.2 


33 


34 


.5667 


462.5 


2348.1 


484-9 


2406.7 


508.0 


2465-7 


531.8 


2525.2 


34 


35 


.5833 


462.9 


2349.0 


485-3 


2407.6 


508.4 


2466.7 


532.2 


2526.2 


35 


36 


.6000 


463.2 


2350.0 


485-7 


2408.6 


508.8 


2467.7 


532.6 


2527.2 


36 


37 


.6167 


463-6 


2351-0 


486.1 


2409.6 


509.2 


2468.7 


533.0 


2528.2 


37 


38 


•6333 


463.9 


2352.0 


486.5 


2410.6 


509.6 


2469.7 


533.4 


2529.2 


38 


39 


.6soo 


464.3 


2352.9 


486.9 


2411.6 


510.0 


2470.7 


533-8 


2530.2 


39 


40 


.6667 


464.7 


2353.9 


487.2 


2412.6 


S10.4 


2471.7 


534-2 


2531.2 


40 


41 


.6833 


465.0 


2354.9 


487.6 


2413-5 


510.8 


2472.6 


534-6 


2532.2 


41 


42 


.7000 


465.4 


2355.9 


4?^° 


2414-5 


511.I 


2473.6 


535.0 


2533.2 


42 


43 


.7167 


465.8 


2356.8 


488.4 


2415-5 


511.5 


2474.6 


535.4 


2534.2 


43 


44 


.7333 


466.2 


2357.8 


488.7 


2416.5 


511.9 


2475.6 


535.8 


2535.2 


44 


45 


.7500 


466.5 


2358.8 


489.1 


2417-5 


512.3 


2476.6 


536.2 


2536.2 


45 


46 


.7667 


466.9 


2359-8 


489-5 


2418.5 


512.7 


2477.6 


536.6 


2537-2 


46 


47 


.7833 


467.3 


2360.7 


489-9 


2419-4 


513.I 


2478.6 


537.0 


2538.2 


47 


48 


.8000 


467.7 


2361.7 


490.3 


2420.4 


513.5 


2479.6 


537.4 


2539.2 


48 


49 


.8167 


468.0 


2362.7 


490.7 


2421.4 


S13.9 


2480.6 


537.8 


2540.2 


49 


50 


.8333 


468.4 


2363.7 


491.0 


2422.4 


514.3 


2481.6 


538.2 


2541.2 


SO 


SI 


.8500 


468.8 


2364.6 


491.4 


2423.4 


514.7 


2482.5 


538.6 


2542.2 


SI 


52 


•?^^7 


469.1 


2365.6 


491.8 


2424.4 


515.I 


2483.5 


539.0 


2543.2 


52 


S3 


.8833 


469.5 


2366.6 


492.2 


2425.3 


S15.5 


2484.5 


539.4 


2544-2 


53 


54 


.9000 


469.9 


2367.6 


492.5 


2426.3 


515.9 


2485-5 


539.8 


2545.2 


54 


SS 


.9167 


470.3 


2368.5 


492.9 


2427-3 


516.3 


2486.5 


S40.2 


2546.2 


5| 


S6 


•9333 


470.6 


2369.5 


493.3 


2428.3 


516.7 


2487.5 


540.6 


2547.2 


56 


57 


.9500 


471.0 


2370.5 


493.7 


2429-2 


517. 1 


2488.5 


541.0 


2548.2 


^l 


58 


.9667 


471.4 


2371.5 


494.1 


2430.2 


517.5 


2489.5 


541.4 


2549.2 


58 


59 


.9833 


471.8 


2372.4 


494.5 


2431.2 


517.9 


2490.5 


541.9 


2550.1 


59 



FUNCTIONS OF ONE-DEGREE CURVE 

Use loo' Chords up to 8" Curves Use 25' Chords up to 32" Curves 
Use so' Chords up to 16" Curves Use 10' Chords above 32° Curves 



361 



1 

G 


*S8 


48" 


49^ 


50° 


51** 


.s 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


542.3 


255I-I 


567.0 


2611.3 


592.4 


2671.9 


618.5 


2733.0 


I 


.0167 


542^7 


2552.1 


567-4 


2612.3 


592.8 


2672.9 


618.9 


2734.1 


I 


2 


.0333 


543-1 


2553.1 


567.8 


2613.3 


593.2 


2673.9 


619.3 


2735.1 


2 


3 


.0500 


543.5 


2554^1 


568.3 


2614.3 


593.7 


J!675.o 


619.8 


2736.1 


3 


4 


0667 


543-9 


2555.1 


568.7 


2615.3 


594.1 


2676.0 


620.2 


2737.1 


4 


5 


•0833 


544-3 


2556.1 


569.1 


2616.3 


594.5 


2677.0 


620.7 


2738.2 


5 


6 


.1000 


544-7 


2557.1 


569-5 


2617.3 


594.9 


2678.0 


621. 1 


2739.2 


6 


7 


.1167 


545-1 


2558.1 


569.9 


2618.3 


595-4 


2679.0 


621.6 


2740.2 


7 


8 


.1333 


545-5 


2559.1 


570.3 


2619.3 


595.8 


2680.0 


622.0 


2741.2 


8 


9 


.1500 


546-0 


2560.1 


570.8 


2620.4 


596.2 


2681.1 


622.5 


2742.3 


9 


10 


.1667 


546-4 


2561.1 


571.2 


2621.4 


596.7 


2682.1 


622.9 


2743.3 


10 


II 


.1833 


546-8 


2562.1 


571.6 


2622.4 


597.1 


2683.1 


623.3 


2744.3 


II 


12 


.2000 


547.2 


2563.1 


572-0 


2623.4 


597.5 


2684.1 


623.7 


2745.3 


12 


13 


.2167 


547-6 


2564.1 


572.4 


2624.4 


598.0 


2685.1 


624.2 


2746.4 


13 


14 


.2333 


548.0 


2565.1 


572.8 


2625.4 


598.4 


2686.1 


624.6 


2747.4 


14 


IS 


.2SOO 


548.4 


2566.1 


573-3 


2626.4 


598.9 


2687.2 


625.1 


2748.4 


15 


16 


.2667 


548.8 


2567.1 


573-7 


2627.4 


599.3 


2688,2 


625.5 


2749.4 


16 


17 


•2833 


549-2 


2568.1 


574-1 


2628.4 


599.7 


2689.2 


626.0 


2750.5 


17 


18 


.3000 


549-6 


2569.1 


574.5 


2629.4 


600.1 


2690.2 


626.4 


2751.5 


18 


19 


.3167 


550.1 


2570.1 


574.9 


2630.4 


600.6 


2691.3 


626.9 


2752.5 


19 


20 


•3333 


550.5 


2571-1 


575.3 


2631.4 


601.0 


2692.3 


627.3 


2753.5 


20 


21 


.3500 


550.9 


2572.1 


575.8 


2632.5 


601.S 


2693.3 


627.8 


2754.6 


21 


22 


.3667 


551-3 


2573-1 


576.2 


2633-5 


601.9 


2694.3 


628.2 


2755.6 


22 


23 


.3833 


5SI-7 


2574-1 


576.6 


2634-5 


602.3 


2695.3 


628.7 


2756.7 


23 


24 


.4000 


552.1 


2575-1 


577.0 


2635-5 


602.7 


2696.3 


629.1 


2757.7 


24 


25 


.4167 


552-5 


2576.1 


577.5 


2636.5 


603.2 


2697.4 


629.6 


2758.7 


25 


26 


•4333 


552.9 


2577-1 


577.9 


2637.5 


603.6 


2698.4 


630.0 


2759.7 


26 


27 


.4500 


553-3 


2578.1 


578.3 


2638.5 


604.1 


2699.4 


630.5 


2760.8 


27 


28 


.4667 


553.7 


2579-1 


578.7 


2639-5 


604.5 


2700.4 


630.9 


2761.8 


28 


29 


.4833 


554-2 


2580.1 


579.2 


2^40.5 


604.9 


2701.4 


631.4 


2762.8 


29 


30 


.5000 


554.6 


2581.1 


579-6 


2641.S 


605.3 


2702.4 


631.8 


2763.8 


30 


31 


.5167 


55S.O 


2582.1 


580.0 


2642.5 


605.8 


2703.5 


632.3 


2764.9 


31 


32 


.5333 


555.4 


2583.1 


580.4 


2643-5 


606.2 


2704-5 


632.7 


2765.9 


32 


33 


•SSoo 


555.8 


2584.1 


580.9 


2644.6 


606.6 


2705.S 


633.2 


2766.9 


33 


34 


.5667 


556.2 


2585.1 


581.3 


2645.6 


607.0 


2706.5 


633.6 


2767.9 


34 


35 


.5833 


556.6 


2586.2 


581.7 


2646.6 


607.5 


2707.6 


634.1 


2769.0 


35 


36 


.6000 


557.0 


2587.2 


582.1 


2647.6 


607.9 


2708.6 


634.5 


2770.0 


36 


37 


.6167 


557.4 


2588.2 


582.6 


2648.6 


608.4 


2709.6 


634-9 


2771.0 


H 


38 


.6333 


557.8 


2589.2 


583.0 


2649.6 


608.8 


2710.6 


^JH 


2772.0 


38 


39 


.6500 


558.3 


2590.2 


583.4 


2650.6 


609.3 


2711.6 


635.8 


2773.1 


39 


40 


.6667 


558.7 


2591.2 


583.8 


2651.6 


609.7 


2712.6 


636.2 


2774.1 


40 


41 


.6833 


559-1 


2592.2 


584.3 


2652.7 


610.1 


2713.7 


636.7 


2775.2 


41 


42 


.7000 


559-5 


5593.2 


584.7 


2653-7 


610.S 


2714.7 


637.1 


2776.2 


42 


43 


.7167 


559-9 


2594.2 


585.1 


2654^7 


611.0 


2715.7 


637.5 


2777.2 


43 


44 


.7333 


560.3 


2595-2 


585.5 


2655-7 


611.4 


2716.7 


638.0 


2778.2 


44 


45 


.7500 


S60.8 


2596.2 


586.0 


2656.7 


611.9 


2717.8 


638.5 


2779.3 


"^l 


46 


.7667 


561.2 


2597.2 


586.4 


2657-7 


612.3 


2718.8 


638.9 


2780.3 


46 


47 


•7833 


561.6 


2598.2 


586.8 


2658.7 


612.8 


2719.8 


639.4 


2781.3 


47 


48 


.8000 


562.0 


2599.2 


587.2 


2659.7 


613.2 


2720.8 


639.8 


2782.3 


48 


49 


.8167 


562.4 


2600.2 


587.7 


2660.8 


613.7 


2721.8 


640.3 


2783.4 


49 


SO 


•8333 


S62.8 


2601.2 


588.1 


2661.8 


614.1 


2722.8 


640.7 


2784.4 


50 


SI 


.8500 


563-3 


2602.2 


588.5 


2662.8 


614.5 


2723.9 


641.2 


2785.4 


51 


52 


.8667 


563-7 


2603.2 


588.9 


2663.8 


614.9 


2724.9 


641.6 


2786.4 


52 


53 


.8833 


564-1 


2604.2 


589.4 


2664.8 


615.4 


2725.9 


642.1 


^7^2'^ 


53 


54 


.9000 


564.5 


2605.2 


589.8 


2665.8 


615.8 


2726.9 


642.S 


2788.S 


54 


55 


.9167 


564.9 


2606.2 


590. 2 


2666.8 


616.3 


2728.0 


643.0 


2789.6 


H 


56 


.9333 


565-3 


2607.2 


590.6 


2667.8 


616.7 


2729.0 


643.4 


2790.6 


56 


H 


•9500 


565.8 


2608.3 


591.1 


2668.9 


617.2 


2730.0 


643.9 


2791.6 


57 


58 


.9667 


566.2 


2609.3 


591.5 


2669.9 


617.6 


2731.0 


644.3 


2792.6 


58 


59 


•9833 


566.6 


2610.3 


592.0 


2670.9 


1 618.1 


2732.0 


644-8 


2793.7 


59 



362 



THE SURVEY 





Use 100' Chords 


UD to 8 


° Curves 


Use 


25' Chords up to 
10' Chords above 


K^""" 


ves 




Use 50' 


Chords up to 16 


° Curves Use 


J 32" Curves 


"3 




52° 


53*" 


54° 


55° 


"3 
c 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


645^2 


2794-7 


672.7 


2856.9 


700.9 


2919.S 


729.9 


2982.8 
2983.9 





1 


.0167 
.0333 

.0500 


645-7 


2795-8 


673.2 


2857.9 


701.4 


2920.6 


730.4 


I 


2 


646.1 


2796.8 


673.7 


2858.9 


701.9 


2921.6 


730.9 


2984.9 


2 


3 
4 


646.6 


2797.8 


674.2 


2860.0 


702.4 


2922.7 


731.4 


2986.0 


3 


.0667 


647.0 


2798.8 


674.6 


2861.0 


702.8 


2923.8 


731.9 


2987.1 


4 


c 


.0833 

.1000 


647.5 


2799-9 


675.1 


2862.1 


703.3 


2924.9 


732.4 


2988.2 


5 


6 


647-9 


2800.9 


675-5 


2863.1 


703.8 


2925.9 


732.9 


2989.2 


6 


7 

8 


.1167 
.1333 


648.4 


2802.0 


676.0 


2864.2 


704.3 


2927.0 


733-4 


2990.3 


7 


648.9 


2803.0 


676.4 


2865.2 


704.8 


2928.0 


733.8 


2991.3 


8 


9 


.1500 


649^4 


2804.0 


676.9 


2866.3 


705.3 


2929.1 


734.3 


2992.4 


9 


10 


.1667 


649.8 


2805.0 


677-4 


2867.3 


705.7 


2930.1 


734.8 


2993.4 


10 


II 


.1833 

.2000 


650-3 


2806.1 


677-9 


2868.4 


706.2 


2931.2 


735-3 


2994.5 


II 


12 


650.7 


2807.1 


678.3 


2869.4 


706.7 


2932.2 


735-8 


^^^H 


12 


13 


.2167 


651.2 


2808.2 


678.8 


2870.5 


707.2 


2933.3 


736.3 


2996.6 


13 


14 


.2333 


651.6 


2809.2 


679.2 


2871.5 


707.7 


2934.3 


736.8 


2997-7 


14 


;^ 


.2500 
.2667 


652.1 


2810.2 


679-7 


2872.5 


708.2 


2935.4 


737.3 


2998.8 


15 


652.5 


2811.2 


680.2 


2873.5 


708.6 


2936.4 


737.8 


2999-8 


16 


17 

18 


.2833 

."^OOO 


653.0 


2812.3 


680.7 


2874.6 


709.1 


2937-5 


738-2 


3000.9 


^l 


653-4 


2813.3 


681. 1 


2875.6 


709.6 


2938.5 


738.7 


3001.9 


18 


19 


.3167 


653-9 


2814.4 


681.6 


2876.7 


710.1 


2939.6 


739.2 


3003.0 


19 


20 


•3333 


654-3 


2815.4 


682.0 


2877.7 


710.5 


2940.6 


739.7 


3004.0 


20 


21 


.3500 


654-8 


2816.4 


682.5 


2878.8 


711.0 


2941.7 


740.2 


3005.1 
3006.2 


21 


22 


.3667 


655-2 


2817.4 


683.0 


2879-8 


7II-5 


2942.7 


740.7 


22 


23 
24 


.3833 
.4000 


655.7 


2818.5 


683.5 


2880.9 


712.0 


2943-8 


741.2 


3007.3 


23 


656.2 


2819.5 


683.9 


2881.9 


712.S 


2944-8 


741.7 


3008.3 


24 


25 


.4167 


656.7 


2820.6 


684.4 


2883.0 


713-0 


2945.9 


742.2 


3009.4 


25 


26 


•4333 


657-1 


2821.6 


684.9 


2884.0 


713-4 


2946.9 


742.7 


3010.4 


26 


27 


.4500 


657.6 


2822.6 


685.4 


2885.1 


713-9 


2948.0 


743-2 


3011.5 


27 
28 


28 


.4667 


658.0 


2823.6 


685.8 


2886.1 


714-4 


2949.0 


743-7 


3012.5 
3013.6 


29 


•4833 


658.5 


2824.7 


686.3 


2887.1 


714.9 


2950.1 


744.2 


29 


30 


.«;ooo 


658.9 


2825.7 


686.7 


2888.1 


71S-3 


2951.1 


744-7 


3014.7 


30 


31 


•3 T^ 
.5167 


659.4 


2826.8 


687.2 


2889.2 


715.8 


2952-2 


745-2 


3015.8 


31 


32 
33 
34 


•5333 
.5500 
.5667 


659.8 


2827.8 


687.7 


2890.2 


716.3 


2953-2 


745-7 


3016.8 


32 


660.3 


2828.8 


688.2 


2891.3 


716.8 


2954-3 


746.2 


3017.9 


33 


660.7 


2829.8 


688.6 


2892.3 


717-3 


2955-3 


746.7 


3018.9 


34 


35 
36 
37 
38 
39 


.5833 
.6000 


661.2 


2830.9 


689.1 


2893.4 


717.8 


2956.4 


747.2 


3020.0 


35 
36 


66x6 


2831.9 


689.6 


2894.4 


718.2 


2957.S 


747.7 


3021.1 


.6167 
.6333 
.6500 


662.1 


2833.0 


690.1 


2895-5 


718.7 


2958.6 


748.2 


3022.1 


11 


662.5 


2834.0 


690.5 


2896.5 


719.2 


2959.6 


748.7 


3023.2 


663.0 


2835.1 


691.0 


2897.6 


719-7 


2960.7 


749.2 


3024.3 


39 


40 


.6667 


663.5 


2836.1 


691.5 


2898.6 


720.2 


2961.7 


749.7 


3025.3 
3026.4 


40 


41 
42 
43 


•6833 
.7000 
.7167 


664.0 


2837.2 


692.0 


2899.7 


720.7 


2962.8 


750.2 


41 


664.4 
664.9 


2838.2 
2839.2 


692.4 
692.9 


2900.7 
2901.8 


721.1 
721.6 


2963.8 
2964.9 


750.7 
751.2 


3027.5 
3028.6 
3029.6 


42 

43 


44 


•7333 


665.3 


2840.2 


693.4 


2902.8 


722.1 


2965.9 


751.7 


44 


45 


.7500 


665.8 


2841.3 


693.9 


2903.9 


722,6 


2967.0 


752.2 
752.6 


3030.7 


46 


46 


.7667 


666.2 


2842.3 


694-3 


2904.9 


723.1 


2968.0 


3031.7 
3032.8 
3033.8 


47 


•7833 


666.7 


2843.4 


694.8 


2906.0 


723-6 


2969.1 


753.1 
753.6 


47 
48 


48 


.8000 


667.2 


2844.4 


695-3 


2907.0 


724-1 


2970.1 


49 


.8167 


667.7 


2845-5 


695-8 


2908.1 


724.6 


2971.2 


754.1 


3035.0 


49 


50 


.8333 


668.1 


2846.5 


696.2 


2909.1 


725.0 


2972.2 


754.6 


3036.0 


50 


51 


.8500 


668.6 


2847.5 


696.7 


2910.2 


725-5 


2973.3 


75S-I 
755-6 


3037.1 
3038.1 


51 


52 


.8667 


669.0 


2848.5 


697.1 


2911.2 


726.0 


2974.4 


52 


S3 


.883J 


669-5 


2849.6 


697.6 


2912.3 


726.5 


2975.S 


756.1 


3039.2 


53 


54 


.9000 


669.9 


2850.6 


698.1 


2913.3 


727.0 


2976.5 


756.6 


3040.2 


54 


u 


•9167 
•9^33 
.9500 
.9667 
.9833 


670.4 
670.9 


2851.7 
2852.7 


698.6 
699.0 


2914.4 
2915.4 


727.S 
728.0 


2977-6 
2978.6 


757-1 
757-6 


3041.3 
3042.4 


11 


57 
58 
59 


671^4 
671.8 


2853.8 
2854.8 


699-5 
700.0 


2916.5 
2917.5 


728.5 
729.0 


2979.7 
2980.7 


758.6 


3043.5 
3044.5 
3045.6 


11 


672.3 


2855.9 


700.5 


2918.5 


. 729-5 


2981.8 


759.1 


59 



FUNCTIONS OF ONE-DEGREE CURVE 



363 





Use icx)' Chords up to 8 


° Curves 


Use 2. 


;' Chords 


up to 32° Curves 




Use 50 


' Chords up to 16 


° Curves Use 10' Chords above 32° Curves 


s 




56'' 


57° 


58° 


59** 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


759.6 


3046.6 


790.2 


3111.1 


821.4 


3176.1 


853-S 


3241.9 





I 


.0167 


760.1 


3047.7 


790.7 


3112.2 


821.9 


3177-2 


854.0 


3243.0 


I 


2 


-0333 


760.6 


3048.8 


791-2 


3113.3 


822.5 


3178.3 


854.6 


3244.1 


2 


3 


.0500 


761. 1 


3049.9 


791.7 


3114.4 


823.0 


3179.4 


855.1 


3245.2 


3 


4 


.0667 


761.6 


3050.9 


792.2 


3115.4 


823.5 


3i'8o.5 


855-7 


3246.3 


4 


5 


.0833 


762.2 


3052.0 


792.8 


3116.5 


824.1 


3181.6 


856.2 


3247.4 


5 


6 


.1000 


762.7 


3053.1 


793.3 


3117.6 


824.6 


3182.7 


856.8 


3248.5 


6 


7 


.1167 


763.2 


3054-2 


793.8 


3118.7 


825.2 


3183.8 


857.3 


3249.6 


7 


8 


-1333 


763.7 


3055-2 


794.3 


3119.7 


825.7 


3184.9 


857-9 


3250.7 


8 


9 


.1500 


764.2 


3056.3 


794-8 


3120.8 


826.2 


3186.0 


858.5 


3251.8 


9 


10 


.1667 


764.7 


3057-4 


795.3 


3121.9 


826.7 


3187.1 


859.0 


3252.9 


10 


II 


.1833 


765.2 


3058.5 


795.8 


3123.0 


827.3 


3188.2 


859-S 


3254-0 


II 


12 


.2000 


765-7 


3059.5 


796.3 


3124.1 


827.8 


3189.2 


860.0 


3255.1 


12 


13 


.2167 


766.2 


3060.6 


796.9 


3125.2 


828.4 


3190.3 


860.6 


3256.2 


13 


14 


.2333 


766.7 


3061.6 


797-4 


3126.2 


828.9 


3191.4 


861.1 


3257.3 


14 


IS 


.2500 


767.2 


3062.7 


797.9 


3127.3 


829.4 


3192.5 


861.7 


3258.4 


IS 


16 


.2667 


767.7 


3063.8 


798.4 


3128.4 


829.9 


3193.6 


862.2 


3259.5 


16 


17 


.2833 


768.2 


3064.9 


798.9 


3129.5 


830.5 


3194.7 


862.8 


3260.6 


17 


18 


.3000 


768.7 


3065.9 


799.4 


3130.6 


831.0 


3195.8 


863.3 


3261.7 


18 


19 


.3167 


769.2 


3067.0 


799-9 


3131.7 


831.5 


3196.9 


863.8 


3262.8 


19 


20 


.3333 


769.7 


3068.1 


800.S 


3132.7 


832.1 


3198.0 


864.4 


3263.9 


20 


21 


.3500 


770.3 


3069.2 


801.0 


3133.8 


832.5 


3199.1 


864.9 


3265.0 


21 


22 


.3667 


770.8 


3070.2 


801.5 


31349 


833-1 


3200.2 


865.S 


3266.1 


22 


23 


.3833 


771.3 


3071.3 


802.0 


3136.0 


833-6 


3201.3 


866.0 


3267.2 


23 


24 


.4000 


771-8 


3072.4 


802.5 


3137-0 


834-2 


3202.4 


866.6 


3268.3 


24 


^1 


.4167 


772.3 


3073.5 


803.1 


3138.1 


834-7 


3203.5 


867.1 


3269.4 


25 


26 


.4333 


772.8 


3074.5 


803.6 ■ 


3139.2 


835.3 


3204.5 


867.7 


3270.5 


26 


27 


.4500 


773.3 


3075.6 


804.2 


3140.3 


835.8 


3205.6 


868.2 


3271.6 


27 


28 


.4667 


773.8 


3076.6 


804.7 


3141-4 


836.3 


3206.7 


868.8 


3272.7 


28 


29 
30 


.4833 
.5000 


774.3 
774.8 


3077.7 
3078.8 


805.2 
805.7 


3142.5 


836.8 


3207.8 
3208.9 


869.3 
869.9 


3273.8 
3274.9 


29 
30 


3143-5 


837.4 


31 


-5167 


775.3 


3079.9 


806.3 


3144-6 


837.8 


3210.0 


870.5 


3276.0 


31 


32 


-5333 


775.8 


3080.9 


806.8 


3145-7 


838.4 


3211.1 


871.0 


3277.1 


32 


33 


.5500 


776.3 


3082.0 


807.3 


3146.8 


838.9 


3212.2 


871.6 


3278.2 


33 


34 


.5667 


776.8 


3083.1 


807.8 


3147.9 


839.5 


3213-3 


872.1 


3279.4 


34 


35 


.5833 


777.3 


3084.2 


808.3 


3149.0 


840.0 


3214.4 


872.7 


3280.5 


35 


36 


.6000 


777.8 


3085.2 


808.8 


3150.0 


840.6 


3215.5 


873-2 


3281.6 


36 


H 


.6167 


778.4 


3086.3 


809.4 


3151-1 


841. 1 


3216.6 


873.8 


3282.7 


37 


38 


.6333 


778.9 


3087.4 


809.9 


3152.2 


841.6 


3217.7 


874.3 


3283.8 


38 


39 


.6500 


779.4 


3088.5 


810.4 


3153.3 


842.1 


3218.8 


874-9 


3284.9 


39 


40 


.6667 


779.9 


3089.6 


810.9 


3154-4 


842.7 


3219.9 


875.4 


3286.0 


40 


41 


.6833 


780.4 


3090.7 


811. 5 


3155.5 


843.1 


3221.0 


876.0 


3287.1 


41 


42 


.7000 


780.9 


3091.7 


812.0 


3156.6 


843.8 


3222.1 


876.5 


3288.2 


42 


43 


.7167 


781.4 


3092.8 


812.5 


3157.7 


844.2 


3223.2 


877.0 


3289.3 


43 


44 


.7333 


781.9 


3093-9 


813.0 


3158.7 


844.9 


3224.3 


877.6 


3290.5 


44 


45 


.7500 


782.5 


3095.0 


813.6 


3159.8 


845.5 


3225.4 


878.1 


3291.6 


45 


46 


.7667 


783.0 


3096.0 


814.1 


3160.9 


846.0 


3226.5 


878.7 


3292.7 


46 


47 


.7833 


783.5 


3097.1 


814.6 


3162.0 


846.5 


3227.6 


879.2 


3293.8 


47 


48 


.8000 


784.0 


3098.2 


815. 1 


31.63 I 


847.0 


3228.7 


879.8 


3294.9 


48 


49 


.8167 


784.5 


3099.3 


815.7 


3164-2 


847.6 


3229.8 


880.3 


3296.0 


49 


50 


.8333 


785.0 


3100.3 


816.2 


3165.3 


848.1 


3230.9 


880.9 


3297.1 


50 


SI 


.8500 


785.5 


3101.4 


816.7 


3166.4 


848.7 


3232.0 


881.5 


3298 2 


51 


52 


•?5^7 


786.0 


3102.5 


817.2 


3167.4 


849.2 


3233.1 


882.0 


3299.3 


52 


S3 


•8833 


786.6 


3103.6 


817.8 


3168.5 


849.8 


3234.2 


882.6 


3300.4 


53 


54 


.QCXXJ 


787.1 


3104.6 


818.3 


3169.6 


850.3 


3235.3 


883.1 


3301.5 


54 


55 


.9167 


787.6 


3105.7 


8x8.8 


3170.7 


850.9 


3236.4 


883.7 


3302.6 


55 


S6 


•9333 


788.1 


3106.8 


819.3 


3171.8 


851.4 


3237.5 


884.2 


3303.8 


56 


57 


.9500 


788.6 


3107.9 


819.9 


3172.9 


852.0 


3238.6 


884.8 


3304.9 


57 


S8 


.9667 


789.1 


3108.9 


820.4 


3174.0 


852.5 


3239.7 


885.3 


3306.0 


58 


59 1 .9833 


789.7 


3110.0 


820.9 


3175. 1 


853.0 


3240.8 


885.9 


3307.1 


59 



364 



THE SURVEY 



Use loo' Chords up to 8° Curves 
Use 50' Chords up to 16° Curves 



Use 25' Chords up to 32* Curves 
Use 10' Chords above 32° Curves 



s 

a 




60° 


61" 


62*^ 


63° 


1 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


886.4 


3308.2 


920.2 


3375.2 


954.8 


3442.9 


990.3 


3511.3 


I 


.0167 


886.9 


3309.3 


920.8 


3376.3 


955.4 


3444.1 


990.9 


3512.4 


I 


2 


.0333 


887.5 


3310.4 


921.4 


3377.4 


956.0 


3445.2 


991.5 


3513.6 


2 


3 


.0500 


888.1 


3311.5 


922.0 


3378.5 


956.6 


3446.3 


992.1 


3514.8 


3 


4 


.0667 


888.7 


3312.7 


922.S 


3379.7 


957.2 


3447.5 


992.7 


3515.9 


4 


5 


.0833 


889.3 


3313.8 


923.0 


3380.8 


957-7 


3448.6 


993.3 


3517.1 


5 


6 


.1000 


889.8 


3314.9 


923.6 


3381.9 


958.3 


3449.7 


993.9 


3518.2 


6 


7 


.1167 


890.3 


3316.0 


924.2 


3383.1 


958.9 


3450.9 


994.S 


3519.3 


7 


8 


•1333 


890.9 


3317. 1 


924.8 


3384.2 


959-5 


3452.0 


995.1 


3520.5 


8 


9 


.1500 


891-5 


3318.2 


925.3 


3385.3 


960.1 


3453.2 


995.7 


3521.6 


9 


10 


.1667 


892.0 


3319.3 


925.9 


3386.4 


960.7 


3454.3 


996.3 


3522.8 


10 


II 


.1833 


892.6 


3320.5 


926.5 


3387.5 


961.3 


3455-4 


996.9 


3524.0 


II 


12 


.2000 


893.1 


3321.6 


927-1 


3388.7 


961.9 


3456.6 


997.5 


3525.1 


12 


13 


.2167 


893.7 


3322.7 


927.6 


3389.8 


962.4 


3457.7 


998.1 


3526.2 


13 


14 


.2333 


894.3 


3323.8 


928.2 


3390.9 


963-0 


3458.8 


998.7 


3527.4 


14 


15 


.2500 


894.8 


3324.9 


928.7 


3392-1 


963-6 


3460.0 


999.3 


3528.6 


IS 


16 


.2667 


895.4 


3326.0 


929.3 


3393-2 


964.2 


3461.1 


999.9 


3529.7 


16 


17 


.2833 


895.9 


3327.1 


929.9 


3394.3 


964.8 


3462.3 


1000.5 


3530.9 


^l 


18 


.3000 


896.5 


3328.3 


930.5 


3395-4 


965.4 


3463.4 


lOOI.I 


3532.0 


18 


19 


.3167 


897.0 


3329.4 


931.0 


3396.6 


966.0 


3464.6 


IOOI.7 


3533.i_ 


19 


20 


.3333 


897.6 


3330.5 


931.6 


3397.7 


966.6 


3465.7 


1002.3 


3534.3 


20 


21 


•3500 


898.2 


3331.6 


932.2 


3398.8 


967.2 


3466.8 


1002.9 


3535.4 


21 


22 


.3667 


898.8 


3332.7 


932.8 


3399.9 


967.8 


3467.9 


1003.5 


3536.6 


22 


23 


.3833 


899.3 


3333.8 


933.3 


3401.1 


968.3 


3469.0 


1 004. 1 


3537-8 


23 


24 


.4000 


899.9 


3334.9 


933.9 


3402.2 


968.9 


3470.2 


1004.7 


3538.9 


24 


25 


.4167 


900.5 


3336.1 


934.5 


3403.3 


' 969.5 


3471.3 


1005.3 


3540.0 


25 


26 


.4333 


901.0 


3337.2 


935.1 


3404.4 


970.1 


3472.5 


1005.9 


3541.2 


26 


27 


.4500 


901.6 


3338.3 


935.7 


3405-6 


970.7 


3473.6 


1006.5 


3542.3 


27 


28 


.4667 


902.1 


3339.4 


936.3 


3406.7 


971.3 


3474.7 


1007. 1 


3543.5 


28 


29 


.4833 


902.7 


3340.5 


936.8 


3407.8 


971.9 


3475.9 


1007.8 


3544.6 


29 


30 


.5000 


903.2 


3341.6 


937.4 


3408.9 


972.S 


3477.0 


1008.4 


3545-8 


30 


31 


•5167 


903.8 


3342.7 


938.0 


3410.1 


973.0 


3478.1 


1009.0 


3546.9 


31 


32 


•5333 


904.4 


3343.9 


938.6 


3411.2 


973.6 


3479.3 


1009.6 


3548.1 


32 


33 


•5SOO 


904.9 


3345.0 


939.1 


3412.3 


974.2 


3480.S 


I0I0.2 


3549.2 


33 


34 


.5667 


905.5 


3346.1 


939.7 


3413-5 


974.8 


3481.6 


I0I0.8 


3550.4 


34 


35 


.5833 


906.1 


3347.2 


940.4 


3414.6 


975-4 


3482.7 


IOII.4 


3551.6 


35 


36 


.6000 


906.6 


3348.3 


940.9 


3415-7 


976.0 


3483.9 


I0I2.0 


3552.7 


36 


37 


.6167 


907.2 


3349.5 


941.5 


3416.8 


976.6 


3485.0 


IOI2.6 


3553.8. 


H 


38 


.6333 


907.7 


3350.6 


942.1 


3418.0 


977.2 


3486.2 


IOI3.2 


3555.0 


38 


39 


.6500 


908.2 


3351.7 


942.6 


3419-2 


977.8 


3487.4 


IOI3.9 


3556.2 


39 


40 


.6667 


908.8 


3352.8 


943.2 


3420.3 


978.4 


3488.5 


IOI4.5 


3557-3 


40 


41 


.6833 


909.4 


3353.9 


943.8 


3421.4 


979.0 


3489.6 


IOI5.I 


3558.4 


41 


42 


.7000 


910.0 


3355.0 


944-4 


3422.5 


979.6 


3490.7 


IOI5.7 


3559.6 


42 


43 


.7167 


910.6 


3356.1 


944.9 


3423-6 


980.2 


3491.9 


IOI6.3 


3560.8 


43 


44 


.7333 


911.1 


3357.3 


945.5 


3424-8 


980.8 


3493.0 


IOI6.9 


3562.0 


44 


45 


.7500 


911.7 


3358.4 


946.1 


3426.0 


981.4 


3494.2 


IOI7.5 


3563.2 


45 


46 


.7667 


912.3 


3359-5 


946-7 


3427-1 


982.0 


3495.3 


IOI8.I 


3564.3 


46 


47 


.7833 


912.8 


3360.6 


947.2 


3428.2 


982.6 


3496.4 


IOI8.7 


3565.5 


4? 


48 


.8000 


913.4 


3361.8 


947.8 


3429.3 


983.2 


3497.6 


IOI9.3 


3566.6 


48 


49 


.8167 


913.9 


3362.9 


948.4 


3430.4 


983.8 


3498.7 


1020.0 


3567.7 


49 


50 


•8333 


914.S 


3364.0 


949.0 


3431-6 


984.4 


3499.9 


1020.6 


3568.9 


50 


51 


.8500 


915.1 


3365.1 


949.6 


3432.8 


984.9 


3501.0 


I02I.2 


3570.0 


51 


52 


.8667 


915.7 


3366.2 


950.2 


3433-6 


985.5 


3502.2 


I02I.8 


3571.2 


52 


53 


.8833 


916.2 


3367.3 


950.7 


3434-0 


986.1 


3503.3 


1022.4 


3572.3 


53 


54 


.9000 


916.8 


3368.5 


951.3 


3436.1 


986.7 


3504.5 


1023.0 


.^573.5 


54 


55 


.9167 


917.4 


3369.6 


951.9 


3437-2 


987.3 


3505.6 


1023.6 


3574.6 


55 


56 


.9333 


918.0 


3370.7 


952.5 


3438.4 


9?Z-9 


3506.8 


1024.2 


3575.8 


56 


57 


.9500 


918.6 


3371.9 


953.0 


3439-6 


988.5 


3507.9 


1024.8 


3576.9 


H 


58 


.9667 


919.1 


3373.0 


953-6 


3440.7 


989.1 


3509.0 


1025.4 


3578.1 


58 


59 


.9833 


919.6 


3374.1 


954.2 


3441.8 


989.7 


3510.1 


IO26.I 1 3579.3 


59 



FUNCTIONS OF ONE-DEGREE CURVE 



365 



Use icx>' Chords up to 8° Curves 
Use 50' Chords up to 16** Curves 



Use 25' Chords up to 32° Curves 
Use 10' Chords above 32° Curves 



1 




64° 


65'. 


66'' 


67*^ 


CO 

0) 

.S. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan 


Ext. 


Tan. 





.0000 


1026.7 


3580.4 


1064.0 


3650.4 


1102.2 


3721.1 


1141-5 


3792.6 





I 


.0167 


1027.3 


3581.6 


1064.6 


3651.6 


1102.9 


3722.3 


1142.2 


3793.8 


I 


2 


.0333 


1027.9 


3582.8 


1065.2 


3652.8 


1103.5 


3723.4 


1142.8 


3795.0 


2 


3 


.0500 


1028.6 


3583.9 


1065.9 


3654.0 


1104.2 


3724.6 


1143.5 


3796.2 


3 


4 


.0667 


1029.2 


3585.1 


1066.5 


3655.1 


1 104.8 


3725.8 


1144.1 


3797.4 


4 


S 


.0833 


1029.8 


3586.3 


1067.1 


3656.3 


1105.5 


3727.0 


1144.8 


3798.6 


5 


6 


.1000 


1030.4 


3587.4 


1067.7 


3657.5 


1106.1 


3728.2 


1145.4 


3799.8 


6 


7 


.1167 


1031.1 


3588.6 


1068.4 


3658.6 


1106.8 


3729.4 


1146.1 


3801.0 


7 


8 


.1333 


1031.7 


3589.7 


1069.0 


3659.8 


1107.4 


3730.6 


1146.7 


3802.2 


8 


9 


.1500 


1032.3 


3590.9 


1069.6 


3661.0 


1108.1 


3731.7 


1147.4 


3803.4 


9 


10 


.1667 


1032.9 


3592.1 


1070.2 


3662.2 


1108.7 


3732.9 


1148.1 


3804.6 


10 


11 


.1833 


1033.S 


3593.3 


1070.9 


3663.4 


1109.4 


3734.1 


1148.8 


3805.8 


11 


12 


.2000 


1034.1 


3594.4 


1071.5 


3664.5 


IIIO.O 


3735.3 


1 149.4 


3807.0 


12 


13 


.2167 


1034.8 


3595.5 


1072. 1 


3665.7 


III0.7 


3736.5 


1150.1 


3808.2 


13 


14 


.2333 


1035.4 


3596.7 


1072.7 


3666.9 


1II1.3 


3737.7 


1150.7 


3809.4 


14 


IS 


.2500 


1036.0 


3597.9 


1073.4 


3668.0 


I1I2.0 


3738.9 


1151.4 


3810.6 


15 


16 


.2667 


1036.6 


3599.1 


1074.0 


3669.2 


III2.6 


3740.1 


1152.0 


3811.8 


16 


17 


.2833 


1037.3 


3600.3 


1074.6 


3670.4 


III3-3 


3741.3 


1152.7 


3813.0 


17 


l8 


.3000 


1037.9 


3601.4 


1075.2 


3671.6 


1113.9 


3742.4 


1153.3 


3814.2 


18 


19 


.3167 


1038.5 


3602.6 


1075.9 


3672.8 


1114.6 


3743.6 


1154.0 


3815.4 


19 


20 


.3333 


1039.1 


3603.7 


1076.6 


3673.9 


1115.2 


3744.8 


1154.7 


3816.6 


20 


21 


.3500 


1039-7 


3604.8 


1077.2 


3675.0 


1115.9 


3746.0 


1155.4 


3817.8 


21 


22 


.3667 


1040.3 


3606.0 


1077.8 


3676.2 


1116.5 


3747.2 


1156.0 


3819.0 


22 


23 


.3833 


1 041.0 


3607.2 


1078.5 


3677.4 


1117.2 


3748.4 


1156.7 


3820.2 


23 


24 


.4000 


1 041. 6 


3608.4 


1079.1 


3678.6 


1117.8 


3749.6 


1157.4 


3821.4 


24 


25 


.4167 


1042.2 


3609.5 


1079.8 


3679.7 


1118.5 


3750.7 


1158.1 


3822.6 


25 


26 


■4333 


1042.8 


3610.7 


1080.4 


3680.9 


1119.1 


3751.9 


1158.7 


3823.8 


26 


27 


.4500 


1043. 5 


3611.9 


io8i.i 


3682.1 


1119.8 


3753.1 


1159-4 


3825.0 


27 


28 


.4667 


1044. 1 


3613.0 


1081.7 


3683.3 


1120.4 


3754.3 


1160.1 


3826.2 


28 


29 


.4833 


1044.7 


3614.1 


1082.4 


3684.5 


1121.1 


3755.5 


I160.8 


3827.4 


29 


30 


.5000 


1045.3 


361S.3 


1083.0 


3685.6 


1121.7 


3756.7 


I161.4 


3828.6 


30 


31 


.5167 


1045.9 


3616.5 


1083.6 


3686.8 


1122.3 


3757.9 


1162. 1 


3829.8 


31 


32 


•5333 


1046.5 


3617.7 


1084.2 


3688.0 


1123.0 


3759.1 


1162.8 


3831.0 


32 


33 


.5500 


1047.2 


3618.9 


1084.9 


3689.2 


1123.7 


3760.3 


1163.5 


3832.2 


33 


34 


.5667 


1047.8 


3620.0 


1085.5 


3690.4 


1124.3 


3761.5 


1164.1 


3833.4 


34 


35 


.5833 


1048.4 


3621.1 


1086.2 


3691.6 


1125.0 


3762.7 


1164.8 


3834-6 


35 


36 


.6000 


1049.0 


3622.3 


1086.8 


3692.7 


1125.6 


3763.9 


I165.5 


3835.9 


36 


H 


.6167 


1049.7 


3623.5 


1087.5 


3693.9 


1126.3 


3765.1 


I166.2 


3837.1 


37 


38 


.6333 


1050.3 


3624.7 


1088.1 


3695.1 


1126.9 


3766.3 


1166.8 


3838.3 


38 


39 


.6500 


1050.9 


3625.8 


1088.8 


3696.2 


1127.6 


3767.5 


1167.5 


3839.5 


39 


40 


.6667 


1051.5 


3627.0 


1089.4 


3697.4 


1128.3 


3768.7 


1168.2 


3840.7 


40 


41 


.6833 


1052. 1 


3628.2 


1090.0 


3098.6 


1129.0 


3769.9 


1168.9 


3841.9 


41 


42 


.7000 


1052.7 


3629.4 


1090.6 


3699.8 


1129.6 


3771.0 


1169.5 


3843.1 


42 


43 


.7167 


1053.4 


3630.5 


1091.3 


3701.0 


1130.3 


3772.2 


1170.2 


3844.3 


43 


44 


.7333 


1054.0 


3631.7 


1091.9 


3702.2 


1 130.9 


3773.4 


1170.9 


3845.5 


44 


4^ 


.7500 


1054.6 


3632.8 


1092.6 


3703.3 


1131.6 


3774.6 


I171.6 


3846.7 


45 


46 


.7667 


1055.2 


3634.0 


1093.2 


3704.5 


1132.2 


3775.8 


I172.2 


3847.9 


46 


^l 


.7833 


1055.9 


3635.2 


1093.9 


3705.7 


1132.9 


3777.0 


1172.9 


3849.1 


47 


48 


.8000 


1056.5 


3636.4 


1094.5 


3706.9 


1133.5 


3778.2 


1173.6 


3850.4 


48 


49 


.8167 


1057.1 


3637.5 


1095.2 


3708.1 


1134.2 


3779.4 


1 1 74.3 


3851.6 


49 


SO 


.8333 


1057.7 


3638.7 


1095.8 


3709.3 


1134.9 


3780.6 


1174.9 


3852.8 


SO 


SI 


.8500 


1058.4 


3639.9 


1096.4 


3710.5 


1135.6 


3781.8 


1175-6 


3854.0 


51 


52 


•?5^7 


1059.0 


3641.1 


1097.0 


3711.6 


1136.2 


3783.0 


I176.3 


3855.2 


52 


S3 


.8833 


1059.6 


3642.3 


1097.7 


3712.8 


1136.9 


3784.2 


1177.0 


3856.4 


53 


S4 


.9000 


1060.2 


3643.4 


1098.3 


3714.0 


1137.5 


3785.4 


1177.6 


3857.6 


54 


H 


.9167 


1060.9 


3644.6 


1099.0 


3715.1 


1138.2 


3786.6 


1178.3 


3858.8 


55 


S6 


.9333 


1061.5 


3645.7 


1099.6 


3716.3 


1138.8 


3787.8 


1179.0 


3860.0 


S6 


H 


.9500 


1062. 1 


3646.9 


1100.3 


3717.5 


1139.5 


3789.0 


1179.7 


3861.2 


57 


S8 


.9667 


1062.7 


3648.1 


1100.9 


3718.7 


1140.1 


3790.2 


1180.3 


3862.S 


S8 


59 


.9833 


1063.4 


3649.2 


1101.6 


3719.9 


1140.8 


3791.4 


1181.0 


3863.7 


S9 



366 



THE SURVEY 



Use loo' Chords up to 8** Curves Use 25' Chords up to 32° Curves 
Use so' Chords up to 16° Curves Use 10' Chords above 32 Curves 



1 

.a 





68° 


69° 1 


70° 


71° 




Ext. Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


.0000 


1181.6 


3864^9 


1222.9 


3938.1 


1265.0 


4012. 1 


1308.4 


4087.1 





I 


,0167 


1182.3 


3866.1 


1223.6 


3939.4 


1265.7 


4013.4 


1309.2 


4088.4 


I 


2 


.0333 


1183.0 


3867.3 


1224.3 


3940.6 


1266.4 


4014.6 


1309.9 


4089.7 


2 


3 

4 


.0500 


1183.7 


3868.5 


1225.0 


3941.8 


1267.2 


4015.9 


1310.6 


4091.0 


3 


.0667 


1184.4 


3869^7 


1225.7 


3943.0 


1267.9 


4017. 1 


1311.3 


4092.2 


4 


K 


.0833 


1185.1 


3870.9 


1226.4 


3944.2 


1268.6 


4018.4 


1312.1 


4093.5 


S 


6 


.1000 


ii85^7 


3872.2 


1227. 1 


3945.5 


1269.3 


4019.6 


1312.8 


4094.7 


6 


7 


.1167 


1186.4 


3873-4 


1227.8 


3946.7 


1270.1 


4020.8 


1313.5 


4096.0 


7 


8 


.1333 


1187.1 


3874^6 


1228. 5 


3947.9 


1270.8 


4022.1 


1314.2 


4097.2 
4098.S 


8 


9 


.1500 


1187.8 


3875.8 


1229.2 


3949.2 


1271.5 


4023.4 


1315.0 


9 


10 


.1667 


1188.5 


3877-0 


1229.9 


3950.4 


1272.2 


4024.6 


1315.7 


4099.8 


10 


II 


.1833 


1189.2 


3878.2 


1230.6 


3951.6 


1272.9 


4025.8 


1316.5 


4101.1 


" 


12 


.2000 


1189.8 


3879-S 


1231.3 


3952.9 


1273.6 


4027.1 


1317.2 


4102.3 


12 


13 


.2167 


1190.5 


3880.7 


1232.0 


3954.1 


1274.4 


4028.4 


1317.9 


4103.6 
4104.8 


13 


14 


.2333 


1191.2 


3881.9 


1232.7 


3955.3 


1275.1 


4029.6 


1318.6 


14 


15 


.2500 


1191.9 


3883.1 


1233.4 


3956.6 


1275.8 


4030.8 


1319.4 


4106.1 


15 


16 


.2667 


1192.6 


3884.3 


1234.1 


3957-8 


1276.5 


4032.1 


1320.1 


4107.3 
4108.6 
4109.8 


16 


17 


.2833 


ii93^3 


3885.6 


1234.8 


3959.0 


1277.3 


4033.4 


1320.8 


H 


18 


.3000 


ii93^9 


3886.8 


1235.5 


3960.2 


1278.0 


4034.6 


1321.5 


18 


19 


.3167 1 


1194.6 


3888.0 


1236.2 


3961.5 


1278.7 


4035.9 


1322.3 


4111.1 


19 


20 


•3333 ' 


ii9S^3 


3889.2 


1236.9 


3962.7 


1279.4 


4037.1 


1323.0 


4112.4. 


20 


21 


•3500 


1196.0 


3890.4 


1237.6 


3964-0 


1280.1 


4038.4 


1323.7 


4113.7 


21 


22 


.3667 ! 


1196.7 


3891.6 


1238.3 


3965-2 


1280.8 


4039.6 


1324.4 


41 14.9 
4116.2 


22 


23 


.3833 1 


1197.4 


3892.9 


1239.0 


3966.4 


1281.6 


4040.9 


1325.2 


23 


24 


.4000 : 


II 98.0 


3894.1 


1239.7 


3967-6 


1282.3 


4042.1 


1325.9 


4117.4 


24 


25 


.4167 1 


1198.7 


3895.3 


1240.4 


3968.9 


1283.0 


4043.4 


1326.7 


4118.7 


'I 


26 


•4333 


1199.4 


3896.5 


1241. 1 


3970.1 


1283.7 


4044.6 


1327.4 


4119.9 


26 


27 


•4500 


1 200.1 


3897.7 


1241.8 


3971.3 


1284.5 


4045.9 


1328.2 


4121.2 


^l 


28 


.4667 ; 


1200.8 


3898.9 


1242.5 


3972.5 


1285.2 


4047.1 


1228.9 


4122.4 


28 


29 


.4833 


1201.S 


3900.2 


1243.2 


3973.8 


1285.9 


4048.4 


1329.7 


4123.7 


29 


30 


.5000 


1202. 1 


3901.4 


1243.9 


3975.0 


1286.6 


4049.6 


1330.4 


4125.0 
4126.3 


30 


31 


.5167 1 


1202.8 


3902.6 


1244.6 


3976.3 


1287.3 


4050.9 


1331.1 
1331.8 


31 


32 


.5333 


1203.S 


3903.8 


1245.3 


3977.5 


1288.0 


4052.1 


4127.S 
4128.7 


32 


33 


•5500 


1204.2 


3905.0 


1246.0 


3978.8 


1288.8 


4053.4 


1332.6 


33 


34 


.5667 


1204.9 


3906.3 


1246.7 


3980.0 


1289.5 


4054.6 


1333-3 


4x30.0 


34 


35 


.5833 


1205.6 


3907.5 


1247.4 


3981.2 


1290.2 


4055.9 


1334-1 
1334.8 


4131.5 
4132.6 


^1 


36 


.6000 


1206.2 


3908.7 


1248. 1 


3982.4 


1290.9 


4057-1 


36 


37 


.6167 


1206.9 


3909.9 


1248.8 


3983.7 


1291.7 


4058.4 


1335.6 


4133.9 


H 


38 


•6333 


1207.6 


3911.2 


1249.5 


3984.9 


1292.4 


4059.6 


1336.3 


4135. 1 
4136.4 


38 


39 


.6500 


1208.3 


3912.4 


1250.2 


3986.1 


1293.1 


4060.9 


1337.1 


39 


40 


.6667 


1209.0 


3913.6 


1250.9 


3987.4 


1293.8 


4062.1 


1337.8 


4137.7 


40 


41 


.6833 


1209.7 


3914.9 


1251.6 


3988.7 


1294.6 


4063.4 


1338.5 


4139.0 


41 


42 


.7000 


1210.3 


3916.1 


1252.3 


3989.9 


1295.3 


4064.6 


1339.2 


4140.2 


42 


43 


.7167 


1211.0 


3917.3 


1253.0 


3991. 1 


1296.0 


4065.9 


1340.0 


4141.S 


43 


44 


.7333 


1211.7 


3918.5 


1253.7 


3992.3 


1296.7 


4067.1 


1340.7 


4142.7 


44 


45 


.7500 


1212.4 


3919.8 


1254.4 


3993.6 


1297.5 


4068.4 


1341.5 


4144.0 


ti 


46 


.7667 


1213.1 


3921.0 


1255.1 


3994.8 


1298.2 


4069.6 


1342.2 


4145.3 
4146.6 
4147.8 


47 


•7833 


1213.8 


3922.2 


1255.8 


3996.0 


1298.9 


4070.9 


1343.0 


:i 


48 


.8000 


1214.S 


3923.4 


1256.5 


3997.3 


1299.6 


4072.1 


1343.7 


49 


.8167 


1215.2 


3924.7 


I257«2 


3998.6 


1300.4 


4073.4 


1344-S 


4149.1 


49 


SO 


.8333 


I2I5^9 


3925.9 


1257.9 


3999.8 


1301.1 


4074.6 


1345-2 
1346.0 


4150.4 


50 


SI 


.8500 


1216.6 


2927.1 


1258.6 


4001.0 


1301.9 


4075.9 


4151.7 


SI 


52 


.8667 


1217.3 


3928.3 


1259.3 


4002.2 


1302.6 


4077.1 


1346.7 


4152.9 


S2 


S3 


.8833 


1218.0 


3929.6 


1260.0 


4003.4 


1303.3 


4078.4 


1347.5 


4154.2 


53 


54 


.9000 


1218.7 


3930.8 


1260.7 


4004.7 


1304.0 


4079-6 


1348.2 


4155.4 


54 


55 
56 
57 


.9167 
.9333 

c^oo 


1219.4 
1220.1 


3932.0 
3933.2 


I26I.4 
1262. 1 


4006.0 
4007.2 


1304.8 
1305.5 


4080.9 
4082.1 


1349.0 
1349.7 


4156.7 
4158.0 


55 
56 


1220.8 


3934.4 


1262.8 


4008.5 


1306.2 


4083.4 


1350.S 


4159.3 
4160.5 
4161.8 


11 

59 


58 
S9 


.9667 
.9833 


1221.5 
1222.2 


3935.7 
3936.9 


1263.5 
1264.3 


4009.7 
4010.9 


1306.9 
1307.7 


4084.6 
4085.9 


1351.2 
I3S2.0 



FUNCTIONS OF ONE-DEGREE CURVE 



367 



Use 100' Chords up to 8° Curves 
Use so' Chords up to 16° Curves 



Use 25' Chords up to 32" Curves 
Use 10' Chords above 32° Curves 



s 

a 




72° 


73° 


74° 


75° 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


1352.7 


4163-1 


1398.1 


4240.0 


1444.7 


4317-8 


1492.5 


4396.7 





I 


.0167 


1353-5 


4164.4 


1398.9 


4241.3 


1445.5 


4319-2 


1493-3 


4398.1 


I 


2 


•0333 


1354-2 


4165-6 


1399.6 


4242.6 


1446.2 


4320.5 


1494-1 


4399-4 


2 


3 


.0500 


1355-0 


4166.9 


1400.4 


4243.9 


1447-0 


'4321.8 


1494-9 


4400.8 


3 


4 


.0667 


1355-7 


4168.2 


1401.2 


4245.1 


1447.8 


4323-1 


1495-7 


4402.1 


4 


S 


.0833 


1356.S 


4169.5 


1402.0 


4246.4 


1448.6 


4324-4 


1496.5 


4403.4 


5 


6 


.1000 


1357-2 


4170.7 


1402.7 


4247.7 


1449.4 


4325-7 


1497-3 


4404-7 


6 


7 


.1167 


1358.0 


4172.0 


1403-5 


4249-0 


1450.2 


4327-0 


1498.2 


4406.1 


7 


8 


.1333 


1358.7 


4173-3 


1404.2 


4250.3 


1451.0 


4328.3 


1499.0 


4407-4 


8 


9 


.1500 


1359^5 


4174.5 


1405.0 


4251.6 


1451.8 


4329-6 


1499-8 


4408.7 


9 


10 


.1667 


1360.2 


4175-8 


1405.8 


4252.9 


1452.6 


4330.9 


1500.6 


4410.0 


10 


II 


•1833 


1361.0 


4177.1 


1406.6 


4254-2 


1453.4 


4332.3 


1501.4 


4411-4 


II 


12 


.2000 


1361.7 


4178.4 


1407.3 


4255.5 


1454.1 


4333-6 


1502.2 


4412.7 


12 


13 


.2167 


1362.S 


4179.7 


1408.1 


4256.8 


1454.9 


4334-9 


1503.0 


4414.0 


!i3 


14 


.2333 


1363-2 


4181.0 


1408.8 


4258.1 


1455.7 


4336.2 


1503-8 


4415-3 


14 


15 


.2500 


1364-0 


4182.3 


1409.6 


4259.4 


1456.5 


4337-5 


1504-6 


4416.6 


15 


16 


.2667 


1364.7 


4183.5 


1410.4 


4260.7 


1457.3 


4338.8 


1505-4 


4418.0 


16 


17 


.2833 


1365.5 


4184.8 


1411.2 


4262.0 


1458.1 


4340.1 


1506.2 


4419.4 


17 


18 


.3000 


1366.2 


4186.1 


1411.9 


4263.2 


1458.9 


4341-4 


1507-0 


4420.7 


'18 


19 


.3167 


1367.0 


4187.4 


1412.7 


4264.5 


1459.7 


4342.7 


1507.9 


4422.0 


J19 


20 


.3333 


1367-7 


4188.6 


1413-5 


4265.8 


1460.5 


4344-0 


1508.7 


4423-3 


I20 


21 


.3500 


1368.S 


4189.9 


1414-3 


4267.1 


1461.3 


4345-4 


1509-5 


4424-6 


21 


22 


.3667 


1369-2 


4191.2 


1415-1 


4268.4 


1462.0 


4346.7 


1510.3 


4426.0 


22 


23 


.3833 


1370.0 


4192.5 


1415-9 


4269.7 


1462.8 


4348.0 


1511.2 


4427.3 


23 


24 


.4000 


1370.7 


4193-7 


1416.6 


4271.0 


1463-6 


4349-3 


1512.0 


4428.6 


24 


25 


.4167 


1371.5 


4195-0 


14174 


4272.3 


1464.4 


4350.6 


1512.8 


4430.0 


25 


26 


•4333 


1372.2 


4196.3 


1418.2 


4273.6 


1465.2 


4351-9 


1513-6 


4431-3 


26 


27 


.4500 


1373-0 


4197.6 


1419.0 


4274.9 


1466.0 


4353-2 


1514.S 


4432.7 


27 


28 


.4667 


1373-7 


4198.8 


1419.7 


4276.2 


1466.8 


4354-5 


1515-3 


4434.0 


28 


29 


.4833 


1374.5 


4200.1 


1420.5 


4277.5 


1467.6 


4355-8 


1516.1 


4435-3 


29 


30 


.5000 


1375.2 


4201.4 


1421.3 


4278.8 


1468.4 


4357-1 


1516.9 


4436.6 


30 


31 


•5167 


1376.0 


4202.7 


1422. 1 


4280.1 


1469.2 


4358.5 


1517.7 


4438.0 


31 


32 


•5333 


1376.7 


4204.0 


1422.9 


4281.4 


1469.9 


4359-8 


1518.5 


4439.3 


32 


33 


.5500 


1377.5 


4205.3 


1423-7 


4282.7 


1470.7 


4361.1 


1519-4 


4440.7 


33 


34 


.5667 


1378.2 


4206.5 


1424.4 


4284.0 


1471-5 


4362.4 


1520.2 


4442.0 


34 


35 


•5833 


1379-0 


4207.8 


1425.2 


4285.3 


1472.3 


4363-8 


1521.0 


4443.3 


35 


36 


.6000 


1379.7 


4209.1 


1426.0 


4286.6 


1473-1 


4365-1 


1521.8 


4444.6 


36 


37 


.6167 


1380.S 


4210.4 


1426.8 


4287.9 


1473-9 


4366.4 


1522.7 


4446.0 


37 


38 


.6333 


1381.2 


4211.7 


1427-5 


4289.2 


1474-7 


4367-7 


1523-5 


4447.3 


38 


39 


.6500 


1382.0 


4213.0 


1428.3 


4290.5 


1475-6 


4369-0 


1524-3 


4448.7 


39 


40 


.6667 


1382.8 


4214.3 


1429.1 


4291.8 


1476.4 


4370.3 


1525-1 


4450.0 


40 


41 


•6833 


1383-6 


4215.6 


1429.9 


4293-1 


1477.2 


4371-7 


1525-9 


4451.4 


41 


42 


.7000 


1384-3 


4216.8 


1430.7 


4294.4 


1478.0 


4373-0 


1526.7 


4452.7 


42 


43 


.7167 


1385-I 


4218.1 


1431.5 


4295.7 


1478.8 


4374-3 


1527-6 


4454.0 


43 


44 


.7333 


1385-8 


4219.4 


1432.2 


4297.0 


1479-6 


4375-6 


1528.4 


4455-3 


44 


45 


•7500 


1386.6 


4220.7 


1433.0 


4298.3 


1480.4 


4377-0 


1529-2 


4456.7 


45 


46 


.7667 


1387.4 


4222.0 


1433.8 


4299.6 


1481.2 


4378.3 


1530.0 


4458.0 


46 


47 


•7833 


1388.2 


4223.3 


1434-6 


4300.9 


1482.0 


4379-6 


1530.9 


4459-4 


47 


48 


.8000 


1388.9 


4224.5 


1435-3 


4302.2 


1482.8 


4380.9 


1531.7 


4460.7 


48 


49 


.8167 


1389-7 


4225.8 


1436.1 


4303.5 


1483-6 


4382.2 


1532.5 


4462.1 


49 


SO 


.8333 


1390.4 


4227.1 


1436.9 


4304.8 


1484-4 


4383-5 


1533-3 


4463.4 


50 


SI 


.8500 


1391-2 


4228.4 


1437.7 


4306.1 


1485-2 


4384-9 


1534-1 


4464-7 


51 


52 


.8667 


1392.0 


4229.7 


1438.5 


4307-4 


1486.0 


4386.2 


1534-9 


4466.0 


52 


S3 


.8833 


1392.8 


4231.0 


1439.3 


4308.7 


1486.9 


4387.5 


1535-8 


4467-4 


53 


54 


.9000 


1393-5 


4232.3 


1440.0 


4310.0 


1487-7 


4388.8 


1536.6 


4468.7 


54 


55 


.9167 


1394-3 


4233.6 


1440.8 


4311-3 


1488.5 


4390.2 


1537.4 


4470.1 


55 


56 


.9333 


1395.0 


4234.8 


1441.6 


4312.6 


1489-3 


4391-5 


1538.2 


4471.4 


56 


57 


.9500 


1395-8 


4236.1 


1442.4 


4313-9 


1490.1 


4392.8 


1539-1 


4472.7 


57 


S8 


.9667 


1396.6 


4237.4 


1443.1 


4315-2 


1490.9 


4394-1 


1539-9 


4474-1 


58 


59 


.9833 


1397.4 


4238.7 


1443.9 


4316.5 


1491-7 


4395.4 


1540.7 


4475-4 


59 



368 



THE SURVEY 





Use 100' Chords up to 8 


° Curves 


Use 


25' Chords up to 


32° Curves 




Use 50 


Chords up to 16 


° Curves Use 


10' Chords above 32" Curves 


1 




76" 


77° 


78° 


79° 


i 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


IS4I.S 


4476.7 


1591.7 


4557.8 


1643.1 


4640.0 


1696.0 


4723.4 


I 


.0167 


1542.4 


4478.1 


1592.6 


4559.2 


1644.0 


4641.4 


1696.9 


4724-8 


I 


2 


•0333 


1543.2 


4479.4 


1593.4 


4560.5 


1644.8 


4642.8 


1697.7 


4726.2 


2 


3 


.0500 


1544.1 


4480.8 


1594.3 


4561.9 


1645.7 


4644.2 


1698.6 


4727.6 


3 


4 


.0667 


1544.9 


4482.1 


1595.1 


4563.3 


1646.6 


4645.6 


1699.5 


4729.0 


"4 


5 


.0833 


1545.7 


4483.S 


1596.0 


4564-7 


1647.5 


4647.0 


1700.4 


4730.4 


5 


6 


.1000 


1546.5 


4484.8 


1596.8 


4566.0 


1648.3 


4648.3 


1701.3 


4731.8 


6 


7 


.1167 


1547-4 


4486.2 


1597.7 


4567.4 


1649.2 


4649-7 


1702.2 


4733-3 


7 


8 


• 1333 


1548.2 


4487.5 


1598.5 


4568.7 


1650.1 


4651. 1 


1703.1 


4734-7 


8 


9 


.1500 


1549.1 


4488.9 


1599-4 


4570.1 


1651.0 


4652.5 


1704.0 


4736.1 


9 


10 


.1667 


1549.9 


4490.2 


1600.2 


4571.S 


1651.8 


4653.9 


1704.9 


4737.5 


10 


II 


.1833 


1550.7 


4491.6 


1601.1 


4572.9 


1652.7 


4655-3 


170S-8 


4738.9 


II 


12 


.2000 


1551.5 


4492.9 


1601.9 


4574-2 


1653-6 


4656.7 


1706.6 


4740.3 


12 


13 


.2167 


1552.4 


4494.3 


1602.8 


4575-6 


1654-S 


4658.1 


1707.S 


4741.7 


13 


14 


.2333 


1553.2 


4495.6 


1603.6 


4576.9 


1655-3 


4659.4 


1708.4 


4743.1 


14 


IS 


.2500 


1554.1 


4497.0 


1604.5 


4578.3 


1656.2 


4660.8 


1709.3 


4744-5 


IS 


16 


.2667 


1554-9 


4498.3 


1605.3 


4579.7 


1657.1 


4662.2 


1710.2 


4745.9 


16 


17 


.2833 


1555-7 


4499.7 


1606.2 


4581.1 


1658.0 


4663.6 


1711.1 


4747.3 


17 


18 


.3000 


1556.5 


4501.0 


1607.0 


4582.4 


1658.8 


4665.0 


1712.0 


4748.7 


18 


19 


.3167 


1557.4 


4502.4 


1607.9 


4583.8 


1659.7 


4666.4 


1712.9 


4750.1 


19 


20 


.3333 


1558.2 


4503.7 


1608.7 


4585.1 


1660.6 


4667.7 


1713-8 


4751.S 


20 


21 


.3500 


1559.1 


4505.0 


1609.6 


4586.5 


1661.5 


4669.1 


1714.7 


4752.9 


21 


22 


.3667 


1559-9 


4506.3 


1610.4 


4587.9 


1662.3 


4670.5 


1715-6 


4754-3 


22 


23 


.3833 


1560.7 


4507.7 


1611.3 


4589.3 


1663.2 


4671.9 


1716.5 


4755-7 


23 


24 


.4000 


1561.5 


4509.0 


1612.1 


4590.6 


1 664. 1 


4673.3 


1717.4 


4757.1 


24 


25 


.4167 


1562.4 


4510.4 


1613.0 


4592.0 


1665.0 


4674.7 


1718.3 


4758.6 


25 


26 


.4333 


1563.2 


4511.7 


1613.8 


4593.3 


1665.8 


4676.0 


1719-2 


4760.0 


26 


27 


.4500 


1564.I 


4513.1 


1614.7 


4594.7 


1666.7 


4677-4 


1720.1 


4761.4 


27 


28 


.4667 


1564.9 


4514.4 


1615.5 


4596.0 


1667.6 


4678.8 


1721.0 


4762.8 


28 


29 


.4833 


1565.7 


4515.8 


1616.4 


4597.4 


1668.5 


4680.2 


1721.9 


4764.2 


29 


30 


.5000 


1566.5 


4517.1 


1617.3 


4598.8 


1669.3 


4681.6 


1722.8 


4765.6 


30 


31 


.S167 


1567.4 


4518.5 


1618.2 


4600.2 


1670.2 


4683.0 


1723-7 


4767.0 


31 


32 


.S333 


1568.2 


4519.8 


1619.0 


4601.5 


1671.1 


4684.4 


1724.6 


4768.4 


32 


33 


•SSOO 


1569.1 


4521. 1 


1619.9 


4602.9 


1672.0 


4685.8 


1725-S 


4769.8 


33 


34 


.5667 


1569.9 


4522.5 


1620.7 


4604.3 


1672.8 


4687.2 


1726.4 


4771.2 


34 


35 


.S833 


1570.7 


4523.9 


1621.6 


4605.7 


1673-7 


4688.6 


1727.3 


4772.7 


35 


36 


.6000 


1571.5 


4525.3 


1622.4 


4607.0 


1674.6 


4689.9 


1728.2 


4774.1 


36 


37 


.6167 


1572.4 


4526.7 


1623.3 


4608.4 


1675-S 


4691.3 


1729.1 


4775-5 


37 


38 


.6333 


1573.2 


4528.0 


1624.1 


4609.8 


1676.3 


4692.7 


1730.0 


4776.9 


38 


39 


.6500 


1574.0 


4529.4 


1625.0 


4611.2 


1677.3 


4694.1 


1731.0 


4778.3 


39 


40 


.6667 


.1574.8 


4530.7 


1625.9 


4612.5 


1678.2 


4695.5 


1731.9 


4779.7 


40 


41 


.6833 


1575.6 


4532.1 


1626.8 


4613.9 


1679.1 


4696.9 


1732.8 


4781.1 


41 


42 


.7000 


1576.4 


4533.4 


1627.6 


4615.3 


1679-9 


4698.3 


1733.7 


4782.6 


42 


43 


.7167 


1577.3 


4534.8 


1628.5 


4616.7 


1680.8 


4699.7 


1734-6 


4784.0 


43 


44 


.7333 


1578.I 


4536.1 


1629.3 


4618.0 


1681.7 


4701.1 


1735-S 


4785.4 


44 


4| 


.7500 


1579.0 


4537.5 


1630.2 


4619.4 


1682.6 


4702.5 


1736.4 


4786.8 


45 


46 


.7667 


1579-8 


4538.8 


1631.0 


4620.8 


1683.S 


4703.9 


1737.3 


4788.2 


46 


47 


.7833 


1580.7 


4540.2 


1631.9 


4622.2 


1684.4 


4705.3 


1738.2 


4789.6 


47 


48 


.8000 


1581.5 


4541.5 


1632.7 


4623.5 


1685.3 


4706.7 


1739.1 


4791.0 


48 


49 


.8167 


1582.4 


4542.9 


1633.6 


4624.9 


1686.2 


4708.1 


1740.0 


4792.S 


49 


SO 


.8333 


1583.2 


4544.2 


1634.5 


4626.3 


1687.1 


4709.5 


1740.9 


4793.9 


SO 


SI 


.8500 


1584.1 


4545.6 


1635.4 


4627.7 


1688.0 


4710.9 


1741-8 


4795.3 


SI 


S2 


.8667 


1584.9 


4S47.0 


1636.2 


4629.0 


1688.8 


4712.2 


1742.7 


4796.7 


52 


S3 


.8833 


1585.8 


4548.4 


1637.1 


4630.4 


1689.7 


4713-6 


1743-6 


4798.1 


53 


S4 


.9000 


1586.6 


4549.7 


1637.9 


4631-8 


1690.6 


471S-0 


1744.S 


4799.S 


S4 


H 


.9167 


1587.S 


4551.1 


1638.8 


4633.2 


1691.5 


4716.4 


1745.4 


4801.0 


55 


56 


.9333 


1588.3 


4552.4 


1639.6 


4634.5 


1692.4 


4717.8 


1746.3 


4802.4 


56 


H 


.9500 


1589.2 


4553.8 


1640.5 


4635.9 


1693.3 


4719.2 


1747.2 


4803.8 


57 


S8 


.9667 


1590.0 


4555. 1 


1641.3 


4637.3 


1694.2 


4720.6 


1 748.1 


4805.2 


58 


59 


.9833 


1590.9 


4556.5 


1642.2 


4638.7 


1695.1 


4722.0 


1749.1 


4806.6 


59 



ITTNCTIONS OF ONE-DEGREE CURVE 

Use loo' Chords up to 8° Curves Use 25' Chords up to 32° Curves 
Use 50' Chords up to 16° Curves Use 10' Chords above 32° Curves 



369 



1 

d 

3 




80" 


81° 


82° 


83- 


1 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


1750.0 


4808.0 


1805.5 


4893.9 


1862.3 


4981.0 


1920.6 


5069.4 





I 


.0167 


1750.9 


4809.5 


1806.4 


4895.4 


1863.3 


4982.5 


1921.6 


5070.9 


I 


2 


•0333 


1751.8 


4810.9 


1807.3 


4896.8 


1864.2 


,4983.9 


1922.6 


5072.4 


2 


3 


.0500 


1752.8 


4812.3 


1808.3 


4898.3 


1865.2 


4985.4 


1923.6 


5073.9 


3 


4 


.0667 


1753-7 


4813.7 


1809.2 


4899.7 


I866.I 


4986.8 


1924.6 


5075.4 


4 


5 


•0833 


1754.6 


4815.2 


1810.2 


4901.2 


I867.I 


4988.3 


1925.6 


5076.9 


5 


6 


.1000 


1755.5 


4816.6 


1811.1 


4902.6 


I868.I 


4989.8 


1926.5 


5078.4 


6 


7 


.1167 


1756.5 


4818.0 


1812.1 


4904.0 


I869.I 


4991.3 


1927.5 


5079.9 


7 


8 


•1333 


1757.4 


4819.4 


1813.0 


4905.4 


1870.0 


4992.7 


1928.S 


5081.4 


8 


9 


.1500 


1758.3 


4820.9 


1814.0 


4906.9 


I87I.O 


4994.2 


1929.S 


5082.9 


9 


10 


.1667 


1759.2 


4822.3 


1814.9 


4908.3 


I87I.9 


4995.7 


1930.5 


5084.4 


10 


II 


.1833 


1760.1 


4823.7 


1815.9 


4909.8 


1872.9 


4997.2 


1931.5 


5085.9 


II 


12 


.2000 


1761.0 


4825.1 


1816.8 


4911.2 


1873.9 


4998.6 


1932.4 


5087.3 


12 


13 


.2167 


1762.0 


4826.6 


1817.7 


4912.7 


1874.9 


5000.1 


1933.4 


5088.8 


13 


14 


.2333 


1762.9 


4828.0 


1818.6 


4914.1 


1875.8 


5001.5 


1934.4 


5090.3 


14 


15 


.2500 


1763.8 


4829.4 


1819.6 


4915.5 


1876.8 


5003.0 


1935.4 


509 1. 8 


15 


16 


.2667 


1764.7 


4830.8 


1820.5 


4917.0 


1877.7 


5004.5 


1936.4 


5093.3 


16 


17 


.2833 


1765.7 


4832.3 


1821.5 


4918.5 


1878.7 


5006.0 


1937.4 


5094.8 


17 


18 


.3000 


1766.6 


4833.7 


1822.4 


4919.9 


1879.7 


5007.4 


1938.4 


5096.3 


18 


19 


.3167 


1767^5 


4835.1 


1823.3 


4921.4 


1880.7 


5008.9 


1939.4 


S097.8 


19 


20 


•3333 


1768.4 


4836.5 


1824.2 


4922.8 


I88I.6 


5010.3 


1940.4 


5099-3 


20 


21 


•3500 


1769.3 


4838.0 


1825.2 


4924.3 


1882.6 


5011.8 


1941.4 


5100.8 


21 


22 


.3667 


1770.2 


4839.4 


1826.1 


4925.7 


1883.5 


5013.3 


: 1942.4 


5102.3 


22 


23 


.3833 


i77i^2 


4840.8 


1827.1 


4927.2 


1884.5 


5014.8 


1943.4 


5103.8 


23 


24 


.4000 


1772.1 


4842.2 


1828.0 


4928.6 


1885.5 


5016.2 


1944-4 


5105.2 


24 


25 


.4167 


1773.0 


4843.7 


1829.0 


4930.1 


1886.5 


5017.7 


1945.4 


5106.7 


25 


26 


.4333 


1773.9 


4845.1 


1829.9 


4931.5 


1887.4 


5019.2 


1946.4 


5108.2 


26 


27 


.4500 


1774-9 


4846.5 


1830.9 


4933 -o 


1888.4 


5020.7 


1947.4 


5109-7 


27 


28 


.4667 


1775.8 


48479 


1831.8 


4934.4 


1889.3 


5022.1 


1948.4 


5111.2 


28 


29 


.4833 


1776.7 


4849.4 


1832.8 


4935-8 


1890.3 


5023.6 


1949.4 


5112.7 


29 


30 


.5000 


1777.6 


4850.8 


1833.7 


4937.2 


I89I.3 


5025.0 


1950.4 


5114-2 


30 


31 


.5167 


1778.5 


4852.3 


1834.7 


4938.7 


1892.3 


5026.5 


1951.4 


5115.7 


31 


32 


.5333 


1779-4 


4853-7 


1835.6 


4940.2 


1893.2 


5028.0 


1952.4 


5117.2 


32 


33 


.5500 


1780.4 


4855.1 


1836.6 


4941.7 


1894.2 


5029.5 


1953.4 


5118.7 


33 


34 


.5667 


1781.3 


4856.S 


1837.5 


4943-1 


I895.I 


5031.0 


1954.4 


5120.2 


34 


35 


.5833 


1782.2 


4858.0 


1838.5 


4944.6 


I896.I 


5032.S 


1955.4 


5121.7 


35 


36 


.6000 


1783.1 


4859.4 


1839.4 


4946.0 


I897.I 


5033.9 


1956.4 


5123.2 


36 


37 


.6167 


1 784.1 


4860.9 


1840.4 


4947.5 


I898.I 


5035.4 


1957-4 


5124.7 


37 


38 


.6333 


1785.0 


4862.3 


1841.3 


4948.9 


1899.0 


5036.9 


1958.4 


5126.2 


38 


39 


.6500 


1785.9 


4863.7 


1842.3 


4950.4 


1900.0 


5038.4 


1959.4 


S127.7 


39 


40 


.6667 


1786.8 


4865.1 


1843.2 


4951.8 


1 901.0 


S039.8 


1960.4 


5129-2 


40 


41 


.6833 


'7?7-7 


4866.6 


1844.2 


4953.3 


1902.0 


5041.3 


1961.4 


5130.7 


41 


42 


.7000 


1788.6 


4868.0 


1845-1 


4954.7 


1902.9 


5042.8 


1962.4 


5132.2 


42 


43 


.7167 


1789.6 


4869.5 


1846.1 


4956.2 


1903.9 


5044.3 


1963.4 


5133.7 


43 


44 


.7333 


1790.5 


4870.9 


1847.0 


4957.6 


1904.9 


S045.8 


1964-4 


5135.2 


44 


45 


.7500 


1791.5 


4872.4 


1848.0 


4959.1 


1905.9 


S047.3 


1965.4 


S136.7 


45 


46 


.7667 


1792.4 


4873.8 


1848.9 


4960.6 


1906.9 


5048.7 


1966.4 


5138.2 


46 


47 


.7833 


1793-4 


4875.2 


1849.9 


4962.1 


1907.9 


5050.2 


1967.4 


5139.7 


47 


48 


.8000 


1794-3 


4876.6 


1850.8 


4963.5 


1908.8 


5051.7 


1968.4 


5141.2 


48 


49 


.8167 


1795.3 


4878.1 


1851.8 


4965.0 


1909.8 


5053-2 


1969.4 


5142.8 


49 


50 


.8333 


1796.2 


4879.5 


1852.7 


4966.4 


I9I0.8 


5054-6 


1970.4 


5144.3 


50 


51 


.8500 


1797.1 


4880.9 


1853.7 


4967.9 


I9II.8 


5056.1 


1971.4 


5145.8 


SI 


52 


.8667 


1798.0 


4882.4 


1854.6 


4969.3 


I9I2.8 


5057.6 


1972.4 


5147-3 


52 


53 


.8833 


1799.0 


4883.9 


1855.6 


4970.8 


1913 8 


5059.1 


1973-4 


5148.8 


53 


54 


.9000 


1709.9 


4885.3 


1856.5 


4972.2 


1914.7 


5060.6 


1974^4 


5150.3 


54 


55 


.9167 


1800.9 


4886.7 


1857.S 


4973.7 


1915.7 


5062.1 


1975.4 


S151.8 


55 


S6 


•9333 


1801.8 


4888.1 


1858.4 


4975-1 


1916.7 


5063.5 


1976.4 


5153.3 


56 


57 


.9500 


1802.8 


4889.6 


1859.4 


4976.6 


1917-7 


5065.0 


1977.4 


5154.8 


57 


S8 


.9667 


1803.7 


4891.0 


1860.3 


4978.0 


1918.7 


5066.5 


1978.4 


5156.3 


58 


59 


•9833 


1804.6 


4892.5 


1861.3 


4979.5 


1919.7 


5068.0 


1979.4 


5157.8 


59 



370 



THE SURVEY 



Use loo' Chords up to 8" Curves 
Use so' Chords up to i6° Curves 



Use 25' Chords up to 32" Curves 
Use 10' Chords above 32" Curves 



s 

d 

3 




84'* 


85° 


86*' 


87° 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


1980.5 


5159.3 


2041.8 


5250.6 


2104.8 


5343.3 


2169.S 


5437.5 





I 


.0167 


1981.5 


5160.8 


2042.9 


5252.1 


2105.9 


5344.9 


2170.6 


5439.1 


I 


2 


•0333 


1982.5 


5162.3 


2043.9 


5253.6 


2106.9 


5346.4 


2171.6 


5440.7 


2 


3 


.0500 


1983-5 


5163.8 


2045.0 


5255.2 


2108.0 


5348.0 


2172.7 


5442.3 


3 


4 


.0667 


1984-5 


5165.3 


2046.0 


5256.7 


2109.1 


5349.5 


2173.8 


5443.9 


4 


5 


.0833 


1985-6 


5166.9 


2047.0 


5258.3 


2110.1 


5351.1 


2174.9 


5445.5 


5 


6 


.1000 


1986.6 


5168.4 ii 2048.0 


5259.8 1 2111.2 


5352.7 


2176.0 


5447.1 


6 


7 


.1167 


1987.6 


5169.9 ij 2049.1 


5261.4 1 2112.3 


5354.3 


2177.1 


5448.7 


7 


8 


•1333 


1 1988.6 


5171.4I! 2050.1 


5262.9 2113.4 


5355.8 


2178.2 


5450.3 


8 


9 


.1500 


1989.6 


5172.911 2051.2 


5264.5 11 2114.5 


5357.4 


2179.3 


5451.9 


9 


10 


.1667 


1990.6 


5174.4! 2052.2 


5266.0 '! 2115.5 


5358.9 


2180.4 


5453-4 


10 


II 


•1833 


1991-7 


5175.9 2053.2 


5267.5 J! 2116.6 


5360.5 


2181.5 


5455.0 


II 


12 


.2000 


1992.7 


5177.5 


! 2054.2 


5269.0 ll 2II7.6 


5362.0 


2182.5 


5456.6 


12 


13 


.2167 I 1993-7 


5179.0 


i 2055.3 


5270.6 


J 2118.7 


5363.6 


2183.6 


5458.2 


13 


14 


.2333 1994-7 
.2500 , 1995-7 


5180.5 


: 2056.3 


5272.1 


2119.8 


5365.2 


2184.7 


5459-8 


14 


IS 


5182.0 


2057.4 


5273.7 


2120.9 


5366.8 


2185.8 


5461.4 


15 


16 


.2667 : 1996.7 


5183.5 


2058.4 


5275.2 


2121.9 


5368.3 


2186.9 


5463-0 


16 


17 


.2833 ' 1997-8 


5185.0 


: 2059.5 


5276.8 •': 2123.0 


5369.9 


2188.0 


5464-6 


17 


18 


.3000 1 1998.8 


5186.6 


2060.5 


5278.3 1 2124.I 


5371.4 


2189. 1 


5466.2 


18 


19 


.3167 


1999.8 


5188.0 


2061.6 


5279.9 1 2125.2 


5373.0 


2190.2 


5467.8 


19 


20 


.3333 


2000.8 


5189.6 


i 2062.6 


5281.4 


2126.2 


5374.6 


2191.3 


5469.4 


20 


21 


.3500 


' 2001.8 


5191.0 


2063.7 


5282.9 


2127.3 


5376.2 


2192.4 


5471.0 


21 


22 


•3667 


1 2002.8 


5192.6 


, 2064.7 


5284.4 


2128.3 


5377.7 


2193.5 


5472.5 


22 


23 


.3833 


2003.9 


5194.0 


j 2065.8 


5286.0 


2129.4 


5379.3 


2194.6 


5474.1 


23 


24 


.4000 


2004.9 


5195.6 


i 2066.8 


5287.5 


2130.5 


5380.8 


2195.7 


5475.7 


24 


25 


.4167 


2005.9 


5197.2 


2067.9 


5289.1 


2131.6 


5382.4 


2196.8 


5477.3 


25 


26 


.4333 


2006.9 


5198.7 


1 2068.9 


5290.6 


2132.6 


5383.9 


2197.9 


5478.9 


26 


27 


.4500 


: 2007.9 


5200.2 


j 2070.0 


5292.2 


2133.7 


5385.5 


2199.0 


5480.5 


^1 


28 


.4667 


2008.9 


5201.7 


2071.0 


5293.7 


2134.8 


5387.1 


2200.1 


5482.1 


28 


29 


.4833 


2010.0 


5203.2 


2072.1 


5295.2 


2135.9 


5388.7 


2201.2 


5483.7 


29 


30 


.5000 


2011.0 


5204.7 


2073.1 


5296.7 


.2136.9 


5390.2 


2202.3 


5485.3 


30 


31 


•5167 


2012.0 


5206.3 


2074.2 


5298.3 


2138.0 


5391.8 


2203.4 


5486.9 


31 


32 


•5333 


2013.0 


5207.8 


2075-2 


5299-8 


2139.0 


5393.4 


2204.5 


5488.5 


32 


33 


.5500 


2014.0 


5209.3 


2076.3 


5301.4 


2146.1 


5395.0 


2205.6 


5490.1 


33 


34 


.5667 


20x5.0 


5210.8 


2077.3 


5302.9 


2141.2 


5396.5 


2206.8 


5491.7 


34 


35 


.5833 


2016.0 


5212.4 


2078.4 


5304.5 


2142.3 


5398.1 


2207.9 


5493.3 


35 


36 


.6000 


2017.0 


5213.9 


2079-4 


5306.1 


2143.3 


5399.7 


2209.0 


5494.9 


36 


37 


.6167 


2018.0 


5215-4 


2080.5 


5307.7 


2144.4 


5401.3 


2210.1 


5496.5 


37 


38 


•6333 


2019.1 


5216.9 


2081.5 


5309.2 


2145.5 


5402.8 


2211.2 


5498.1 


38 


39 


.6500 


2020.1 


5218.4 


2082.6 


5310.8 


2146.6 


5404.4 


2212.3 


5499.7 


39 


40 


.6667 


2021.2 


5220.0 


2083.7 


5312.3 


2147.7 


5406.0 


2213.4 


5501.3 


40 


41 


.6833 


2022.2 


5221.6 


2084.8 


5313.9 


2148.8 


5407.6 


2214.5 


5502.9 


41 


42 


.7000 


2023.2 


5223.1 


2085.8 


5315.4 


2149.8 


5409.1 


2215.6 


55<^4.5 


42 


43 


.7167 


2024.3 


5224.6 


2086.9 


5317.0 


2150.9 


5410.7 


2216.7 


5506.1 


43 


44 


.7333 


2025.3 


5226.1 


2087.9 


5318.5 


2152.0 


5412.3 


2217.8 


5507.7 


44 


45 


.7500 


2026.4 


5227.7 


2089.0 


5320.1 


2153.1 


5413.9 


2218.9 


5509.3 


45 


46 


.7667 


2027.4 


5229.2 


2090.0 


S32I.6 


2154.2 


5415.4 


2220.0 


5510.9 


46 


47 


•7833 


2028.4 


5230.7 


2091. 1 


5323.2 


2155.3 


5417.0 


2221.2 


5512.5 


47 


48 


.8000 


2029.4 


5232.2 


2092.1 


5324.7 


2156.4 


5418.6 


2222.3 


5514.1 


48 


49 


.8167 


2030.5 


5233.8 


2093.2 


5326.3 


2157.5 


5420.2 


2223.4 


5515.7 


49 


50 


.8333 


2031.5 


5235.3 


2094.2 


5327.8 


2158.6 


5421.8 


2224.5 


5517.3 


50 


SI 


.8500 


2032.6 


5236.8 


2095-3 


5329.4 


2159.7 


5423.4 


2225.6 


5518.9 


51 


52 


.8667 


2033.6 


5238.3 


2096.3 


5330.9 


2160.7 


5424-9 


2226.7 


5520.5 


52 


53 


.8833 


2034.6 


5239.9 


2097.4 


5332.5 


2161.8 


5426.5 


2227.9 


5522.1 


53 


54 


.9000 


2035.6 


5241.4 


2098.4 


5334.0 


2I62.-9 


5428.1 


2228.9 


5523.7 


54 


55 


.9167 


2036.7 


5243-0 


2099. 5 


5335.6 


2164.0 


5429.7 


2230.0 


5525.3 


55 


56 


.9333 


2037-7 


5244.5 


2100.6 


5337.1 


2I65.I 


5431.2 


2231. 1 


5526.9 


56 


57 


.9500 


2038.7 


5246.0 


2101.7 


5338.7 


2166.2 


5432.8 


2232.2 


5528.S 


57 


58 


.9667 


2039.8 


5247.5 


2102.7 


5340.2 


2167.3 


5434-4 


2233.3 


5530.1 


58 


59 


.9833 


2040.8 


5249.1 


2103.8 


5341.8 


2168.4 


5436.0 


2234.5 


5531.7 


50 



FUNCTIONS OF ONE-DEGREE CURVE 

Use loo' Chords up to 8" Curves Use 25' Chords up to 32° Curves 
Use 50' Chords up to 16° Curves Use 10' Chords above 32° Curves 



371 



i 

3 
c 

s 


Co; 


SS** 


Sg** 


90*' 


91° 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


2235.6 


5533.3 


2303.6 


5630.8 


2373.4 


S730.0 


2445.1 


5830.9 





I 


.0167 


2236.7 


5535.0 


2304.7 


5632.5 


2374-6 


5731.7 


2446.3 


5832.6 


I 


2 


.0333 


2237.8 


5536.6 


2305.6 


5634-1 


2375.8 


5733.3 


2447-5 


5834.3 


2 


3 


.0500 


2238.9 


5538.2 


2307.2 


5635.8 


2377.0 


5735.0 


2448.8 


5836.0 


3 


4 


.0667 


2240.1 


5539.8 


2308.1 


5637.4 


2378.2 


5736.7 


2450.0 


5837.7 


4 


5 


■0833 


2241.2 


5541.5 


2309.4 


5639.1 


2379.4 


5738.4 


2451.2 


5839.4 


I 


6 


.1000 


2242.3 


5543.1 


2310.5 


5640.7 


2380.5 


5740.0 


2452.4 


5841. 1 


7 


.1167 


2243.5 


5544.7 


2311.6 


5642.4 


2381.7 


5741.7 


2453.6 


5842.8 


7 
8 


8 


.1333 


2244.6 


5546.3 


2312.8 


5644.0 


2382.9 


5743.4 


2454-8 


5844.5 


9 


.1500 


2245.7 


5547.9 


2314.0 


5645.7 


2384.1 


5745.1 


2456.0 


5846.2 


9 


10 


.1667 


2246.8 


5549.5 


2315.1 


5647.3 


2385.3 


5746.7 


2457.2 


5847.9 


10 


II 


.1833 


2248.0 


5551.2 


2316.3 


5649.0 


2386.4 


5748.4 


2458.5 


5849.6 


II 


12 


.2000 


2249.1 


5552.8 


2317.4 


5650.6 


2387.6 


5750.0 


2459.7 


5851.3 


|l2 


13 


.2167 


2250.2 


5554.4 


2318.6 


5652.3 


2388.8 


5751.7 


2460.9 


5853.0 


13 


14 


•2333 


2251.3 


5556.0 


2319.7 


5653.9 


2390.0 


5753-4 


2462.1 


5854.7 


14 


15 


.2500 


2252.5 


5557.6 


2320.9 


5655.5 


2391.2 


5755.1 


2463.3 


5856.4 


15 


16 


.2667 1 2253.6 


5559.2 


2322.0 


5657-1 


2392.4 


5756.7 


2464-5 


5858.1 


16 


17 


.2833, 2254.7 


5560.9 


2323.2 


5658.8 


2393.5 


5758.4 


2465.8 


5859.8 


I17 


18 


.3000 2255.8 


5562.5 


2324.3 


5660.4 


2394-7 


5760.1 


2467.0 


5861.5 


18 


19 


.3167 2257.0 


5564.1 


2325.6 


5662.1 


2395.9 


5761.8 


2468.2 


5863.2 


19 


20 


•3333 '2258.1 


5565.7 


2326.7 


5663.7 


2397.1 


5763.4 


2469.4 


5864.9 


20 


21 


.3500 ; 2259.3 


5567.3 


2327.9 


5665.4 


2398.3 


5765.1 


2470.6 


5866.6 


21 


22 


.3667 


2260.4 


5568.9 


2329.0 


5667.0 1 


2399.5 


5766.8 


2471.9 


5868.3 


22 


23 


.3833 


2261.5 


5570.6 


2330.1 


5668.7 


2400.7 


5768.5 


2473.1 


^0^°-^ 


23 


24 


.4000 


2262.7 


5572.2 


2331.3 


5670.3 


2401.9 


5770.1 


2474.3 


5871.8 


24 


2S 


.4167 


2263.8 


5573.8 


2332.5 


5672.0 


2403.1 


5771.8 


2475.5 


5873.5 


25 


26 


.4333 \ 2264.9 


5575.4 


2333.7 


5673.6 


2404.3 


5773-5 


2476.7 


5875.2 


26 


27 


.4500 2266.0 


5577.0 


2334.8 


5675.3 


2405.5 


5775.2 


2478.0 


5876.9 


27 


28 


.4667 li 2267.2 


5578.6 


2336.0 


-5676.9 


2406.6 


5776.9 


2479.2 


5878.6 


28 


29 


.4833 11 2268.4 


5580.3 


2337.1 


5678.6 


2407.8 


5778.6 


2480.4 


5880.3 


29 


30 


.5000 !i 2269.5 


5581.9 


2338.3 


5680.2 


2409.0 


5780.2 


2481.6 


5??"-° 


30 


31 


.5167 : 2270.6 


5583.5 


2339.5 


5681.9 


2410.2 


5781.9 


2482.9 


5883.7 


31 


32 


.5333 2271.7 


5585.1 


2340.7 


5683.5 


241 1.4 


5783.6 


2484.1 


5885.4 


32 


33 


.5500^ 2272.8 


5586.8 


2341.9 


5685.2 


2412.6 


5785.3 


2485.3 


5887.2 


33 


34 


.5667 2273.9 


5588.4 


2343.0 


5686.8 


2413.8 


5787-0 


2486.5 


5888.9 


34 


35 


.5833 "2275.1 


5590.1 


2344.1 


5688.5 


2415.0 


5788.7 


2487.8 


5890.6 


35 


36 


.6000 ! 2276.2 


5591.7 


2345.3 


5690.2 


2416.2 


5790.3 


2489.0 


5892.3 


36 


37 


.6167; 2277.3 


5593.3 


2346.5 


5691.9 


2417.4 


5792.0 


2490.3 


5894-0 


37 


38 


.6333 1 2278.5 


5594.9 


2347.7 


5693.5 


2418.6 


5793.7 


2491.5 


5895-7 


38 


39 


.6500 i 2279.7 


5596.6 


2348.9 


5695.2 


2419.8 


5795.4 


2492.7 


5897.5 


39 


40 


.6667 2280.8 


5598.2 


2350.0 


5696.8 


2421.0 


5797.1 


2493.9 


5899.2 


40 


41 


.6833 j 2281.9 


5599.8 i 


2351.2 


5698.5 


2422.2 


5798.8 


2495.2 


5900.9 


41 


42 


.7000 2283.0 


5601.4 2352.3 


5700.1 


2423.4 


5800.4 


2496.4 


5902.6 


42 


43 


.7167 ' 2284.1 


5603.1 2353.5 


5701.8 


2424.6 


5802.1 


2497.7 


5904.3 


43 


44 


.7333 


2285.3 


5604.7 . 2354.7 


5703.4 


2425.8 


5803.8 


2498.9 


5906.0 


44 


45 


.7500 


2286.5 


5606.4 ll 2355.8 


5705.1 


2427.0 


5805.5 


2500.1 


5907.7 


45 


46 


.7667 


2287.6 


5608.0 ; 2357.0 


5706.8 


2428.2 


5807.2 


2501.3 


5909.4 


46 


47 


.7833' 2288.7 1 


5609.6 i 2358.1 


5708.5 


2429.4 


5808.9 


2502.6 


5911.2 ; 


47 


48 


.8000 


2289.9 


5611.2 i 2359.3 


5710.1 


2430.6 


5810.6 


2503.8 


5912.9 


48 


49 


.8167 


2291. 1 


5612.9 2360.5 


5711.8 


2431.8 


5812.3 


2505.1 


5914.6 


49 


50 


.8333 


2292.2 


5614.5 2361.7 


5713.4 


2433.0 


5814.0 


2506.3 


5916.3 


50 


51 


.8500 


2293.3 


5616.2 ; 2362.9 


5715. 1 


2434.2 


5815.7 


2507.5 


5918.1 


51 


52 


.8667 


2294.4 


5617.8 2364.0 


5716.7 


2435.4 


5817.3 


2508.7 


5919.8 


52 


53 


.8833 


2295.6 


5619.4 \\ 2365.1 


5718.4 


2436.6 


5819.0 


2510.0 


5921.5 


53 


54 


.9000 


2296.7 


5621.0 2366.3 


5720.0 


2437.9 


5820.7 


2511.2 


5923.2 


54 


55 


.9167 


2297.9 


5622.7 ! 2367.5 


5721.7 


2439.1 


5822.4 


2512.5 


5925.0 


55 


56 


•9333 


2299.0 


5624.3 || 2368.7 


5723.4 


2440.3 


5824.1 


2513.7 


5926.7 


56 


57 


.9500 


2300.2 


5625.9 2369.9 


5725.1 


2441.5 


5825.8 


2515-0 


5928.4 


57 


58 


.9667 


2301.3 


5627.5112371.0 


5726.7 


2442.7 


5827.5 


2516.2 


5930.1 


58 


59 


•9833 


2302.4 


5629.2 II 2372.2 


5728.4 


2443.9 


5829.2 


2517.5 


5931.9 


59 



372 



THE SURVEY 





Use 100' Chord* 


, UD to 8 


' Curves 


Use 


2s' Chords up to 32" Curves 




Use so' Chords up' to i6° Curves Use lo' Chords above 32° Curves 




^g 


92° 


93° 


94° 


95° 




a 





Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 







.0000 


2518.7 


5933.6 


2594.2 


6038.2 


2671.8 


6144.7 


2751.5 


6253.2 


I 


.0167 


2520.0 


5935-3 


2595-5 


6040.0 


2673.1 


6146.5 


2752.9 


6255.1 


I 


2 


•0333 


2521.2 


5937.0 


2596-8 


6041.7 


2674.4 


6148.3 


2754.2 


6256.9 


2 


3 


.0500 


2522.4 


5938.8 


2598.1 


6043.5 


2675.7 


6150.1 


2755-6 


6258.7 


3 


4 


.0667 


2523.6 


5940.5 


2599.3 


6045.2 


2677.0 


6151.9 


2756.9 


6260.5 


4 


5 


.0833 


2524.9 


5942.3 


2600.6 


6047.0 


2678.4 


6153.7 


2758.3 


6262.4 


s 


6 


.1000 


2526.1 


5944.0 


2601.9 


6048.7 


2679.7 


6155.4 


2759-6 


6264.2 


6 


7 


.1167 


2527-4 


5945-7 


2603.2 


6050.5 


2681.0 


6157.2 


2761.0 


6266.0 


7 


8 


•1333 


2528.6 


5947.4 


2604.4 


6052.2 


2682.3 


6159.0 


2762.3 


6267.8 


8 


9 


.1500 


2529.9 


5949.2 


2605.7 


6054.0 


2683.6 


6160.8 


2763.7 


6269.7 


9 


10 


.1667 


2531-1 


5950.9 


2607.0 


6055.8 


2684.9 


6162.6 


2765.0 


6271.5 


10 


II 


.1833 


2532.4 


5952.7 


2608.3 


6057.5 


2686.3 


6164.4 


2766.4 


6273.4 


II 


12 


.2000 


2533-6 


5954-4 


2609.6 


6059.3 


2687.6 


6166.2 


2767.7 


6275.2 


12 


13 


.2167 


2534-9 


5956.1 


2610.9 


6061. 1 


2688.9 


6168.0 


2769.1 


6277.0 


13 


14 


.2333 


2536.1 


5957-8 


2612. 1 


6062.8 


2690.2 


6169.8 


2770.4 


6278.8 


14 


IS 


.2500 


2537.4 


5959.6 


2613.4 


6064.6 


2691.5 


6171.6 


2771.8 


6280.7 


IS 


16 


.2667 


2538.6 


5961.3 


2614.7 


6066.4 


2692.8 


6173.4 


2773-1 


6282.5 


16 


17 


.2833 


2539-9 


S963.1 


2616.0 


6068.2 


2694.2 


6175.2 


2774-5 


6284.4 


17 


18 


.3000 


2541-1 


5964.8 


2617.3 


6069.9 


2695.6 


6177.0 


2775-8 


6286.2 


18 


19 


.3167 


2542.4 


5966.5 


2618.6 


6071.7 


2696.9 


6178.8 


2777.2 


6288.0 


19 


20 


.3333 


2543-6 


5968.2 


2619.8 


6073.4 


2698.1 


6180.6 


2778.S 


6289.8 


20 


21 


.3500 


2544.9 


5970.0 


2621. 1 


6075.2 


2699-5 


6182.4 


2779-9 


6291.7 


21 


22 


.3667 


2546-1 


5971.7 


2622.4 


6077.0 


2700.8 


6184.2 


2781.2 


6293.5 


22 


23 


.3833 


2547.4 


5973.5 


2623.7 


6078.8 


2702.1 


6186.0 


2782.6 


6295.4 


23 


24 


.4000 


2548.6 


5975.2 


2625.0 


6080.5 


2703.4 


6187.8 


2784.0 


6297.2 


24 


25 


.4167 


2549-9 


5977.0 


2626.3 


6082.3 


2704-8 


6189.7 


2785.4 


6299.1 


^1 


26 


.4333 


2551-2 


5978.7 


2627.6 


6084.1 


2706.1 


6191.5 


2786.7 


6300.9 


26 


27 


.4500 


2552.5 


5980.5 


2628.9 


6085.9 


2707.4 


6193-3 


2788.1 


6302.7 


^l 


28 


.4667 


2553.7 


5982.2 


2630.2 


6087.6 


2708.7 


6195-1 


2789.4 


6304.6 


28 


29 


.4833 


2555.0 


5983.9 


2631.5 


6089.4 


2710.1 


6196.9 


2790.8 


6306.4 


29 


30 


.5000 


2556.2 


5985.6 


2632.7 


6091.2 


2711.4 


6198.7 


2792.1 


6308.2 


30 


31 


.5167 


2557-5 


5987.4 


2634.0 


6093.0 


2712.7 


6200.5 


2793.5 


6310.1 


31 


32 


•5333 


2558.7 


5989.1 


2635.3 


6094.7 


2714.0 


6202.3 


2794-9 


6311.9 


32 


33 


.5500 


2560.0 


5990.9 


2636.6 


6096.5 


2715-4 


6204.1 


2796.3 


6313.8 


33 


34 


.5667 


2561.2 


5992.6 


2637.9 


6098.3 


2716.7 


6205.9 


2797.6 


6315.6 


34 


35 


.5833 


2562.5 


5994.4 


2639.2 


6100.1 


2718.0 


6207.7 


2799-0 


6317.S 


35 


36 


.6000 


2563.8 


5996.1 


2 640. 5 


6101.8 


2719-3 


6209.5 


2800.3 


6319.3 


36 


37 


.6167 


2565-1 


5997.9 


2641.8 


6103.6 


2720.7 


6211.4 


2801.7 


6321.2 


37 


38 


.6333 


2566.3 


5999.6 


2643.1 


6105.4 


2722.0 


6213.2 


2803.1 


6323.0 


38 


39 


.6500 


2567.6 


6001.4 


2644.4 


6107.2 


2723.4 


6215.0 


2804.S 


6324.9 


39 


40 


.6667 


2568.8 


6003.1 


2645.7 


6109.0 


2724-7 


6216.8 


2805.8 


6326.7 


40 


41 


.6833 


2570.1 


6004.9 


2647.0 


6110.8 


2726.0 


6218.6 


2807.2 


6328.6 


41 


42 


.7000 


257.1.3 


6006.6 


2648.3 


6112.5 


2727.3 


6220.4 


2808.6 


6330.4 


42 


43 


.7167 


2572.6 


6008.4 


2649.6 


6114-3 


2728.7 


6222.3 


2810.0 


6332.3 


43 


44 


.7333 


2573.9^ 


6010.1 


2650.9 


6116.1 


2730.0 


6224.1 


2811.3 


6334.1 


44 


45 


.7500 


2575.2 


6011.9 


2652.2 


6117.9 


2731.4 


6225.9 


2812.7 


6336.0 


45 


46 


.7667 


2576.4 


6013.6 


2653.5 


6119.7 


2732.7 


6227.7 


2814.1 


6337.8 


46 


47 


.7833 


2577.7 


6015.4 


2654.8 


6121.5 


2734-1 


6229.S 


2815.5 


6339.7 


47 


48 


.8000 


2578.9 


6017.1 


2656.1 


6123.2 


2735-4 


6231.3 


2816.8 


6341.5 


48 


49 


.8167 


2580.2 


6018.9 


2657.4 


6125.0 


2736.7 


6233.2 


2818.2 


6343.4 


49 


SO 


.8333 


2581.5 


6020.6 


2658.7 


6126.8 


2738.0 


6235.0 


2819.6 


6345.2 


SO 


SI 


.8500 


2582.8 


6022.4 


2660.0 


6128.6 


2739.4 


6236.8 


2821.0 


6347.1 


51 


52 


.8667 


2584.0 


6024.1 


2661.3 


6130.4 


2740.7 


6238.6 


2822.3 


6349.0 


52 


S3 


.8833 


2585.3 


6025.9 


2662.6 


6132.2 


2742.1 


6240.5 


2823.7 


6350.9 


53 


54 


.9000 


2586.6 


6027.6 


2663.9 


6133.9 


2743.4 


6242.3 


2825.1 


6352.7 


54 


55 


.9167 


2587.9 


6029.4 


2665.3 


6135.7 


2744.8 


6244.2 


2826.5 


6354.6 


55 


56 


.9333 


2589.1 


603 1. 1 


2666.6 


6137.5 


2746.1 


6246.0 


2827.8 


6356.4 


S6 


57 


.9500 


2590.4 


6032.9 


2667.9 


6139.3 


2747. S 


6247.8 


2829.2 


6358.3 


57 


58 


.9667 


2591.7 


6034.6 


2669.2 


6141.1 


2748.8 


6249.6 


2830.6 


6860.1 


S8 


59 


.9833 


2593.0 


6036.4 


2670.S 


6142.9 


2750.2 


6251.4 


2832.0 


6362.0 


S9 



FUNCTIONS OF ONE-DEGREE CURVE 



373 



Use loo' Chords up to 8" Curves 
Use 50' Chords up to 16° Curves 



Use 25' Chords up to 32** Curves 
Use 10' Chords above 32" Curves 



09 

a 




96^ 


97" 


98^ 


99° 


1 




Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





.0000 


2833-4 


6363.8 


2917.5 


6476.6 


3004.0 


6591.6 


3092.9 


6709.0 


I 


.0167 


2834.8 


6365.7 


2918.9 


6478.5 


3005. s 


6593.6 


3094.4 


6711.0 


I 


2 


.0333 


2836.1 


6367.5 


2920.3 


6480.4 


3006.9, 


6595.5 


3095.9 


6712.9 


2 


3 


.0500 


2837.5 


6369.4 


2921.8 


6482.3 


3008.4 


6597.S 


3097.4 


6714-9 


3 


4 


.0667 


2838.9 


6371.3 


2923.2 


6484.2 


3009.8 


6599.4 


3098.9 


6716.9 


4 


s 


.0833 


2840.3 


6373.2 


2924.6 


6486.1 


3011.3 


6601.3 


3100.4 


6718.9 


5 


6 


.1000 


2841.7 


6375.0 


2926.0 


6488.0 


3012.8 


6603.2 


3101.9 


6720.8 


6 


7 


.1167 


2843.1 


6376.9 


2927.5 


6489.9 


3014.3 


6605.2 


3103.4 


6722.8 


7 


8 


.1333 


2844.5 


6378.7 


2928.9 


6491.8 


3015.7 


6607.1 


3104.9 


6724.8 


8 


Q 


.1500 


2845.9 


6380.6 


2930.3 


6493.7 


3017.2 


6609.1 


3106.4 


6726.8 


9 


10 


.1667 


2847.2 


6382.S 


2931.7 


6495.6 


3018.6 


6611.0 


3107.9 


6728.8 


10 


II 


.1833 


2848.6 


6384.4 


2933.2 


6497.5 


3020.1 


6613.0 


3109.5 


6730.8 


II 


12 


.2000 


2850.0 


6386.2 


2934.6 


6499.4 


3021.6 


6614.9 


3III.O 


6732*7 


12 


13 


.2167 


2851.4 


6388.1 


2936.1 


6501.3 


3023.1 


6616.9 


3112.5 


6734.7 


13 


14 


.2333 


2852.8 


6389.9 


2937.S 


6503.2 


3024.5 


6618.8 


3114.0 


6736.7 


14 


IS 


.2500 


2854.2 


6391.8 


2938.9 


6505.2 


3026.0 


6620.8 


3115.S 


6738.7 


IS 


16 


.2667 


2855.6 


6393.7 


2940.3 


6507.1 


3027.5 


6622.7 


3117.0 


6740.7 


16 


17 


.2833 


2857.0 


6395.6 


2941.8 


6509.0 


3029.0 


6624.7 


3118.5 


6742.7 


17 


18 


.3000 


2858.4 


6397.4 


2943.2 


6510.9 


3030.4 


6626.6 


3120.0 


6744.6 


18 


19 


.3167 


2859.8 


6399.3 


2944.7 


6512.8 


3031.9 


6628.6 


3121.S 


6746.6 


19 


20 


•3333 


2861.2 


6401.2 


2946.1 


6514.7 


3033.3 


6630.5 


3123.1 


6748.6 


20 


21 


.3500 


2862.6 


6403.1 


2947.5 


6516.6 


3034.8 


6632.5 


3124.6 


6750.6 


21 


22 


.3667 


2864.0 


6404.9 


2948.9 


6518.5 


3036.3 


6634.4 


3126.1 


6752.6 


22 


23 


.3833 


2865.4 


6406.8 


2950.4 


6520.4 


3037.8 


6636.4 


3127.6 


6754.6 


23 


24 


.4000 


2866.7 


6408.V 


2951.8 


6522.3 


3039.3 


6638.3 


3129.I 


6756.6 


24 


25 


.4167 


2868.1 


6410.6 


2953.3 


6524.3 


3040.8 


6640.3 


3130.7 


6758.6 


^1 


26 


.4333 


2869.5 


6412.4 


2954.7 


6526.2 


3042.2 


6642.2 


3132.2 


6760.6 


26 


27 


.4500 


2870.9 


6414.3 


2956.2 


6528.1 


3043.7 


6644.2 


3133.7 


6762.6 


27 


28 


.4667 


2872.3 


6416.2 


2957.6 


6530.0 


3045.2 


6646.1 


3135.2 


6764.6 


28 


29 


.4833 


2873.7 


6418.1 


2959.0 


6531.9 


3046.7 


6648.1 


3136.7 


6766.6 


29 


30 


.5000 


2875.1 


6419.9 


2960.4 


6533.8 


3048.1 


6650.0 


3138.3 


6768.6 


30 


31 


.5167 


2876.5 


6421.8 


2961.9 


6535.8 


3049.6 


6652.0 


3139.8 


6770.6 


31 


32 


.5333 


2877.9 


6423.7 


2963.3 


6537.7 


3051.1 


6653.9 


3141.3 


6772.6 


32 


33 


.5500 


2879.4 


6425.6 


2964.8 


6539.6 


3052.6 


6655.9 


3142.9 


6774.6 


33 


34 


.5667 


2880.8 


6427.5 


2966.2 


6541.S 


3054.1 


6657.8 


3144.4 


6776.6 


34 


35 


.5833 


2882.2 


6429.4 


2967.7 


6543.4 


3055.6 


6659.8 


3145.9 


6778.6 


35 


36 


.6000 


2883.6 


6431.2 


2969.1 


6545.3 


3057.0 


6661.7 


3147.4 


6780.6 


36 


37 


.6167 


2885.0 


6433.1 


2970.6 


6547.3 


3058.5 


6663.7 


3149.0 


6782.6 


H 


38 


•6333 


2886.4 


6435.0 


2972.0 


6549.2 


3060.0 


6665.7 


3150.5 


6784.6 


38 


39 


.6500 


2887.8 


6436.9 


2973.5 


6551.1 


3061.S 


6667.7 


3152.0 


6786.6 


39 


40 


.6667 


2889.2 


6438.8 


2974.9 


6553.0 


3063.0 


6669.6 


3153.5 


6788.6 


40 


41 


.6833 


2890.6 


6440.7 


2976.4 


6555.0 


3064.5 


6671.6 


3155.1 


6790.6 


41 


42 


.7000 


2892.0 


6442.5 


2977.8 


6556.9 


3066.0 


6673.5 


3156.6 


6792.6 


42 


43 


.7167 


2893.4 


6444.4 


2979.3 


6558.8 


3067.5 


6675.5 


3158.2 


6794.6 


43 


44 


.7333 


2894.8 


6446.3 


2980.7 


6560.7 


3068.9 


6677.4 


3159.7 


6796.6 


44 


45 


.7500 


2896.3 


6448.2 


2982.2 


6562.7 


3070.4 


6679.4 


3161.2 


6798.6 


45 


46 


.7667 


2897.7 


6450.1 


2983.6 


6564.6 


3071.9 


6681.4 


3162.7 


6800.6 


46 


47 


.7833 


2899.1 


6452.0 


2985.1 


6566.5 


3073.4 


6683.4 


3164.3 


6802.6 


4^ 


48 


.8000 


2900.5 


6453.9 


2986.5 


6568.4 


3074.9 


6685.3 


3165.8 


6804.6 


48 


49 


.8167 


2901.9 


6455.8 


2988.0 


6570.4 


3076.4 


6687.3 


3167.4 


6806.6 


49 


SO 


.8333 


2903.3 


6457.6 


2989.4 


6572.3 


3077.9 


6689.2 


3168.9 


6808.6 


50 


SI 


.8500 


2904.7 


6459.5 


2990.9 


6574.3 


3079.4 


6691.2 


3170.5 


6810.6 


51 


52 


.8667 


2906.1 


6461.4 


2992.3 


6576.2 


3080.9 


6693.2 


3172.0 


6812.6 


52 


S3 


.8833 


2907.6 


6463.3 


2993.8 


6578.1 


3082.4 


6695.2 


3173.6 


6814.7 


S3 


S4 


.9000 


2909.0 


6465.2 


2995.2 


6580.0 


3083.9 


6697.1 


3175.I 


6816.7 


54 


55 


.9167 


2910.4 


6467.1 


2996.7 


6582.0 


3085.4 


6699.1 


3176.6 


6818.7 


55 


56 


.9333 


2911.8 


6469.0 


2998.1 


6583.9 


3086.9 


6701.1 


3178.1 


6820.7 


56 


57 


.9500 


2913.3 


6470.9 


2999.6 


6585.8 


3088.4 


6703.2 


3179.7 


6822.7 


57 


S8 


.9667 


, 2914.7 


6472.8 


3001.1 


6587.7 


3089.9 


6705.2 


3181.2 


6824.7 


58 


59 


.9833 


2916.1 


6474.7 


3002.6 


6589.7 


3091.4 


6707.1 


3182.8 


6826.8 


59 



374 



THE SURVEY 



Use loo' Chords up to 8° Curves 
Use 50' Chords up to 16° Curves 



Use 25' Chords up to 32" Curves 
Use 10' Chords above 32° Curves 



s 


*o g 


100° 


\S 


g 


^ & 




; "3 






I fl 


s 


OQ 


Ext. 


Tan. 


s 





.0000 


3184-3 


6828.8 





I 


.0167 


3185.9 


6830.8 


I 


2 


•0333 


3187.4 


6832.8 


2 


3 


.0500 


3189.0 


6834.8 


3 


4 


.0667 


3190.5 


6836.8 


4 


5 


.0833 


3192. 1 


6838.9 


5 


6 


.1000 


3193.6 


6840.9 


6 


7 


.1167 


3195.2 


6842.9 


7 


8 


.1333 


3196.7 


6844.9 


8 


9 


.1500 


3198.3 


6847.0 


9 


10 


.1667 


3199.8 


6849.0 


10 


II 


.1833 


3201.4 


6851.0 


II 


12 


.^000 


3202.9 


6853.0 


12 


13 


.2167 


3204.5 


6855-1 


13 


14 


.2333 


3206.0 


6857.1 


14 


15 


.2500 


3207.6 


6859-1 


15 


16 


.2667 


3209.1 


6861.1 


16 


17 


.2833 


3210.7 


6863.2 


17 


18 


.3000 


3212.2 


6865.2 


18 


19 


.3167 


3213.8 


6867.2 


19 


20 


•3333 


3215.4 


6869.2 


20 


21 


.3500 


3217.0 


6871.3 


21 


22 


.3667 


3218.5 


6873.3 


22 


23 


.3833 


3220.1 


6875-4 


23 


24 


.4000 


3221.6 


6877.4 


24 


25 


.4167 


3223.2 


6879.4 


25 


26 


.4333 


3224.7 


6881.4 


26 


27 


.4500 


3226.3 


6883-5 


27 


28 


.4667 


3227.9 


6885.5 


28 


29 


.4833 


3229.5 


6887.6 


29 


30 


.5000 


3231.0 


6889.6 


30 


31 


•5167 


3232.6 


6891.7 


31 


32 


.5333 


3234.1 


6893.7 


32 


33 


.5500 


3235.7 


6895.7 


33 


34 


.5667 


3237.3 


6897.8 


34 


35 


.5833 


3238.9 


6899.8 


35 


36 


.6000 


3240.4 


6901.8 


36 


37 


.6167 


3242.0 


6903.9 


37 


38 


•6333 


3243.5 


6905.9 


38 


39 


.6500 


3245-1 


6908.0 


39 


40 


.6667 


3246.7 


6910.0 


40 


41 


.6833 


3248.3 


6912. 1 


41 


42 


.7000 


3249.8 


6914.1 


42 


43 


.7167 


3251-4 


6916.2 


43 


44 


.7333 


3253-0 


6918.2 


44 


45 


.7500 


3254-6 


6920.3 


45 


46 


.7667 


3256.2 


6922.3 


46 


47 


.7833 


3257-8 


6924.4 


47 


48 


.8000 


3259-3 


6926.4 


48 


49 


.8167 


3260.9 


6928.5 


49 


SO 


.8333 


3262.5 


6930.5 


50 


SI 


.8500 


3264.1 


6932.6 


51 


52 


.8667 


3265.7 


6934.6 


52 


S3 


.8833 


3267.3 


6936.7 


53 


S4 


.9000 


3268.8 


6938.7 


54 


5S 


.9167 


3270.4 


6940.8 


55 


S6 


.9333 


3272.0 


6942.8 


S6 


S7 


.9500 


3273-6 


6944.9 


57 


S8 


.9667 


3275.2 


6946.9 


S8 


59 


.9833 


3276.8 


6949.0 


59 



FUNCTIONS OF ONE-DEGREE CURVE 



375 



Use loo' Chords up to 8° Curves Use 25' Chords up to 32° Curves 
Use 50' Chords up to 16° Curves Use 10' Chords above 32° Curves 



1 


101° 


102° 


103° 


104° 


105° 


1 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





3278.3 


6951.0 


3375.1 


7076.0 


3474.6 


7203.6 


3577-1 


7334-1 


3682.6 


7467.5 





10 


3294'-3 


6971.7 


3391.5 


7097.1 


3491.5 


7225.1 


3594-4 


7356.1 


3700.4 


7490.0 


10 


20 


3310.3 


6992.4 


3407.9 


7118.2 


3508.4 


7246.8 


3611.9 


7378.2 


3718.4 


7512.6 


20 


30 


3326.4 


7013.2 


!3424.5 


7139.4 


3525.5 


7268.5 


3629.4 


7400.4 


3736.5 


7535-3 


30 


40 


3342.5 


7034.03441.1 


7160.7 


3542.6 


7290.3 


3647-1 


7422.7 


3754-6 


7558.1 


40 


so 


3358.8 


7055.0 J3457.8 


7182. 1 


3559.8 


7312.1 


3664.8 


7445-0 


3772.9 


7581.0 


50 


60 


3375.1 


7076.0 


3474.6:7203.6 


3577.1 


7334-1 


3682.6 


7467-5 


3791-2 


7604.0 


60 




106° 


107° 


108'' 


109° 


no" 


S 
3 
c 






















^ 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


^ 





3791.2 


7604.0 


3903.1 


7743.7 


4018.5 


7886.7 


4137.4 


8033.2 


4260.0 


8183.3 





10 


3809.6 


7627.0 


3922.1 


7767.3 


4038.0 


7910.8 


4157-5 


8057.9 


4280.8 


8208.7 


10 


20 


3828.1 


7650.2 


3941.2 


7791.0 


4057.7 


7935.1 


4177-8 


8082.8 


4301.7 


8234.2 


20 


30 


3846.7 


7673.4 


3960.4 


7814.7 


4077.5 


7959.5 


4198.2 


8107.8 


4322.7 


8259.8 


30 


40 


3865.4 


7696.7 


3979.6 


7838.6 


4097.3 


7983.9 


4218.7 


8132.8 


4343-8 


8285.5 


40 


50 


3884.2 


7720.1 


3999.0 


7862.6 


4117.3 


8008.5 


4239-3 


8158.0 


4365.1 


8311-3 


50 


60 


3903-1 


7743.7 


4018.5 


7886.7 


4137.4 


8033.2 


4260.0 


8183.3 


4386.4 


8337.2 


60 


Cfl 


III*' 


112° 


113'' 


114'' 


115° 


^ 


:3 












d 






















^ 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


^ 





4386.4 


^2>S1-2 


4516.9 


8495.1 


4651.6 


8657.1 


4790.7 


8823.4 


4934-4 


8994.3 





10 


4407.9 


8363.2 


4539.1 


8521.8 


4674.5 


8684.5 


4814.4 8851.6 


4958.9 


9023.2 


10 


20 


4429.5 


8389.4 


4561.3 


8548.6 


4697.5 


8712.0 


4838.1 '8879-9 


4983-4 


9052.3 


20 


30 


4451.2 


8415.6 


4583.7 


8575.6 


4720.6 


8739.7 


4862.o'89o8.3l 


5008.1 


9081.5 


30 


40 


4473.0 


8442.0 


4606.2 


8602.6 


4743.9 


8767.5 


4885.08936.8 


5032.9 


9110.8 


40 


50 


4494.9 


8468.5 


4628.9 


8629.8 


4767.2 


8795.4 


4910.2 8965.5 


5057-9 


9140.3 


50 


60 


4516.9 


8495.1 


4651.6 


8657.1 


4790.7 


8823.4 


4934-48994-3 


5083.C 


9169.9 


60 




116° 


117° 


118° 


119° 


120° 

1 


1^ 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 


Ext. 


Tan. 





5083.0 


9169.9 


5236.6 


9350.5 


5395.4 


9536.3 


5559.7 


9727.6 


5730.0 


J 
9,924.6- 





10 


•5108.2 


9199.7 


5262.6I9381.1 


5422.4 


9567-8 


5587.7 


9760.0 


5758.9 


9,958.1! 


10 


20 


5133.6 


9229.6 


5288.9 9411.9 


5449.5 


9599-5 


5015.8 


9792.6 


I5788.0 


9,990.6' 


20 


30 


5159.1 


9259.6 


5315.319442.8 


5476.819631.3 


5644.1 


9825-4 


I5817.3 


10,025.61 


30 


40 


5184.8 


9289.8 


5341.8 


9473.8 


5504.3 


9663.2 


5672.6 


9858.3 


5846.8 


10,059.7 


40 


50 


5210.6 


9320.1 


5368.5 


9505.0 


5532.0 


9695.3 


5701.2 


9891.4 


5876.4 


10,093.7 


50 


60 


5236.6 


9350.5 


5395.4 


9536.3 


5559.7 


9727.6 


5730.0 


9924.6 


5906.1 


10,127.7 


60 



376 



THE SURVEY 



L = loo X -7; = 



Central angle 



X 100. 



D Degree of curvature 

For the convenience of the field engineer column i, Table 32, 
gives the central angle (A) in degrees and minutes (as read by 
the transit); column 2 gives the same angle expressed in degrees 
and decimals for figuring curve lengths. 

Tangent Length and Externals. — Sketch No. 71 shows a general 
curve problem. The deflection angle between the tangents at 
the point of intersection (P. 1.) = the central angle of the curve that 
will fit these tangents; it is referred to as A. 

The tangent distances equal the distance from the P. C (be- 
ginning of curve) to the P, I, or P. I. to P, T. (end of curve) and is 
expressed by the formula 

T = Radius X tangent of — (4) 

Externa!; 
PC. \ Bl. 

-.■^^ ^^ 




'(Center of Curve J 
Pig. 71. 

Therefore, for a given central angle A, the tangent length is di- 
rectly proportional to the radius. If the tangent lengths of a 1° 
curve for different A's are tabulated, the tangent length for any 
desired degree of curve equals tangent length for 1° curve for 
the specified A divided by the degree of the desired curve ex- 
pressed in degrees and decimals of a degree. 

Expressed as a formula this reads: 



Tangent for desired curve = 



__ Tangent 1° curve for specified A 



D 



(5) 



D 



(6) 



and reversing the formula we can determine the desired degree 
of curve for a specified tangent length by the formula 

Tangent 1° curve for specified A 
Specified tangent length desired 

The external is the distance from the P. /. to the curve arc on 
the line between the P, I. and the center of the curve. It is deter- 
mined by the formula : 

Ext. =f : — E.adius = Radius/ 



Gosine- 



\ Cosine- 



■) 



(7) 



CURVE FORMULAE 



377 



iand is directly proportional to the radius in the satne manner as 
the tangent length; therefore, the external of any desired curve 
for a specified A equals the external of a i° curve for that A divided 
by the degree of curvature. 



'Pointof Tang en cy 



;S Angle=^CenlTalAngkA 




^Center of Curve 

Pig. 72. 




Fig. 73. 



Expressed as a formula this reads: 

Ext. 1° curve for specified A 



External for desired curve = 



D 



(8) 



378 THK SURVEY 

and reversing; as for tangents, the desired degree of curvature is 
obtained that gives a specified external distance, by the formula, 

_ Ext. 1° curve for specified A ^ , . 

Specified Ext. distance desired 

Methods of Running Curves. — Curves are run in the field by 
tangent offsets, middle ordinates or deflection angles. Deflec- 
tion angles is the simplest method and is almost universally used. 
It is based on the principle that the angle S between the tangent 
and arc chord, one end of which is at the point of tangency, is 
equal to 3^ the central angle subtended by that chord. Sup- 
pose the angle A is 4° and the arc length ST = 100 feet. This 
curve would then be a 4° curve. From the previous definitions 
locate the point T (Fig. 72) by turning the deflection angle S = 
2° from the tangent and measuring 100 feet of arc in such a position 
that the end of the arc would be on the line of the chord ST. It 
is impossible to conveniently measure the arc distance and for 
all practical purposes a chord length of 100' will answer for a 
4° curve (see discussion, page 379). 

Suppose we wish to locate the points 2, 3, 4, 5, and 6 on the 
4° curve from point i or the P.C. of a curve (Fig. 73). 

Set the transit at the P.C: if we turn a deflection — = 2° from 

2 

the tangent xy the line of sight will pass through the point 2; 

if we turn — = 4° the line of sight will pass through point 3; 6°, 

2 

point 4, etc.; it only remains to measure to these points to locate 
them definitely. This can be done in two ways,^ by measuring 
the distances 1-2, 1-3, 1-4, 1-5, etc., or by measuring 1-2, 2-3, 
3-4, 4-5, etc. 

In the first case the difference between the length of arc and 
the chord length becomes so great that, unless a correction is 
made, the points are not exactly located; that is, the length of 
arc between points i, 2, 3, 4, 5, 6, = 500' while the chord length 
1-6 = 497.5'; also, it takes longer to measure the distances 1-2, 
1-3, 1-4, 1-5, 1-6, etc., than it would 1-2, 2-3, 3-4, 4-5, etc. 

In the second method we can use chords of 100' from 1-2, 2-3, 
etc., with no appreciable error, as the distance measured by chords 
I, 2, 3, 4, 5, 6, = 499-94'- 

Therefore, the method usually adopted is to turn the deflection 

A 
angle — and measure the chord 1-2, which locates the point 2; 

2 

then turn the deflection angle — and measure the chord distance 

2 

2-3, locating point 3, etc. 

The fact has been mentioned that the use of the chord distance 
as equal to the arc introduces an error but that this error is of 
no importance for a 4° curve: As the degree of curvature in- 
creases, the difference between an arc length of 100' and the chord 



SIMPLE CURVE PROBLEM 379 

length becomes greater, and it is necessary to determine the limit of 
curvature that will allow the use of 100' chords in locating curve 
points. On page 324 the statement is made that center line chain- 
ing should be correct to within o.i' per 100' of length, which allows 
a difference in arc and chord of o.i. This occurs when the degree 
of curvature reaches 9° per 100'. The difference can then be 
reduced by the simple expedient of using 50' chords, which re- 
duces the error for this degree of curvature from o.io' per 100' 
of length using 100' chords to 0.02' using 50' chords; 50' chords 
can be used up to 18° curves and beyond that point 25' chords. 

It is better not to use the full limit of allowable error, and a good 
working rule is 100' chords up to 8° curves, 50' chords up to 16° 
curves, 25' chords to 32° and beyond that 10' chords. 

For any given curve the deflection angle and central angle 
are directly proportional to the length of the arc, and if the de- 
flection angle for 100' arc of 10° curve equals 5° the deflection 

angle for one foot of arc of 10° curve equals = = 3 minutes. 

100 100 

An example of a typical simple curve problem can now be given : 
j^^ K 'Ten. Length— -^_pj_^^f^^23t4?.6 B 



Fig. 74. 

To determine the degree of curvature desired from a fixed external 

distance 

At station 23 -|- 42.6 we have a deflection angle of 25° 10' be- 
tween tangents AB and B'C\ suppose upon exaraining the ground 
it is decided that to fit the old roadbed and give good alignment 
the curve should be located somewhere between 13.5' and 14.5' 
to the right of the transit point at station 23 + 42.6. Proceed 
as follows: from table 32 pick out the external for a 1° curve for 
A = 25° 10', this equals 141.0'. 

The problem is to determine the degree of curvature that will 
give an external of between 13.5' and 14.5'. Use formula (9). 

^ Ext. T° curve for 25° 10' 141. o' o 

D = -. = > = 10.44 curve. 

13.5 13.5^ 

^ Ext. 1° curve for 2K° 10' ,141.0' o 

D = -. ^ = = 9.72 curve. 

14.5 14-5 



380 THE SURVEY 

To fit the conditions some curve must be selected between a 
10.44° and a 9.72°. A 10° curve would be naturally selected as 
being the simplest to figure. 

To determine the required degree of curvature for a fixed tangent 

length 

Take the same problem as above except there must be a tangent 
length of between 127' and 129'. Use formula (6). 

^ Tangent 1° curve for 25° 10' 12 79.1' 

D — ; = ;— = 10.07° curve. 

127' 127' 

^ Tangent 1° curve for 25° 10' 12 79.1' o 

D = -. = ~- = 9.91° curve. 

129 129 

Table 32 gives tangent for 25° 10' = 12 79.1'. 

These limiting values would result in the selection of a 10° 
curve. The degree of the desired curve is usually selected in one 
of these two ways; ordinarily it is determined by the external 
distance. 



£>« WR'^ 573.0 
r--IZ7.9L^ 251.7 
RC.-^Sta.2ZH4.7 
P.T.^Sta.24t66.4 



Fig. 75. 

Simple Curve Problem. Case i. — To compute the notes for a 
10° curve for a deflection angle of 25° 10' between tangents at 
station 23 + 42.6. 

Central angle = 25° 10'. 

Table 32 gives the tangent 1° curve for 25° 10' = 1 279.1. 

rr 4. o 1279. 1 

Tangent 10 curve = ^— = 127.91. 

10 

The station of the P.C. then equals station 23 + 42.6 P./. 

minus 127.9' == station 22 + 14.7. 

The length of curve = -7: = ^^'^ o ^ X 100' = 251.7 feet. 

JJ 10 

The station of the P.T. (Tangent point, or end of the curve) 
as measured around the arc is then station (22 + 14.7 P.C.) + 
251.7' = station 24 + 66.4. 

The rule for running curves requires the use of 50' chords for 




SIMPLE CURVE PROBLEM 381 

a 10° curve. We must, therefore, figure the deflections for the 
even stations and the 50' stations as follows: 

Station 22 + 50, 23 + 00, 23 + 50? 24 + 00, 24 + 50, and 
to check the curve station 24 + 66.4. 

For a 10° curve, Table 31. 

The deflection for 100' of arc = 5° 
" " " 50' '' ". = 2° 30' 

u u u jr u u ^ qO ^y 

The distance from the P,C, station 22 + 14.7 to station 22 + 
50 is 35.3'; the deflection per foot = 0° 03', for 35.3' = 35.3 X 
0° 03' = 105.9 minutes = 1° 46'. 

The distance P.C. to station 23 + 00 equals 85.3', or 50' farther 
than for station 22 + 50; the deflection per 50' of arc equals 
2° 30'; therefore, the deflection for station 23 + 00 equals the 
deflections for station 22 + 50 (1° 46') plus 2° 30', the deflection for 
50' of arc or 4° 16'; in a like manner the deflection for station 23 -|- 
50 is 6° 46'; for 24 + 00, 9° 16'; for 24 + 50, 11° 46'; the distance 
from station 24 + 50 to the P.T, station 24 + 66.4 is 16.4'; 
the deflection for 16.4' equals 16.4 X 0° 03' = 49.2'; the deflection 
for station 24 + 66.4 is, therefore (11° 46' + 49') = 12° 35'; 
if the deflection notes have been properly figured this last deflection 
to the P.T. should always be J^ the central angle of the curve; 
in this case J^ of 25° 10', which equals 12° 35', checking the notes. 

To run the curve. Set up the transit at the P./.; sight along 
the tangent {B.A.)y measure off the distance 12 7. 9" (tangent length) 
along this line and set the P.C. exactly on the line. In a like 
manner set the P.T. on the forward tangent {B'.C.) 127.9' from 
the P.I, Then set up the transit on the P.C. and with the vernier 
at 0° 00' sight on the P./., using the lower plate motion. Loosen 
the upper motion and deflect i°l46'; measure along this line 2tS'3\ 
which locates station 22 + 50 on the curve arc; then loosen the 
upper motion and set the vernier to read 4° 16'; measure 50' from 
the just located station 22 + 50, so that the forward end of the 
tape is in line with the transit deflection of 4° 16'; this locates 
station 23+00 on the curve arc. In a like manner deflect 6° 
46' and measure forward 50' from station 23 + 00 to station 23 + 
50, etc., until the \P.T. is reached. If the curve has been correctly 
run the last deflection of 12° 2>S' will strike the previously located 
P.T. and the distance from station 24 + 50 to this P.T. will be 
16.4'; if the distance checks within 0.2' it is sufficiently close. 

The above problem and method of laying out a curve is the 
simplest form encountered; in it we assume that the P./., P.T, 
and all intermediate points on the curve are visible from the P.C, 
and that the P.I. is accessible. 

In nine cases out of ten this method is applicable to road curves, 
but where the P.I. occurs outside of the road fences it sometimes 
is located in a stream, pond, building, etc., and cannot be occupied. 
This is known as the problem of the inaccessible P.I. More 
often it is impossible to see the P.P., or some intermediate point 
on the curve from the P,C.i which necessitates intermediate 



382 THE SURVEY 

transit points on the curve. The problem of inaccessible P.C.s 
or P.T.s is so rare it will not be illustrated. 

Problem of the Inaccessible P. I. Case 2. — The point H (P.L) 
can not be occupied. Locate any two convenient points, 5 and t 
on the tangents A.B, and B'.C. and measure the distance st equals, 
say, 1 10.5'. 

Set the transit at ^ and measure the angle between the line 
A.s. produced and st, say, 5° 10'; in a similar manner measure the 
angle at t between st produced and the forward tangent /C, say, 
20° 00'. The total deflection then between the tangent AsB and 
B'tC or the central angle of the curve to be run is the sum of these 
two deflections, angles (5° 10') + (20° 00') = 25° 10'. 

Assuming a 10° curve is desired we must locate the P,C. from 
the point s and the P.T, from the point /. 



k- /2Z9-- -• -y 

[EC. \S=5fa.2Z+53X, Hj ^l- inaccessible 



Pig. 76. 

In the preceding simple curve problem the tangent length of 
a 10° curve with a central angle of 25° 10' was figured to be 127.9'; 
it, therefore, remains to compute the distance sE which subtracted 
from 127.9' will give the distance from s along the tangent sA to 
the P,C., of the curve.- In a similar manner compute tH, which 
subtracted from 127.9' gives the distance along the forward tangent 
tC to the P,T. of the curve. 

Knowing the station of the point s as measured along the tangent 
A.B. the station of the P.C is determined; then figure the de- 
flections in the usual manner and run the curve. 

For the values given the computations are as follows: 

To determine sU and Ut. Use the law of sines (see Trigono- 
metric formulae, page 843). 
sH :st : sin 20° 00' : sin 25° 10' 

^ff = ^^ sin 20° 00' ^ 1 10.5 X 0.34202 ^ gg , 
sin 25° 10' 0.42525 

5/ sin 5® 10' 1 10.5 X 0.09005 , 

Ht = "o — J- = = 23.4 

sm 25 10 0.42525 

Therefore, the distance from s to the P,C. is 127.9' — 88.9' = 
39.0'. 

The distance from / to the P,T. is 127.9 "" 23.4 = 104.5. 
Having these distances the P.O. and P.T, are located. As- 



CURVE PROBLEMS 



383 



sume that station of 5 was measured along the tangent AB and 
found to be station 22 -f 53-7- 
The station of the P.C, then equals 22 + 14.7 
" " P.L " '' 23 + 42.6 
'' " P.T. " " 24 -f 66.4, using the length of 
curve figured in Case i. 

The deflections are figured and the curve run as in Case i, 
assuming that all the curve points are visible from the P.C. 

Case 3. — Where the P.T, or intermediate points on the curve 
are not visible from the P.C. 

(a) Where an intermediate set-up is required. Use the same 
curve as in Case i. 

The deflections for the different curve points were figured as 
follows: 

Deflections. — Instrument at P.C, foresight on P.I. 



P.C, Station 22 -f 14.7 

22 + 50 

23 + 00 

23 + 50 

24 + GO 
24 + 50 

• • '24 + 66.4 

eC. 22f/4.7 PI. 


Deflection 0° 00' 
1° 46 
4° 16' 
6° 46' 
9° 16' 
11° 46' 
" 12° 35' 


,,.,0 -B~~^ 


^"""^^^-^ 



Z4+50 



JRT. 24 -h 66.4- 



Fig. 77. 



Set up the instrument at the P.C, and locate the points 22 + 50, 
23 + 00 and 23 + 50; suppose 24 + 00 is not visible, set up at 
station 23 + 50, set the vernier at 0° 00' and back sight on the 
P.C; transit the telescope and finish the curve, using the same 
deflections as figured for the instrument set up at the P.C] that is, 
turn the deflection of 9° 16' for station 24 + 00, 11° 46' for 24 + 
50, and 12° 35' for the P.T, In general it can be said that when- 
ever the P.C is used as a backsight from the intermediate set-up, 
set the vernier at 0° 00' when sighting on the P.C; transit the 
'telescope and use original notes for the balance of the curve. 

(b) Where two or more intermediate set-ups are required. 

For the first set-up, say, at 23 + 50, proceed as above and set 
station 24 + 00; suppose 24 -f- 50 is not visible from station 
23 + 50; set up at station 24 -f- 00 and with the vernier reading 
6° 46' back sight on station 23 + 50; transit the telescope, set the 
vernier to read 11° 46' for station 24 + 50, and proceed, using 
the same deflections as originally figured. In general, where 
the P.C, is not visible from the intermediate set-up, set the 
vernier to read the deflection figured for the point used as a 
backsight; transit the telescope and proceed with the curve, 



384 THE SURVEY 

using"3the notes originally figured. That is, if the instrument 
is set up at station 24 + 00 and 22 + 50 used as a backsight, 
the vernier is set at 1° 46', and using the lower motion the wire 
is set on station 22 + 50; then transiting the telescope the curve 
is run by setting the vernier at 11° 46' for station 24 + 50, etc. 

If station 23 + 00 is used as a backsight, set the vernier at 
4° 16' when sighting the machine; then transit and proceed as 
above. 

These three cases cover any ordinary road curve problems. 

(b) NEW LOCATION SURVEYS 

General. — The details of survey work depend entirely on the 
character of the improvement and range from simple alignment 
determination on Mesa Wagon trails to the complete surveys 
required for difficult mountain locations which are to be constructed 
by contract on unit price bids. The following data are for complete 
first-class surveys. The same methods are used for more incom- 
plete surveys but parts of the procedure can often be omitted if the 
work is to be done by force account or convict labor. 

Organization and Equipment. — Eight to ten men parties are a 
convenient and efficient force. 

Locating engineer 

Transitman 

Levelman 

3 Chainmen, rodmen, etc. 

1 to 3 Axemen. 
Cook 

If drafting is to be done in the field add a draftsman and computer 
to the party, but this is not advised as field drafting is rarely 
satisfactory. 
Organization. (First stage of work.) 

T . . • f Picking out line and general 

Locating engineer | supervision. 

Transitman 1 

2 Chainmen I Running base line. 

Necessary axemen [ ° . 

I Stakeman J 

Le elman 1 Running bench levels and check 

^\ \ profile levels. Keeps all this 

^^ J work close up to base line party. 

Organization. (Second stage of work.) 
Locating Engineer 1 Drainage areas. Classification 

1 Assistant J of materials and topography. 

I'nSl } cross-sections. 

Levelman 

2 Assistants 



> Cross-sections. 



SURVEY ORGANIZATIONS 



385 



Extra men moving camp, odd jobs, etc. 

The first stage of the work varies in speed from J^ mile to 3 miles 
per day depending on the character of the county. Three-fourths 
mile per day is a fair average for ordinary mountain work. 

The second stage should make a speed of from i mile to 2 miles per 
day. A fair average is about i J^ miles per day. 

Allowing for unavoidable loss of time, rnoving camp, etc., 10 
miles a month for an eight man party is a fair average when they are 
doing first class work. 

Cost of Survey. — The cost of first class complete mountain road 
location surveys runs from $75 to $150 per mile exclusive of rail- 
road transportation to the job, allowing $150 per month for the 
locating engineer, $120 per month for transitman; $100 per month 
for leveler and $70 to $90 for laborers, etc. Meals are furnished 
free to the men at an average cost of $0.75 per man per day ex- 
clusive of labor or about $1.00 to $1.30 per day including cooks 
salary. 

The average speed for a party of 8 men is approximately 10 miles 
per month of completed survey, at an average cost of $100 to $120 
per mile exclusive of railroad transportation. In easy flat country 
this speed can be easily doubled and the cost halved. 



Depreciation on Engineering Equipment per Mile of Survey 
Assumed 50 miles of survey per season 



Quan- 
tity 


Item 


~ Value 


Years 


Annual 
Deprecia- 
tion 
and 

Repairs 


Rental 
Charge 
per Mile 
Survey 


I 
I 
I 
2 
3 
4 

2 

2 
3 
6 

I 

4 
2 

I 
I 


Transit (mountain) tripod . 

Level (dumpy or Y) 

Locke level 


I300.00 

150.00 

7.00 

33 00 

36.00 

9.00 

30.00 

20.00 

7.00 

6.00 

10.00 

4.00 

4.00 

24.00 

10.00 


10 

10 

3 

5 

2 

2 

I 

5 

I 
I 

10 
2 

3 

4 

I 


$40 . 00 

25 .00 

2.50 

6.00 

18.00 

5 00 

30.00 
4.00 
7.00 
6.00 

1 .00 
2.00 
1.50 
6.00 
10.00 




Abney levels @ 1 16.50 

100' chains @ $12.00 

Range poles (8' wooden) 
@ $2.25 


Level rods, Philadelphia 
13' extension 


Chain repair kits 


Metallic tape boxes, $2.45. 
Metallic fillers 


Set sounding bars (i3'i"-i'' 

and ^i" tool steel) 

Plumb bobs 


Pocket compasses 

Kodak 3-A 


Engineer's trunk 


Totals 


$650.00 




S164.00 


$3.30 

(Say $3.00) 





* Marking crayon. 

* Use a crayon having a large amount of oil as it will last longer. 
On- AH" is a good brand. 



"Stay- 



386 



THE SURVEY 



Camp Drafting Equipment (if desired). — Camp equipment is 
listed in Chapter XII. 

Methods. — The chief of party should precede the men to the 
work and go over the entire line as outlined in the preliminary 
investigation report picking out his camp sites and making all 
necessary arrangements for transportation of camp equipment 
and supplies. He should also mark the base line location for two 
or three miles so that when the party arrives there will be no delay 
in making camp and starting the line work. 

First Stage of Survey. — 

(a) Tracing the location. 

(b) Running base line. 

(c) Running bench levels and base line profile. 

(a) Locating Line. — This work is done by the locating engineer 
who considers all the principles of grade, alignment, etc., discussed 
in Part I. In high altitudes he pays particular attention to avoid- 
ing bad snow conditions which in general means avoiding north 
exposure as much as possible. Very often he can be helped in this 
part of the problem by making a snow map the spring preceding 



^^^^^^^^^^^^^^^^^^X%ss^ 




■ 




^^^^^^^^ 


^^^^^^^^^^^^^^^^ 


/^^^^x^^^^Jvv^^^$$$$$$$VvSS$$*oC^ 



LE6BND. 
Area of Snow April /— 

Area of Snow Maij 1^ 
Area of Snow June l^ 




Note. — This map shows that it is advisable to keep on the 
north side of Buck Creek and the west side of Wind River from 
the standpoint of avoiding snow. It also shows that the Pass was 
open by June ist. 



Fig. 79. 



BASE LINE ' 387 

the survey. This is done by sketching in the areas where snow lies at 
different dates, say April ist, May ist, June ist. When furnished 
with a map of this kind he avoids the areas of late snow where 
possible. Lacking a definite investigation for snow conditions 
the best available local data should be obtained from hunters, etc. 

The different trial lines are traced with an Abney level in open 
country and a combination of Abney level and aneroid in timbered 
country. The line that he decides to adopt is marked at sufficiently 
close intervals either by blazing trees or tall stakes with flags on them 
so that the base line party will have no difficulty in following 
the correct location. This work must be kept far enough ahead 
of the base line party so that there is no danger of the work of 
the main party becoming worthless by the line getting into a loca- 
tion which has to be abandoned and relocated. 

When working on a ruling grade the line should be traced down 
hill from the highest point on the route. When working on a rul- 
ing grade the line in the field should always be traced at a less rate 
of grade than the maximum allowed. That is if the maximum 
grade is set at 7% the locator should trace his line on a 63^ or 6% 
grade in order to give the designer a little leeway for economical 
variations from the field grade and yet keep within the maximum 
rate. When w^orking on portions of the route requiring less than 
the ruling grade it makes no difference in which direction the line is 
traced so long as the base line is run in one direction with con- 
tinuous stationing. 

(b) Base Line. — The base line follows the marked route of the 
location. It is a chained, transit line marked on the ground by 
stakes at least every 100 feet well driven and marked with crayon 
(Stay on All) with the stationor plus of each stake. Stakes are 
placed at each point on the line where a profile shot or cross-section 
will be required and should be well made and well driven so that 
they will remain in place at least three years. The transit points 
(angle points) are marked with well driven hubs with tack center- 
ing; every third or fourth transit point should be permanently 
and carefully referenced by both azimuth and distance (see 
sample notes). The angles in the line are determined by transit 
readings and the bearings of the courses are recorded by azimuth 
using true north as the zero azimuth. The use of true north as the 
reference line in these surveys is desirable on account of permitting 
a check on the accuracy of the transit work at any time; on account 
of retracing a lost line and on account of right-of-way descriptions 
in localities laid out on the U. S. Land system. The methods of 
determining true meridian by polaris and solar observations are 
explained, pages 395 to 415. In fairly flat or rolling topography 
the base line should follow the center line of the proposed improve- 
ment exactly and all curves at tangent intersections should be run 
in the field. It has been found from experience that for the topo- 
graphic conditions mentioned that the field men can pick the best 
location in easy country and also that where the center line is actu- 
ally run and staked that it simplifies the work of cross-sectioning, 
the office design and the staking for construction. 



388 



THE SURVEY 



However, on sidehill locations or any kind of difficult work 
experience has shown that the field men can not pick an exact 
center line which will be economical in design and that under 
these conditions it is a waste of time and money to run in curves. 
Under these conditions the base line is run as a series of tangents 
keeping as close to the probable center line as possible and using 
short tangents iii going around any natural features that will re- 
quire a sharp curve in the finished road. Later when the cross- 
sections are taken they must be extended far enough from the line 
to allow the designer to shift the center line from the base line as 



Skrfion 



Back 
Sight 



Transm Notes . 



Fore, 
Sighf 



I5-I-73.1 



Back 
Ay. 



Fore 



Check '■ 
Angles 



£2fiL 



Wm 



stake- 



Stake 




-0--Q 



StZM. 



I2+3I.3 



19005 



3^05 



lOyiaiidOak 



None 5-I-23.0 



TheAyrnuthbta. 0. to 5+23 was cfeter^ 



TheAy 



^-^ 



mined 



Claris Observation. SeptdOf^ 



1918 Time 10-25 P.M. 



Pig. 8o. 

far as he desires as well as varying his vertical grade from the field 
grade. This requires considerable extra work in cross-sectioning 
as will be taken up later but is well worth while, as in difficult 
country a paper location is always more economical to construct 
than a field location. 

Bench Levels. — Ordinary engineers spirit level work reading 
turning points to nearest o.oi of a foot. Benches figured to nearest 
o.oi ft. in elevation (see sample notes. Figure 8i). 

Permanent benches should be established at least every J^ mile 
and preferably at J-^ mile intervals. The datum for the levels 
should be referred to U. S. Geological Survey datum if possible 
or lacking this reference a datum can be assumed but in any case 
the method of arriving at the elevation of the initial bench mark 
{(Continued page 390) 



TANGENT OFFSET METHOD 



389 



Staking Curves by Tangent Offset 



n 11^' 


Mh i ! I 


ilni / 1 ' 


mil ' 1 1 / 


o.n tlwMt-^-^ t t 1^ 


^0 Illy m J t 1 1 


Mr^hn'- 1 ^ 


• l%Uim-i4^t-. t ^ 


+-• mktuttl-i Z ^-.^1 


^ op; tttUtttu r ti ^ 


I ^^ ^Auuttj.4 ^7 J. ^2 


- MuMUtttl t tfj^^ 


\' ^mUutu^t4 <^j t ^ 


% mt%iuTi4 t m ^ 7. 


t on .^mUulttttj. jM^TjZ^ 


6 ^^ kmttt-U4 t uv.j' 1 


1 MtutT-tti^ 7 '_,^ J. 


t ZMt%7-t4^ tj^thLv 


S MUmTttj- TZj-^v^^Z 


^ ,R mmu4^-/4%w^ 2^v. 


t%%tTttJ fl^l/^ /.'T 


^ 4%%%lti4jl//JX^J^ y 


tm%7-ttiJ7:^'^7^^^s.^'^ 


iS2z5 //_,/' y 7.y ' k 


,0 JMZZCv Z/Z^^^ ^^ ^ , 


'^ M2Z7ZZ/^Z^ .^^^^^^0.^^ 


^m%zi/.'^ziz^^ 7- #"■ 


it J»24^$iz^^^/ ^"^ ^• 


tm^ttt/^' zz.^' y ^^^Tuw- 


iMMyyy^^yyy .^ ^^ ---^ jTcop-" 




^^g^>^/;<^< X •'^^^ -''■ ^-^" qq' - " 


J^^^^yf^'^'^^l^'^,.' ^ _ ^ -^ "^ ^0,2-- 


y '^^^^ ^ ^^ r'^'C--^"^" --■'"' 


^ ^^' —i^^^^j^ --- — 



50 



100 



150 200 



250 



Distance in feet measured along the curve from the P.C. orP.T. 

Pig. 81. 

The following instructions accompany the chart: 
In measuring up to the P. L, leave temporary markers at 
enough points so that the line of the tangent can be readily lo- 
cated by eye. From the newly located P. I. turn off the desired 
deflection angle. Determine the degree of curve necessary to 
fit the conditions from the external and tangent length and take 
from table the tangent and length of curve, and record the station 
of the P.C. and P.T. Make the curve correction for difference in 
length of the sum of the tangents and distance on the curve at 
the P.I., and start measurements along next tangent, leaving 
temporary markers up to the P.T. of the curve. To lay out 
curve, start at the station or plus station near the P.C. and 
measure along the curve, using standard chord lengths, and 
using the offsets from tangent as read from chart, which increases 
as the distance from the P.C. or P.T. increases. 

To be useful a chart of this kind should be drawn to a larger 
scale than we can reproduce in a handbook of this size and this 
has been inserted more to show a convenient method than for 
actual use. In the same manner a chart can be prepared for short 
radii curves from 40' radius to 150' radius that is very useful in 
mountain road location. 



390 



THE SURVEY 



should be fully explained in the notes. The computations of level 
notes should be made in the field and checked each night. 

Profile Levels. — These levels also act as a check on the bench 
levels and therefore require an independent line preferably run in 
the opposite direction. The turns are read to the nearest o.oi 
foot and the profile ground elevations of the base line to the nearest 
O.I foot. In case there is no radical difference in the two lines of 
levels (Bench and Profile) the profile levels are corrected to agree 
with the bench levels at each bench and carried ahead on the bench 
elevations. This is done so that there will be no cumulative differ- 
ence in the levels. An error of o.i foot in running between* benches 



Sfa. 


Sample Bench Levels 


\ 


r^ 11 1 1 1 1 1 1 

Aua I. IcilR 


iiljl 1 MM' '"N 
Cate\ Level 


i- H.l. - Elev. 


1 Remarks 


Thoma5 Rod 












r^ 


A IIIIIIIM 


IMIII " " 


d.M.O. 








52^.?l 


\j 


Y-5-65-5enchcTtHet 


^er. Bron^i ' 


■A^ 


10.43 


5258.64 








Tab let in School 


House. 


T.R 






2.14 


5256.50 








7^ 


6.91 


5265.41 












T.R 






1.22 


5255.19 








7^' 


9.33 


5267.52 












B.MNo.l. 






5. 16 


5262.36 




Spike in Blazed Pi 


neTree lOO'Rtof 


n 


IA7 


5263.83 








Srh. 10-^20 




T.R 






8. 72 


525511 


































r\ 


-r\ - - 
















































































































































































_/\ 














o- 


-\J- -- 




















,__,., 










j 


^ . 


-r- -p 



is allowable (see Figure 82 for sample profile level notes). Level 
computations should be figured and checked each night and a pencil 
profile plotted for the convenience of the locator. 
Second Stage of Work 

(a) Cross-sections. 

{h) Topography. 

{c) Drainage. 

(d) Classification of materials. 

{e) Field drafting. 
{a) Cross-sections. — Cross-sections are the most important 
part of the detail work on survey. The tendency is to slight this 
part of the work as it is tedious and uninteresting. The author 
has seen so much trouble experienced in the office design due to 
inadequate cross-section field work that he wishes to emphasize the 



CROSS-SECTIONING 



391 



importance of taking wide enough sections particularly wjiere a 
paper location is contemplated. 

In level country where center line is exactly run 30 feet each 
side of the center line is enough. 

In hilly countr}^ on side slopes averaging 25° where the center line 
is exactly located 60 feet each side of the line is enough. 

Where the center line is not exactly located the engineer must 
use his judgment but as a rule it is not safe to use less than 100 
feet each side of the line. 

For switchback turns or where a large variation from the survey 
base line is probable a careful stadia survey is desirable. 



C " 


Profile 


Level 




^ 


( yoq'4.)3]8\\ 


M~6uire LeveP" 


Turninq Poinfs 


Remarks: 

1 


Thomas Rod 


9^af/on 


+ 


^ 


H.I. 


"^W 


Elev. r-) 






















B.M.O 










524821 


U.S.eS. School House 


, He her 


7R 


10.20 




5258fH 






llllllllllll Mil 


1 MM 











11.2 


47.2 


Sfa. OfoS No Clean r 


qorOrubbinct- 


1 








10.7 


477 




" * 


2 








9.5 


46. e 






2f25 








8.2 


50.2 






3 








5.1 


53.3 






4 








2.7 


55.7 


Putin l2"Cor.Iron 1 


''ipe. 


5 








2.4 


56.0 






T.F 




2.33 






5256.06r\ 


_r\ 




^ 


8.10 




5264.18 






:2:::::::::::::::; 




e 








8.0 


56.2 


Clean nq Sfa. 5 to 10 . 


Scrub Oak 


e-t2F 








6.5 


573 


" 




7 








e.o 


58.2 






8 








53 


583 






.9 








4.1 


eo.h 






10 








3.1 


61.1 






B.M-No.l. 




1.65 






5262.33 


Be rich Levels 5262.3 


^ Use this 


7^ 


5.27 




526763 


Correc 


ied. 


Elevation Forward 














































Qr 


— 
































^ 





Pig. Z2, 

In flat country cross-sections are taken with the engineers level, 
rod and metallic tape in a similar way to the methods described 
in the first of this chapter for high class improvements. 

In rough country they are generally taken with a hand level, 
rod and tape and each section is referred to the profile ground 
elevation of the base line (see sample notes, Figure 83). The abso- 
lute elevation of each point is figured from the base line ground 
elevation. This is important as while it entails more field com- 
putation they can be done at night, and by the use of the ab- 
solute elevations the office and design work is made simpler, 
cheaper and more accurate. Experience has demonstrated that 
the method of absolute elevations for cross-sections is much superior 
and cheaper in the end than relative elevations. 



392 



THE SURVEY 



Cross-sections are taken at all breaks in the profile and in uniform 
topography at least every loo feet and preferably at shorter 
intervals. 

Special cross-sections are taken for all drainage crossings and 
show the skew angle of the proposed structure (see Figure 83). 

Cross-section notes should be computed and checked each night. 

(&) Topography. — Taken in the same manner as previously 
described (see sample notes, Figure 84) . 

(c) Drainage. — Field drainage notes on new locations must be 
detailed and specific as the recommendations determine the ofiice 
design absolutely; there is no possibility of the designer checking 
the conclusions. 




Such notes should be made personally by the chief ot party and 
should indicate exactly where he wants' the culverts or bridges 
placed and the size of opening of the structure. He uses the 
principles discussed in the chapter on drainage, and determines 
the size of waterway either from the physical evidence of high water 
or from the area of the drainage basin. Areas can be run out by 
paced, hand compass traverses, determining the divide lines with 
a hand level or can be plotted directly in the field on a small 9" 
or 15" plane table. 

The type of structure as log, corrugated pipe, concrete box, etc., 
should be stipulated for each structure, as the field man is the only 
one who can decide on the best type, considering the local materials 
that are available. 



SAMPLE NOTES 



393 






stall 



IS" 

\ 
\ 

\ 



5fa.l0 



Fig. 83. 



SM-ion 


Topo graph q Nofes 




rW/5// M\m\ ^ 


Remarks: 




r^5ufri, Ta;)l 















_C SH^e-hztf --- -- 










































, . , „ . . . (j 12+31 Q 


.12 












f^ n i 














\....JMLll^imJjf - 














ninr *" - » ^'hiai ■ 


10 








' 




\\ T^^f^ W r 














t^rt"" ■ * 














:::::::::|/z!|^r?:::::;:::: :" 


6 












§..._. ..I 












D 


_r ^j..l l-r--~. - . - 












\J 


^ Ml!r>^c:J 


6 












-'''''" 1 














i . t^+i". 














1 m 


4 


























'^'^^7'<3?^:-«-5{?> ^^?: 














J_ I4!'|v,t tin 


2 












:::::::::;s^^:;1l?:::::": :: 














School ^ ^f^)^ ^^ C T^(f ^ 














Hoii^fi ^hl^n' . . -A, . . . 


0-f-O 










^N 


'^ V . 































I 












^: ::;;;::::: :::::;:;:; = ^;:;:;:;:: ;^ 



Fig. 84. 



394 THE SURVEY 

{d) Classification of Material. — The classification of material 
has a marked effect on office design and should be handled by the 
chief. The expenditure of considerable time and money is justified 
in determining the sub-surface conditions within the probable 
limits of proposed excavation where there is reason to believe that 
solid rock will be encountered. This is done by bar soundings and 
test pits. Where the soil contains a large percentage of boulders 
bar soundings are of little value. As a rule it is impracticable to 
determine more than a general classification for the largest part of 
the distance unless rock outcrops show on the surface. 

(e) Field Drafting. — The field drafting should be confined to 
special problems desired by the chief and should only be done 
where there is doubt as to whether sufficient field data has been 
obtained for the office design. 

Complete design in the field is costly and is rarely as satisfactory 
as office design. Camp is no place for careful design. 

Location Survey Reports. — A report should be worked up as the 
survey progresses. The object of this part of the record is to make 
it possible for a man not personally familiar with the ground to 
make a reasonable design. It should include all information of a 
general or special nature not shown in the survey notes such as: 

1. A description of the general topography. 

2. A description of alternate locations and the reasons in detail 
for the selection of the route surveyed. 

3. A statement of the portions of the line where the survey 
alignment should be rigidly adhered to and an undulating grade 
used. 

4. A statement of the portions of the line where the alignment 
can be shifted to fit a grade contour and a ruling grade adhered to. 

5. The portions of the line where both line and grade can be 
varied in the final design. 

6. Snow conditions and how bad exposure is avoided or why 
it can not be avoided. 

7. Special designs to fit unusual conditions. 

8. Special designs utilizing supplies of nearby local materials. 

9. Photographs to illustrate special features or to give a general 
idea of conditions. 

Determination of True North. — The simplest method of deter- 
mining the true meridian is by observation on Polaris at elongation. 
For all practical purposes fairly close results can be obtained by 
observation on Polaris or the Sun at any time. The following 
tables and explanation of simple methods are quoted or briefed 
from the Manual of the United States Geodetic Survey on Mag- 
netism and the determination of the true meridian, and the Metro 
Manual of the Bausch & Lomb Optical Co. 

Meridian by Polaris at Elongation. — For all practical road 
survey purposes a determination of the meridian to the nearest 
minute of angle is sufficiently close. For one-half hour before 
elongation to a half hour after elongation the azimuth of Polaris 
does not vary over 30 seconds of angle which gives plenty of time 
for check determinations and the element of exact standard time 
is of little importance. 



POLARIS MERIDIAN 395 

The following instructions for determining meridian at elongation 
by transit observation and by plumb line and peep sight are quoted 
from the U. S. Geodetic Manual. 



SIMPLE METHODS FOR DETERMINING THE TRUE 
MERIDIAN BY OBSERVATIONS ON POLARIS^ 

(U. S. Geodetic Manual) 

I. To Determine the True Meridian by Observation on 
Polaris at Elongation with a Surveyor's Transit 

(Be sure transit is in good adjustment) 

^' I. Set a stone, or drive a wooden plug, firmly in the ground 
and upon the top thereof make a small distinct mark. 

*' 2. About thirty minutes before the time of the eastern or western 
elongation of Polaris, as given by the tables of elongation. No. 33, 
set up the transit firmly, with its vertical axis exactly over the 
mark, and carefully level the instrument. 

''3. Illuminate the cross hairs by the light from a bull's-eye 
lantern or other source, the rays being directed into the object 
end of the telescope by an assistant. Great care should be taken 
to see that the line of coUimation describes a truly vertical plane. 

*' 4. Place the vertical hair upon the star, which, if it has not 
reached its elongation, will move to the right for eastern and to the 
left for western elongation. 

*' 5. As the star moves toward elongation, keep it continually 
covered by the vertical hair by means of the tangent screw of the 
vernier plate, until a point is reached where it will appear to remain 
on the hair for some time and then leave it in a direction contrary 
to its former motion, thus indicating the point of elongation. 

" 6. At the instant the star appears to thread the vertical hair, 
depress the telescope to a horizontal position; about 100 yards 
north of the place of observation drive a wooden plug, upon which 
by a strongly illuminated pencil or other slender object, exactly 
coincident with the vertical hair, mark a point in the line of sight 
thus determined; then quickly revolve the vernier plate 180°, 
again place the vertical hair upon the star, and, as before, mark 
a point in the new direction; then the middle point between the two 
marks, with the point under the instrument, will define on the 
ground the trace of the vertical plane through Polaris at its eastern 
or western elongation, as the case may be. 

*' 7. By daylight lay off to the east or west, as the case may re- 
quire, the proper azimuth taken from the Table 34; the instrument 
will then define the true meridian, which may be permanently 
marked by monuments for future reference." 

1 In the preparation of this article use has been made of the United States 
Land Office Manual of Instructions, Washington, 1896, 



396 



THE SURVEY 



Table 33. — ^Local Mean (Astronomical) Time or the Culmi- 
nations AND Elongations of Polaris in the Year 191 5 

(Computed for latitude 40° north and longitude 90** or 6^ west of 

Greenwich) 



Date 



East 
Elongation 



Upper Cul- 
mination 



West 
Elongation 



Lower Cul- 
mination 



191S 



Hr. 



Min. 



Hr. 



Min. 



Hr. 



Min. 



Hr. 



Min. 



January i 

January 15. . . 
February i . . . 
February 15. . 

March i 

March 15. • • 

April I 

April 15 

May I 

May IS 

June I 

June 15 

July I 

July IS 

August I 

August 15. . . . 
September i . 
September 15 
October i . . . . 
October is.. • 
November i . , 
November 15 
December i . . 
December 15. 



46.9 
SI. 6 
44 S 
49-2 
S4 o 
58.8 

iL3. 



52.9 
50.0 
55.1 
48.5 
S3 -7 
SI. I 

S6.3 
49-7 
SSO 
48.4 
S3S 
SO. 7 
SS.8 
48.9 
S3. 8 
SO. 8 
S5.6 



42.1 
46.8 
39-7 
44-4 
49.2 
S4 o 
47.1 

S2.0 

49.2 

54-2 
47.6 
52.8 

^jO.2 



51.5 
44.9 
50.2 

43-6 
48.7 
45. 9 
510 
44 I 
49.0 
46.0 
50.8 



44.9 
49.6 
42. 5 
47.2 

52.0 

56.8 

49 9 

54-8 
52.0 
57 o 
50.4 
55-6 
53.0 
58.2 
51.7 
56.9 
SO. 3 
55.4 

,g2J^ 



53.8 
46.9 
51.8 
48.8 
53.6 



A. To refer the above tabular qtmntities to years other than 191 5. 



For year 1919 add 
/add 

1921 add 

1922 add 

1923 add 
TOO. /add 
^924 1 add 

1925 add 

1926 add 

1927 add 
'add 

add 



1928 1 ; 



2 . 5 minutes 

4 . o up to March i 

o . I on and after March i 

1.6 

31 

4-5 

5 . 9 up to March i 

2 . o on and after March i 

3-3 
4.6 

5-9 

7 . 2 up to March i 

3 . 3 on and after March i 



B. To refer to any calender day other than the first and fifteenth 
of each month subtract the quantities below from the tabular quantity 

for the PRECEDING DATE. 




Pases .106 and 397.') 



POLARIS MERIDIAN 



397 



Day of Month 


Minutes 


No. of Days Elapsed 


2 or i6 


3-9 


I 


3 17 


7.8 


2 


4 i8 


II. 8 


3 


5 19 


15.7 


4 


6 20 


19.6 


5 


7 21 


23.5 


6 


8 22 


27.4 


7 


9 23 


31.4 


8 


lo 24 


35-3 


9 


II 25 


39.2 


10 


12 26 


43.1 


II 


13 27 


47.0 


12 


14 28 


5I-0 


13 


29 


54.9 


14 


30 


58.8 


15 


31 


62.7 


6 



C To refer the table to Standard time and to the civil or common 
method of reckoning: 

(**) Add to the tabular quantities four minutes for every degree 
of longitude the place is west of the Standard meridian and Sub- 
tract when the place is east of the Standard meridian. 

(^) The astronomical day begins twelve hours after the civil day, 
i.e., begins at noon on the civil day of the same date, and is reckoned 
from o to 24 hours. Consequently an astronomical time less than 
twelve hours refers to the same civil day, whereas an astronomical 
time greater than twelve hours refers to the morning of the next 
civil day. 

It will be noticed that for the tabular year two eastern elongations 
occur on January 14 and two western elongations on July 13. 
There are also two upper culminations on April 14 and two lower 
culminations on October 14. The lower culmination either follows 
or precedes the upper culmination by ii'' 58"*.o. 

D. To refer to any other than the tabular latitude between the limits 
of 10® and 50° north: Add to the time of west elongation o"*.io 
for every degree south of 40° and subtract from the time of west 
elongation 0*^.16 for every degree north of 40°. Reverse these 
operations for correcting times of east elongation. 

£. To refer to any other than the tabular longitude: Add o"*.i6 
for each 15° east of the ninetieth meridian and subtract 0^.16 
for each 15** west of the ninetieth meridian. 

Standard Times in United States 
(Mean solar for the following meridians) 

Eastern time 75 th meridian standard 

Central '' 90th 

Mountain " 105th " " 

Pacific " i2oth '' '' 

(See plate No. 39.) 



398 



THE SURVEY 



00 
0\ 


O 


o w ^o a 


N lO Ov NvO 


M lo O »0 O 


vO N 00 lO w 


On t^»0 rfro 


uDvOOOvO 
O O O O O 


l> t^ t^OO 00 

o o o o o 


On OnO O m 

O O H M M 


i-i (N <N ro Tf 


rfiovO t>.oO 


M 


- 


<N Tj-t^Ov <N 


lOOO (NO O 


Tfoo r/)oo Tt- 


OMO (NOOnO 


fO M OnoOvO 


>o o o o t^ 
o o o o o 


t-.t^oooo a 

o oo o o 


On On O O M 

O O M M M 


M M M M M 


»ONOvO.b-00 

M M H M M 


M 


o 


lO l^ O C^ lO 


00 (N »r> 0\ fO 


t^ N O M t^ 


ro On VO N On 


NO "^M w O 


vOvO t-t- t- 

o o o o o 


r-oooo 00 On 
O O O O O 


OnO O M M 
O M M M M 


N cs ro -^ -^ 


»onO t-00 On 




o 


00 O roOoo 


M IDOO (N vO 


O lO o »o o 


nO <N OnnO C^ 


OOOO lOrf 


o o o o o 

M 


00 00 00 O On 
O O O O O 


O O M M (S . 

M M M M M 


N fO ro ■^>o 


vOO t^oo On 

M M M H M 




o 


f^ rfOoo (N 


lOOO N to 0\ 


rfoo rooo rf 


O nO N OnvO 


Tl-N ooooo 


o o o o o 


00 00 On Ov 0\ 
O O O O O 


O O M w (N 


fO fO rf Tj-io 


vO t^oO 00 On 


M 




Tt t^ 0\ <N !>:> 


00 M lOOO (N 


t^ M\0 N t^ 


(T) OnvO N O 


t^lO fO N M 


t^ t-r-oo 00 

o o o o o 


00 On O O O 
O O O O M 


O M i-i ri oj 


fO ro Tl-iOvO 

H4 M M M M 


vO t^oo On O 

M M H M M 


0\ 


o 


00 O <N lOOO 


M •rtOO (NO 


o »o O lO o 


vo <^ ao ro 


O On t^O »0 


t^OO 00 00 00 

o o o o o 

H 


On On On O O 

O O O M HH 


M M N (N fO 


CO "^ rf lOvO 


t^ t--00 On O 

H M M M N 




o 


M r0"O 00 M 


TfOO M ioOn 


•<too rooo Tl" 


O t^ (N 0\0 


rtM M OnOn 


00 00 00 00 0\ 

o o o o o 


gg222 


M M CNi N r<3 


Tfrf lo loO 


t-oo On On O 










o 

0^ 


o 


rfO a> M rt- 


t^ M Tfl^ (N 


i> fs vo cs r^ 


roONvO re O 


OOO "tfO N 


00 00 00 a a 
o o o o o 

M 


OnO O O M 

O M M W M 


M cj M ro fO 

M M 1-1 M M 


TfTt lOvO t^ 


t^OO On O w 

M M M N CS 


M 
O 
H 


o 


b-a <^» "^t- 


O Tl-OO mnO 


O »00 liO H 


t-roONvO "^ 


M onoo r^NO 


CO 00 Ov 0\ 0\ 

o o o o o 

M 


O O O M M 


N CN ro ro ^ 


Tfin lovO t^ 


00 00 OnO M 
M M M CS N 


00 
M 
0\ 
M 


o 


O M »O00 O 


rht^M ioOn 


rooc r^oo rt 


OnO POO t> 


lOCO w O O 


0^ OOsOO 
O O O O M 

H 


O O M M M 


M N ro ro ■^ 


H M M H H 


00 On O w (N 
M M (N N (N 


1 


o 


O M N PO Tt 

M M M M M 


too t^OO o> 

M M M M M 


O M M ro ■^ 

N Cl CS CS M 


lOvO t^OO O 
M <N 0» <N <N 


O w (N ro ''f 
rOfOfOrofO 



POLARIS MERIDIAN 



399 



N <N ro -rtm 


t^O fO t>M 


00 ^ N O On 


O 

M 


0\ O "-" N ro 
t-i N W (N CS 


Tj-vO t^OO o 
M c^ (S M ro 


M ro v> t^oo 
rororororo 


vOOvOOO O 


M Tj-00 MO 


<N ao 't'?*- 


M 


0\ O M (N CO 
M C< <N Ol M 


»oO t>-Ov O 
N « cs N fO 


M roiO t^ On 
fOrororo ro 


O O O <N fO 


lOOO (NO M 


O ro M 0\ 0» 


0\ 

M 

M 


O M N fO Tt 

N N N M CN 


lOOOO Ov M 
N c^ N (N ro 


M T^O t^O\ 
ro roro ro fO 


-^f rt rj- to l> 


O NO O lO 


M 00 vo •rfro 




O M (N CO Tt 
M M CS CS «S 


»o 1^00 O w 
cs N <N ro ro 


ro rtO 00 O 
ro rororo '^ 


t^t^OO O M 


roo O "^a 


ir> M O 00 00 




O M (N roio 
N CS IN N CS 


O t^a O M 
N PJ M ro ro 


rou^ t-oo O 

ro roro ro "I- 


M H <S fOlO 


t>.0 -^00 Tl- 


GO '^fO ro 


ro 


M CI r*5 '^ lo 

N N W CS CN 


OOO 0\0 <N 
M N r^ ro ro 


-^lOt^ON M 

ro ro ro ro ■^ 


i/^i/^O t^oo 


M Tl-00 N 00 


Tt M O\00 i-- 


00 
ro 

M 


N «S CS (N cq 


t^OO 0\ M <N 

M r^ N ro ro 


rfO t>-0\ M 

ro fO ro ro rf 


00 On O M fO 


lOOO C» 00 <N 


00 ir» ro r? N 


ro 


N (N N CS (N 


l>oo O w ro 

M c^ ro ro ro 


•^Ooo O c^ 
fO ro ro ^ ^ 


M 


<N rO fO I'J »> 


OnmO mo 


ro Ooo t^ t^ 


00 

5 


N (N CS M M 


t^ O O c^ ro 
<N M ro fO fO 


»o t^OO O c^ 

ro ro ro -^ ■^ 


OO r^ 0\ H 


roo O lo M 


t^ Tf N ISl M 


ro 

M 


<N (N (N CS <N 


00 0\ M N "=t 

w c>< ro ro ro 


vo i> 0\ M ro 
ro ro ro^t Tf 


O O M <N IT) 


t>o »oO\ir> 


MOO t^OO 


M 


(N N <N M <N 


00 O M <N Tt 

N rOPOroro 


O t^ On M ro 
roforo -"^Tj- 


too 1^00 0\ 

ro PO fO fO f*5 


O M p< ro^ 


ir>0 t-oo On 


o 

lO 



400 



THE SURVEY 



Table No. 34 was computed with the mean declination of 
Polaris for each year. A more accurate result will be had by 
applying to the tabular values the following correction, which 
depend on the difference of the mean and the apparent place of the 
star. The deduced azimuth will, in general, be correct within o'.3. 



For Middle of Correction 


For Middle of 


Correction 


January 

February 

March 

April 

May 

June 


-05 
-0.4 
-0.3 
0.0 
+0.1 
+0. 2 


July 

August 

September 

October 

November 

December 


/ 
+0.2 
+0.1 
— 0. I 
-0.4 
-0.6 
-0.8 



II. — To Determine the True Meridian by Observation on 
Polaris at Elongation with a Plumb Line and Peep Sight 

" I. Attach the plumb line to a support situated as far above the 
ground as practicable, such as the limb of a tree, a piece of board 
nailed or otherwise fastened to a telegraph pole, a house, barn, or 
other building affording a clear view in a north and south direction. 

" The plumb bob may consist of any weighty material, such as a 
brick, or a piece of iron or stone, weighing 4 to 5 pounds, which 
will hold the plumb line straight and vertical fully as well as one of 
turned and finished metal. 

" Strongly illuminate the plumb line just below its support by a 
lamp or candle, care being taken to obscure the source of light 
from the view of the observer by an opaque screen. 

*' For a peep sight, cut a slot about one-sixteenth of an inch wide 
in a thin piece of board, or nail two strips of tin, with straight 
edges, to a square block of wood, so arranged that they will stand 
vertical when the block is placed flat on its base upon a smooth 
horizontal rest, which will be placed at a convenient height south 
of the plumb line and firmly secured in an east and west direction, 
in such a position that when viewed through the peep sight Polaris 
will appear about a foot below the support of the plumb line. 

" The position may be determined by trial the night preceding 
that set for the observation. 

" About thirty minutes before the time of elongation, as given in 
the tables of elongation, bring the peep sight into the same line 
of sight with the plumb line and Polaris. 

" To reach elongation the star will move off the plumb line to the 
east for eastern elongation, or to the west for western elongation; 
therefore by moving the peep sight in the proper direction, east 
or west, as the case may be, keep the star on the plumb line until 
it appears to remain stationary, thus indicating that it has reached 
its point of elongationc 



POLARIS MERIDIAN 40I 

" The peep sight will now be secured in place by a clamp or weight, 
and all further operations will be deferred until the next morning. 

" By daylight place a slender rod at a distance of 200 or 300 
feet from the peep sight and exactly in range with it and the 
plumb line; carefully measure this distance. 

",Take from the Table 34 the azimuth of Polaris corresponding 
to the latitude of the station and year of observation; find the 
natural tangent of said azimuth and multiply it by the distance 
from the peep sight to the rod; the product will express the distance 
to be laid off from the rod exactly at right angles to the direction 
already determined (to the west for eastern elongation or to the 
east for western elongation) to a point which with the peep sight 
will define the direction of the true meridian with a fair degree 
of accuracy," 



To Determine the True Meridian by Means of an Obser- 
vation OF Polaris at Any Hour when the Star is Visible, 
THE Correct Local Mean Time Being Known^ 

" This method requires a knowledge of the local mean time within 
one or two minutes, as in the extreme case when Polaris is at 
culmination its azimuth changes i' (arc) in 23^ minutes (time). 
The Standard time can usually be obtained at a telegraph office 
from the signals which are sent out from observatories. From this 
the local mean time may be derived by subtracting four minutes of 
time for every degree of longitude west of the Standard meridian 
or adding four minutes for every degree east of the Standard me- 
ridian. The local mean time may be obtained also by observa- 
tions of the sum, one method being ^explained later. 

* * The following table, 35, is intended to be used in connection with 
the American Ephemeris and Nautical Almanac. The surveyor 
should read carefully the chapter in that publication in which 
the formation and use of the Ephemeris are explained, especially 
the portion defining the different kinds of time. 

''•'The following example explains the use of the table and the 
derivation of the hour angle of Polaris:" 

Position,- latitude 36° 20' N., longitude . 80° oy'.s or s^ 20'" 30* W. of 

Greenwich. 

h. m. s. 
Time of observation, July 10, 1908, standard (75th mer.) 

mean time 8 52 40 p. m. 

Reduction to local time (5° 07' west of 75th mer.) — 20 30 

Local mean time 8 32 10 

Reduction to sidereal time (Table III, Amer. Ephem.) . . + 01 24 

Sidereal time mean noon, Greenwich, July 10, 1902. ... 7 12 02 
Correction for longitude s^ 20"* 30s (Table III, Amer. 

Ephem.) + 00 53 

Local sidereal time 15 46 29 

Apparent right ascension of Polaris, July 10, 1908 i 26 05 

Hour angle before upper culmination 9 39 36 

1 cf. Appendix No. 10, Coast and Geodetic Survey Report for 1895. 



402 THE SURVEY 



Declination for which Table 35 applies 88 51 

Apparent declination, July 10, 1908 88 48.7 

Decrease in declination — 2.3 

Azimuth from Table 35 (interpolated) ... 48 39 

Correction for 2'. 3 decrease in declination. + i 37 



Computed azimuth 50 16 East of north. 

"It is to be remembered that Polaris is east of the meridian for 
twelve hours before, and west of the meridian for twelve hours 
after, upper culmination. 

"Without the American Ephemeris the table' may be conveniently 
used for obtaining the true meridian, in connection with Table 2>2> 
giving the approximate mean times of culminations of Polaris, 
and the additional knowledge of the fact that the mean declination 
of Polaris is 88° 51'.! in 1915 and increasing at the rate of about 
o'.3 per year. Without the use of the Ephemeris the computation 
would be as follows: 

h. m. s. 
Time of observation, July 10, 1908 standard (75th mer.) 

mean time 8 52 40 p. m. 

Reduction to local mean time — 20 30 

Local mean time 8 32 10 

Local mean time of upper culmination of Polaris (Table 

33 and A) 18 10 12 

Mean time of observation before upper culmination 9 38 02 
Reduction to sidereal time -f- 01 35 

Hour angle before upper culmination 9 39 37 

o / 

Declination for which Table 35 applies ... 88 51.0 
Mean declination, 1908 88 49 - o 

Decrease in declination — 2.0 

o / /r 

Azimuth from Table 35 o 48 40 

Correctionfor 2'. o decrease in declination. + i 24 

Computed azimuth o 50 04 East of north. 

Tables are generally given in books on surveying for reducing 
mean solar to sidereal time, but for this computation it is near 
enough to consider the correction 10* an hour, as the stars gain 
very nearly four minutes on the Sun each day."^ 

Solar Meridian by Direct Observation with an Ordinary Transit. — 
Where the method of Polaris at elongation is not used, Direct 
Solar Observation is the most convenient method of meridian 
determination as while it involves more computation and introduces 
more chances of error the work can be done during daylight hours 
and the accuracy that can be attained (within 01' of arc) with 
the usual facilities is close enough for all practical purposes of 
ordinary surveys. 

1 The sidereal correction always increases the hour angle. 



SOLAR MERIDIAN 403 

There are a number of different forms of the fundamental 
formulae governing the determination; the following form has 
found considerable favor: 

sin [5 -(90°- alt.)] sin [5—(90° - lat.)] 
sm sm [o — (90 — dec.) J 

In the formula A is the angle of the sun from the true north 
measured to the right in the morning and to the left in the afternoon. 

S is one-half the sum of (90° — the observed altitude of the sun 
corrected for refraction) plus (90° — the latitude of the point of 
observation) plus (90° — the declination of the sun at the time 
of observation). 

Note. — Notice carefully the sign of the declination. A south 
declination is a — declination which would make the expression 
(90° — ( — south declination)) = 90° + south declination. 

A solar ephemeris from which the sun's declination is found 
is necessary for the computations. All instrument makers publish 
small pocket editions each year which can be obtained from them 
for ten cents. 

An ordinary well regulated watch set for standard time at 
the nearest telegraph office serves for the time determination on 
which the sun's declination depends and any good transit with 
vertical circle can be used for observing the horizontal angle and 
altitude of the sun 'but observers are cautioned that it must be 
in good adjustment and the observer must work with reasonable 
care. 

If standard time is not available mean local time can be determined 
by observation as explained la4er on page 413. 

The latitude of the point of observation can generally be deter- 
mined closely enough from U. S. Geological Survey Maps or 
Land Office Maps and if these are not available can be determined 
by observation as explained on page 413. 

Longitude for standard time correction can be taken from any 
good map. If these are not available determine local mean time 
by observation. 

Considering all the different sources of error, time, latitude and 
observed altitude the best time of day to make the observation 
is between 9.00 and 10.00 A. M. and between 2.00 and 3.00 P, M. 
{Continued page 412.) 



404 



THE SURVEY 



Correction 
for I' In- 
crease in De- 
clination of 
Polaris 


jfs 


5 


"too po 

1 1 T 


M (N <N (N 
1 1 1 1 


(N vC 0\ (S 

fO fO ro -^ 

i 1 1 1 


lOOO M PO 
Tj- "^ lO lO 

1 1 1 1 


tOt^ON M 
to to IOnO 

1 1 1 1 


N c^ PO PO 

NO NO nO NO 

Mil 


2|-= 


i 


•^00 CN 

1 1 T 


M (N (M (N 

1 1 1 1 


fO fO fO ^ 

1 1 1 1 


rONO On m 
""^■^ -^lO 

1 1 1 1 


rotovCoo 

to to lO to 

1 1 1 1 


OnO O m 

too NO NO 

i 1 1 1 






*. 


O OvO 
»0 CO <>« 


OwOOC (N 


t^ rooo M 


<N On MOO 


On -^(N N 
^O O ^ 


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POLARIS MERIDIAN 



405 



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4o6 



THE SURVEY 



Correction 
for i^ In- 
crease in De- 
clination of 
Polaris 


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POLARIS MERIDIAN 



407 



O^00 l> 
1 1 1 1 


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vO 

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-? 


M M M M 


M 000 vO 
M M 


Tj-MOO TO 
10 10 


P^OO lr>M 
VO TtTt^ 


\C N 00 PO 
PO PO N P< 


ONTtONTt 
M M 


Tt 


8% 






M M 


0000 


0000 


0000 


M 


-Si to 


Tf p*5 CI ro 

10 -^ M <H 




\0 w PJ t^ 

■TfM P^ M 


0\ t^POOO 

UO P^ Tt Tt 


POOO 1010 

TtN PO 


On On TtoO 
to M ro Tt 


to 
to 


^^ 


roPOPON 

M M M M 


M OvOO vO 

M 


PO l-l 00 10 

10 10 


MOO TtO 
UOTt TtTt 

0000 


vO woo PO 
PO PO N P^ 

0000 


00 TfONTt 
M M 

0000 


PO 


gOO 

5 10 

-Si to 










^^XO 


t^ M 0\ 
'^N POPO 


N On I> 
N Tj-O »0 


0\ l^PO 

Tl-O p< PO 


OnvO in t^ 

P> M 10 P< 


PJ PO MVO 
10 M PO Tt 





«o2^ 


M M M H 


Ot^vi 

H 
M M M M 


POOOO rt 
lOVO 

M M 


MOO -to 

lOTt Tt^ 
0000 


\0 PI r^ PO 
PO PO C^ <N 

0000 


00 TtON Tt 
W M 

0000 


PO 

M 
M 


^ to 


>o »J^ 

M PO Tl- 


w^O v: 

M PO Tt 


li^ 10 
M PO ""t 


100 V) 

M POTt 


»0 V5 

M PO Tt 


too to 

M PO-^. 


U 


^ 




vOvOvOO 


t^l^ t>» b- 


00 00 00 00 


OOvOnOn 


0000 

M M M M 


MM M M W)S 


a 




4o8 



THE SURVEY 



Correction 

for I' 

Increase in 

Declination 

of Polaris 


Lati- 
tude 
40° 


- 


lO OO 

1 "{^ 


MVO HVO 

P« M roco 
1 1 1 1 


tn 0\ ro 

Tt'-t ^10 

1 1 1 1 


t^O fOO 

toooo 

1 1 1 1 


0\ N "^to 
l^ l^ t^ 

i 1 1 1 


r^oooo 
1 1 1 1 


j5" 


- 


lOOvrl- 
1 1 T 


00 CO t^ H 
M c< M ro 

1 i 1 1 


to 0\ roO 
roro rl■»t 
l 1 1 1 


roOOO 
10 10 to to 

1 1 1 1 


M CO TfO 
0000 

1 1 1 1 


MM 


So 

00 

c 

.2 

a 
a 

a 

s 
1 

a 

e 

o 
U 
«) 

•n 

*o 
:2 

a 
< 




o 


O t- <N 

O »o >o 

O M t^ 
OHM 

o o o 


NO H »» 
rtCS O C^ 

roaioo 

N N ro -^ 
O O O O 


N to 10 On 

'^'^roO 

too too 
rj-io to 

M 


00 0\ csO 
c< cs M ro 

rl-oo <N to 
H M 

M M M M 


rototo 

■"^M rtTt 
00 M CO to 

M C» CS N 

M M M M 


COOO 000 
c^ ro ro »0 

t^oo On On 
N M N N 

M M M M 


*3„ 


o 


Ttt^VO 

lOTl-fO 

lO M t^ 

O M M 

o o a 


M 0\0 M 

rooo tJ-On 
O O O O 


N 000 
^H 

too rfO\ 
Tt to to to 

0000 


M OvOnO 
CO N fO 

CO l^ M ^ 
H M 


M N N M 

ro H coro 

t-O « "^ 
M C>J W N 


t^M PI M 

N H Tf 

t^oooo 

N N W PI 








j5" 


o 


0\ r^ M 

lO M t^ 

O M M 

o o o 


H TtO t^ 

O roo H 

rooo rtO\ 
cs N ro fO 

O O O O 


rooo 0>iO 

N M 10 N 

rtO> rooo 

Tl" TflO to 

0000 


r- MOO t- 
CO roO N 

c^O ro 
H M 


to roO 
W N N 

0\ H ro 

M M N Ci 


1000 0\ t» 
to to PI 

TtOO t- 

N PI p^ PI 








j-2 " 


- 


TtN O 

to M t^ 

O M M 

o o o 


N H N Tt 

-"tM rOTf 

MOO rooo 
o« cl rofO 

O O O O 


TtrOH ro 

rooo ro t^ 
-<tTj-toto 

0000 


to t^ M t^ 

tJ-co h W 

M lOO\« 
H 


roO ixs 

N H M 

1000 N 

M M C« W 


On On t^ 

'"ttOTj-M 

fOTftOO 
N PJ PI PI 








■m 


■ 


OOO ro 
rJ-M in 

1/5 mnO 

O M M 

OOO 


Tj-OO lO "^ 

CS rtO H 

N t^ rooo 
N N ro ro 

O O O O 


«s 00 N w 
M voroto 

POt^ <NO 

Tj-TtlOtO 

0000 


too 
to -^M CO 

rfoo M 

H 


TfO\ TfOO 
C« to M 

•^0 0»H 
M M M (M 

M M M M 


M ro ro H 
Tj-io-^M 

PI CO '* to 
N PI W PI 

M M M M 


sf^ 


- 


roO "«t 

1/ MVO 

O M M 

OOO 


»ot- O rj- 
O <N -"t"^ 

N N ro ro 
O O O O 


00 M (SOO 

ro <^ to 

N t^ mO 
Tt^t 10 to 

0000 


to "^tO 

M 10 N CO 

ro r-o 

H 


00 M Tj-t^ 
N H 

roOoo 

M M M CI 


o»o 000 

roto-rfo 

M PI rorf 
M PI PI P< 

M M M M 


rt3„ 


o 


M M t>. 

roo N 

V) MvO 
O M M 

OOO 


OvO lOO 

U^ O M M 
M t^ N t^ 

N c« ro fO 
O O O O 


t^O ro t^ 
^H Ci 

ClO H to 

Tj-TttOtO 

0000 


1000 to ■'t 

N ro -"t 


rtOOO 0\ 
rOO H 

N tOt^ON 

M M M M 


t- 
^tO TfO 

H PI ro 
P« PI PI PI 










o 


t^roO 

Ci I/) M 

li^OO 

O M M 

OOO 


fO rj-io Tf 

M O HvO 

N N ro ro 
O O O O 


t^ ro t^ t^ 

ro H CO "^ 

*-t^ '^ 

rtTttOtO 

0000 


CO TfOO Tt 

•^N rflO 
00 N 1000 

too 

M M M 


rororo't 

-"tH N M 

M TfOOO 
M M M M 

M M M M 


Ttrl-Pi 

Tt to TtH 

OnO h pi 

H PI PI PI 

M H M M 


j5" 


o 


ro»r! Tt 
w Tt O 

w^OO 

O M M 

OOO 


21 19 
26 28 
31 30 
36 24 


00 M CI 

"^O w 

M too Tf 
Tj-Tj-lOlO 

0000 


C^ M COOO 

rl-O 

00 H 1000 
too 


Tt ro N M 
toM ro N 

rotot^ 

M M M M 


M OnOO to 

1010 rfM 

00 OnO H 

M M PI PI 








j5" 


o 


OOO rj- 
w roto 

irsO »o 

O M M 

OOO 


in M On 
H 

MO y^^ 
N w ro ro 

0000 


M M a^i- 

TfM C« CO 

toaro 

T|-'^'<ttO 

0000 


to H ro 
N CI e« 

t^ M rt t^ 
too 


00 toco H 
rO"^PO 

N -to 

M M M M 


0000 ro 
to PI 

00 On OnO 

M M M PI 








m 


o 


t^ M Tj- 

M ro Tf 

IDO W5 

OHM 

OOO 


M rfOvt^ 
loiOTl-ro 

too v> 

c« ct roro 

0000 


to c< t-O 

M TtlOO 

0^00 ro 
■^TftlO 

0000 


00 C* H 


N rJ-iOTt 

0\M coto 
H M M 


M On t^-^ 
M M ro 

1^00 On On 

M M M M 








w"5 




8 t/50 1/5 

• ^ M r«5 Tt 

JS O O O. 


to to 

w ro "^ 

M H MM 


too to 

M ro Tt 

« « N N 


too to 

H roTj- 
rorororo 


too to 
M rOTt 


10101010 



POLARIS MERIDIAN 



409 



00 00 l^O 

t^ t^ t^ r^ 

1 1 1 1 


II 1 1 


rtMOO 

vOOO »o 

MM 


-too (^ 
lOiO -^-^ 

MM 


00 Tj-Os -^ 
fO PO P^ P^ 

MM 


too to 

<N M M 

Mil 


00 PO 

1 + 


OnoO t^ 

MM 


\0 10 ^c< 

MM 


l><^M 

\0 10 to to 

MM 


00 »o PS 00 
^'^'^ro 

MM 


PO PO 0« M 

MM 


00 POOv^ 

^^ 1 1 


?■: 


^0 


t>. M M 

fO»0 rJ-H 


w N Tl-Os 
N M Tj-iO 


t^Ovt^ M 

to po c^ 


-"ttOt^O 

N M lOPO 


tOM fO-t 


to J. 00 

'^ 


O.O\O>00 
ro N w <N 


<N W M <N 


t^TfOvO 
M M M 


PS 00 rl-Os 
lOtO -* 

MOOO 


^O\P000 
^PO PO N 

0000 


CS t^M to 

CJ M M 

0000 


gNO 

P^ « to 

M.<» to 








r-O 000 

•^fOlOTf 


TtOO M Tf 

« fOrOO 


toro 

M M -^O 


-^O <N 
10 CS Tj- 


t^ ro On t^" 
"^"^P^ 


00 POTffO 

POO c^ "t 


%»t 


0000 t>->o 

<N 0« C^ N 


lOPO w Os 

« (>» C« M 


vO POOvO 

M M 


CJ t^ POOO 

to to -^ 

MOOO 


POOO POOO 
rt-POPOP< 

0000 


PS t^M to 

PS M M 

0000 


M^ to 








fO M CO.PO 


-"^O too 
M ro cs to 


TtM OvO 
M M ^M 


rtn-a M 

M fOO 


P^ N C» Tt 

M M "«t 


tooo 

PS to M fO 


PO^ N 


(N (N <N <S 


N N N M 


to C^ 00 to 

M M 


M t^ NOO 

toto^t 

MOOO 


rooo fO !>• 
•st-rOPO <N 

0000 


cso M to 

P^ M M 

0000 


N 5: 10 

M -Si to 








w N W 


t^ to MOO 

N N to 


vO -^toa 

M M 10 M 


t^OoO "t 
C^ <N 10 CN 


0\ PS l> PO 
PO ""tPOPS 


PO t- t^*"* 
POO PO 


M '^ fO 


\00 lOrJ- 
N (N (M (M 

M M M M 


row ao 

«N <N M M 

M M M M 


Tj-M t^Tf 
M M 

M M M M 


OnO m t^ 
lOtO Tf 

MOOO 


PS t^ PS t^ 

rJ-rOfO N 

0000 


(NnO m to 

P^ M M 

0000 


NO gNO 

w fe to 
M-si to 


t^ M Tj-rJ- 
Hi N P< 


N N 


M Tj-M 

cs w PO 


fOOO 0\ 


t^ rtCl PO 
M M 


NO ''too 
•*PS tOPO 


00 ,- Oi 

M «^ CO 


\n\nrtr*i 

<N N <N w 


N 000 
N N M M 


POO t-rO 

M M 


0\ to MVO 

10 to to Tt 

0000 


TffOPOP^ 

0000 


mnO to 

N M M 

0000 


lOgO 
N *= 10 

M J* to 










rf-tTl-lO 

N N 


NO 00 to 
N POM Tt 


OvOO POvO 
to to "^M 


t^oo PO 
po^to^ 


M fO mnO 

fO M to cs 


?-5 


(N <M N CS 


M o\ t^ to 

<^^ M M M 


M 


00 ^00 

lOlOtO Tt 


M \0 M nO 

TtPOPO P^ 


mnO to 

CS M M 


CS 5: 10 


M M M M 


M M M M 


M M M M 


0000 


0000 


0000 


M^ to 


M 10 W (N 


VOOO OM 

<N ro H 


NO M 0\ M 

PO^N 


00 000 "^ 

M N ^ 


00 P» 00 to 
PS N N 


NO P< POPS 
M -"tPS 


M '^ 10 


fO N N M 

(N (N (N e« 


0000 Tt 

C» M M M 


MOO to C^ 
M 


T30 T^o to 
tototo ■>+ 

0000 


M\0 MvO 

"tPOPO P^ 

0000 


mnO to 

es M M 

0000 


PO eo 

p< S: to 

M.« 10 








M N N 


(^ »O00 c< 

M CO ro N 


t^tovO 


0\P0iO PO 

PO'SfPOM 


MOO t-.00 

^too 


N MvO 0\ 
tOPO M 


M "^ 


M P» M 
CS <N N P< 


o\ t^tofo 

M H H M 


t^TfM 
MOOO 


t>.POO\tO 
10 to •*"«* 

0000 


tOMNO 

"^POPON 

0000 


H too to 

es M M 

0000 


CS ^ to 

M^ to 










Tl-CTi- 


M M TtO 
M ^ 


CS 0^ PO rj- 
Tf 


tOlO t- M 

M fO-^to 


Ov M C> to 
rJ-rJ-N M 


CS ,-00 

w '^ 


M M OV 
C< N N H 


000 "^N 

H M H M 


t^<*o 

MOOO 


t^ro O^'-t 
lOtO"^-^ 

0000 


too 10 

■tPOPoes 

0000 


too to 

CS M M 

0000 


M g t^ 

CS ?: to 

M-« 10 








«0 M-O 


rotoO ^ 


00 0\ -^PO 

M OJ <S 


00 PO t^ 

N POPOM 


-"too 10 
to M cs PO 


NO M CO N 
PO PO P^ M 


S-? 


O\00 

M N M M 


t^lOTj-M 

H H H M 


?^?§ 


NO P^OO Tt 
lOtOTt-'l- 

0000 


otoo to 

PO PO PO PS 

0000 


too to 

PS M M 

0000 


s t^ 

CS ^ to 

M-^ 10 












NO 0\0 t^ 
rO^^C< 


to to 


i^ PO 

CS to M CS 


CS N M 


rt«0 CS 


O\O\00 t^ 

M M M H 


NO to POM 
H M M M 


00 to PJ 0\ 

>o 


to PS 00 ro 
lOlO '^'^ 


a^+o to 

PO PO PO P< 


to to 

CS M M 


0<g r- 

M 5: to 


M M M M 


l-l H M M 


M M M 


0000 


0000 


0000 


M.4» to 


100 to 

M ro-* 


st?a^ 


too to 

M PO'«t 


too to 

M fO "<t 


too to 

M fO-t 


to to •• 
M po-^c ^ 


^ 




yO>OvO>0 


t^t^t-t» 


00 00 00 00 


0^0^0^0^ 


0000 


M H M M' 


§1 s 















4IO 



THE SURVEY 



Correction 

for i' 

Increase in 

Declination 

of Polaris 


Lati- 
tude 
SO" 


i 


NO fc a 


lO NOO CO 

CM ro CO '^ 
1 1 1 1 


On ^Ov rj- 
1 1 1 1 


00 NnO 

NO t^ t^OO 

1 1 1 1 


POOOO 
00 00 00 On 

MM 


H N POTj- 

ONa On On 

i M 1 




- 


M M 
1 1 1 


HvO wnO 
CM CM PO PO 

Mil 


tA OnCO 

1 1 1 1 


txO coo 

IOvOnOO 

MM 


On cm rfiO 
NO t^ t^ t^ 

MM 


NO t»oooo 
t^ t^ t^ t^ 

MM 


M 

% 

00 

g 

a 
o 

p 

1 

3 

! 

"o 

1 

< 




o 


W M t^ 
M CS <S 

t^ rj- M 
O M <S 

O O O 


28 27 
35 18 
42 01 
48 31 


On M t^ rt 

•^lo CO 

TtOvO CM 
to M 


CM to l> 
M CM cs 

» mno 

M CM CM CO 


tOt^ TtlO 

M CM 

Tft^ CM 
PO rO'-t "^ 


On to Tj-O 
M Ttrj-M 

Tj-iovO t^ 












"^ 


nroo 
o o o 

t-Tt-M 

O l-l (N 

o o o 


M TfOO 
10 ro rO 

t^ tJ-m i> 
CM fO"^"^ 

0000 


ID CO "«t 

rj-co M CO 

C0 0>»00 
10 100 M 

M M 


vOOO l> 10 

PO M CO CO 

to TtOO 
M CM CM CM 

M M M M 


00 t^ M On 
M M 

c^ tooo 

PO PO PO >* 

M M M M 


M rf to 
M POPO 

M PO rtiO 
rt-rt rj-rt 

M M M M 




o 


vO rOO 
O M cs 

O O O 


r- MOO CO 
M 10 M ro 

l>roOO 
0000 


10 CM -St On 
CO M 10 

M 00 ro On 
icuoo 

M M 


10 M vO On 
rtto Tt 

TtOO CM 
M M (N CM 

M M M M 


00 TJ-VO 

M N cq 

pOnOoo 
CO PO PO CO 

M M M M 


rt M CM 

M POPO 

M CM PO 
rJ-Tj-Ttrt 

M M M M 




o 


O O O 
•"tfOM 

O M CM 

o o o 


»0 CM 000 
TfM (VJ PO 

vO fOCMD 
POrOfO -^ 

0000 


CO •^O 00 
COM TtTt 

M t^ CM t^ 
10 100 

M M 


On 000 

COM CM 

CM t^ M to 
M M CM CM 

M M M M 


"^PO rl-OQ 
PO PO M CM 

00 M n-NO 

C^ PO PO PO 

M M M M 


000 TflO 

M PO PO 
00 On M 
CO PO rt"^ 

M M M M 




o 


00 Tj-t^ 

fO M Tf 

o o o 


M ro '■t'^ 

vO NOO -* 
CM rorO-"^ 

0000 


10 On 0> CM 
CO C^ fO 

CO MvO 
li^iOO 

M M 


t^ PO On PO 

M Tt TJ-PO 

M to On PO 

M M M CM 
M M M M 


Tj-Tj-O M 

10 to PO '^ 

vO 0>CM rh 
CM CJ POCO 

M M M M 


t^OO ''t -^ 
P< rt^M 

nO t^oO On 

CO PO PO PO 

M M M M 


iP 


o 


M O »0 

roO CM 

o o o 


ii-> On ro i^ 
T^io »0 

10 MOO 00 
CM ro CO rf 

0000 


Onoo cm 
ro c^ CM 

On »0 »^ 
rtlOO 


M M ro 

CM CM 
rJ-00 CM 

M M M C>J 


M t^ On 
CM M to to 

tooo CM 

CS pq popo 


rt TtON On 
rt to M 

Td-sOO t- 
PO PO PO PO 










m 


o 


CM Tl-O 

o o o 


00 lO fO M 
M CM C^ M 

10 M t^ CO 
(^ rOfO -"t 

0000 


t- 000 M 
Tf M M H 

00 TfON "^ 

TtlO »0 

M 


vO POO t^ 
"^0.0 CO 

00 PO t- 

M M M 


pOnOnO PO 
10 -^M M 

POnO On m 
C^ CM CM PO 


NO to 

M M to 

PO rtto to 

POPOPO PO 








m 


o 


o o o 


CNl fO »0 t^ 

lOiO-^CM 

CM CO ro^ 
0000 


t^ 1000 \0 

lOM M 

t^ rooo CO 
Tj-ioio 

M 


vO OvCOO 

CO '^'^M 

t^ M 10 0\ 

M M M 


00 On t>- M 
CM M rtio 

CM to t^ On 
CM M CM CM 


Tt CM to 10 

PO to rl-M 

M M CO "^ 
PO PO POPO 










o 


M M t^ 

M CM CM 

o o o 


00 C^ 00 »o 
CM CM ■^ 

rtOO M 
CM fO rO "^ 

0000 


CM M Tt 
M CM CM 

TfiO 10 

M 


On On On 
POPO N to 

vO "tt^ 

M M M 
M M M M 


OOvO CMvO 
to CM P< 

M POnOOO 
CM N CM CM 


NO pOnO to 
CM M rt 

M CM e« 
CO POPOPO 

M M M M 




o 


u^ 0\ 0\ 

o o o 

vO CMOO 
O M M 

o o o 


24 04 
29 53 
35 34 
41 05 


\ri POO XT) 
CM ro CM 

\0 MVO M 

-^ 10 100 

M 


00 CM OnvO 
CM PO M Tt 

10 On poo 

M M 


CM 00 <S PO 

to POO 

0» CM to t^ 
M CM CM CM 


CM 00 
rttOlO C« 

00 On M 
M CM PO PO 










o 


O t^ CM 
O lOlO 

O M t^ 
O M H 

o o o 


CM vO M t^ 
rtCM CM 

CO On 100 
CM M CO "^ 

0000 


<N inio On 
""t Tl-coO 

I/:) »00 
rj-io to 

M 


00 On MNO 
CM CM M CO 

rfoo P^ to 

M M 


PO to to 

00 M PO to 

M cs CM CM 


PO 00 00 
CM PO PO to 

t-00 On On 
CM CM CS CM 










§ 

a 
1 

o 


fc M roTl■ 
^ O O O 


»0 10 

M fO^ 
M H M H 


too 10 

M COTl- 
M (S CM Ci 


t>50 to 

M port 

POCOPOCO 


to »o 

M PO Tf 


too to 

M PO rt 

to to to to 



POLARIS MERIDIAN 



411 



fOfO N M 


0\ l^ 10 N 


0\0 N 00 


-^CMO 


VOO TfO\ 


rooo NO 


MM 


00 00 00 00 

MM 


1 M 1 


10 10 ir> 

MM 


MM 


N M M 

Mil 



oooot^O i/^P0NO\ O'+i-ioO ^OON OOTfOsrf OtOOiO 
r^ i> t^ t^ t^t^t^O OOOio loio-^-^ rr> fO N N n m m 

I I I I I I I I I I I I I I I I I I I I I I I I 



> 



<>o ^0 

M 10 '^ 


N mO »0 
liO M M 


M 100 t^ 

10 10 N 


00 NOO 
CO ro N 


10 N 10 

p<5 N M rf 


000 PO M 
N -"tiO 


M 

N 


-Si 


t^OO '^ 


CO 00 10 


M 00 fO 0\ 

ro N N M 


rto 'too 
M 10 


NO PO 
10 Tt rt r<5 

0000 


l^O POO 
N N M 

0000 




^ 10 












OiO t^ 

"^lOTj- 


00 '-OO N 
10 10 M p, 


N l> ro 
N M 10 


ro 

M M 10 N 


POPO N 


00 'tio Ti- 
ro N t 


M 


-^ 


10 "stPO N 


000 fO 


00 N J> 

ro N N M 


rooo N t^ 

M »0 


M lOO fO 

10 't PO PO 

0000 


POO 

N-N M 
0000 




♦= 10 












rfO M 
rj-io Tf 


mO l> rt 
to N fO 


a M ro 't 
M Ttrj-N 


l> N M 10 

Tf 10 n-M 


10 00 00 
PO '* t N 


00 N 00 
TtM ro 


00 




'•K 


fO N H 


00 "TfM 

fO fO fO fO 


00 -^oo 

N N N M 


mO MO 
M »iO 


'too N 
li-; Tt ro fO 

00 


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N M M 

0000 


PO 
rj- 

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^0 ^ 


00 N N 
H Tj-io 


M t-TtO 
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00 ■^PO 
N PO PO M 


"^00 PO 

rt 10 10 10 


0000 

PO N W^ N 


M 
M 


-? 


M 000 


l>»0 N 0\ 
ro fO fO N 


N N M M 


»r»o »o 

M 10 


POt^ M 

't -^POPO 

0000 


10 NO 

N M M 
0000 


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M 


e to 










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M 10 M 


li^lO NO 
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ro^^ 


PC 10 

M N N M 


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M Tl-N 



N 


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10 M I>fO 
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1010 


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0000 


to NO 
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0000 



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M 


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looo r^ -^ 


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10 N 't't 


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10 

PO 


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fOfO N N 


fO 00 N 
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1010 


t- NO 
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0000 


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^ to 












mOOO I> 

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M 10 M M 


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N N M 



10 


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roro N N 


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N M M M 


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voio 


t-MO 

""trl-rOPO 
0000 


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N M M 

0000 


10 

PO 
M 


s 1/5 










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N M M 


M 00 N 10 


t-00 ""t 

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N PO 't 


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100 


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0000 PO 

ro N N N 


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10 mO M 
1010 


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POOO NO 
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't 

PO 


s;;^ 


M M M l-l 


M M M M 


M M M M 


M M 


0000 


0000 


M 


-Si to 


N Tj- 
10 roio Tl- 


10 rtMO 

M N M ro 


MONO 

TtN lOlO 


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10 N f=t 


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t^oo -"too 

fO TflOlO 


»0 


-u 


N N M 
fj PO fO fO 


CM^iD N 
N N N N 


00 NOO 
M M M 


10 vo 


1/5 'to 
■^'t PO N 

0000 


rO t- M 10 

N M M 

0000 


N 
fO 

M 


SK5 

^ to 










10 t^o 

N N N 


•rfio Tt N 
lO »0 N 


t^O t^ 

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N ^"^ 

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N 00 ^ 
•^ N 10 


N Tf N 
M fO 'tiO 



N 


"§ 


M M 

ro fO PO N 


t^O fO M 

N N N N 


00 tC M t^ 

M M M 


ro "to 
10 lo 10 


b-O^oO 
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fO t^ M 10 
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PO 


go 
^ 10 


W M M M 


M M M M 


M M M M 


MOOO 






M 




■"too ro 
""to 


l>0 M W 


M N rl-O 

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l> 0M> M 
\C PO ©"N 


Tj-int^ 
N M 10 PO 


10 M ro 1^ 


10 




00 

^0 


Ov aoo 
ro N N N 


TtN 
N N N N 


MM 2"^ 


N 00 ^J-O 
ic »o 't 


'to POOO 
tPOPO N 


N t^ M 10 

N M M 




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go 








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0000 


0000 


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^ to 



t^ t^ i> t>. 00 00 00 00 0000 0000 



O to O to •• . 

O M ro ""t C • 

O^ 









o 



412 



THE SURVEY 



The following table gives the correction for observed altitude 
due to atmospheric refraction. This correction is always minus 
as the sun always appears to be higher than it actually is. 

A Table of Mean Refractions Due to Altitude 
Bar. 30 in., Ther. 5o°F. 



App. 

Alt. 


Ref. 


App. 
Alt. 


Ref. 


App. 

Alt. 


Ref. 


"SI. 


Ref. 


7° 

8° 
9° 


9' 46" 
8' 23" 
7' 20" 
6' 30" 
5' 49" 


10° 

12° 

14° 
16° 
18° 


5' 16" 

4' 25" 
3' 47" 

3; < 

2' 56" 


20° 


2' 37" 
2' 03" 
i' 40" 
i' 22" 
1' 09" 


5°: 

60° 
70° 
80° 
90" 


0' 48" 

0' 21" 
0' 0" 



A Table of Semi-diameters of the Sun 
Jan. I, i6'i8" Apr. i, i6'o2" July i, i5'46'' Oct. i, i6'oi" 
Feb. I, i6'i6" May i, is'sV' Aug. i, i5'48" Nov. i, i6'o9'' 
Mar. I, i6'io" June i, i5'48" Sept. i, i5'53" Dec. i, i6'i5" 

Effect of Errors in Latitude and Declination on Meridian 
Determination. — It is well to bear in mind the effect of wrong 
latitude, or time (which affects the declination), on your meridian 
computations. 

The following table prepared by Professor J. B. Johnson of Wash- 
ington University, St. Louis, Mo., reprinted in the Metro Manual of 
the Bausch & Lomb Optical Co. shows the effect of error in lati- 
tude and declination for different latitudes and dift'erent hours in the 
day. 

Errors in Azimuth (by Solar Observation) for i Minute 
Errors in Declination and Latitude 



TT/^<ii< 




For I Min. Error in 
Declination 


For I Min. Error in 
Latitude 




Lat. 
30° 


Lat. 
40° 


Lat. 
50° 


Lat. 
60° 


Lat. 
30° 


Lat. 
40° 


Lat. 
50° 


Lat. 
60° 


11.30 A. M. i 

12.30 P. M. 

11.00 A. M. 1 
1. 00 P. M. 1 

10.00 A. M. 1 
2.00 P. M. 1 
9.00 A. M. 1 
3.00 P. M. J 
8.00 A. M. 1 
4.00 P. M. 
7.00 A. M. 
5.00 P. M. 1 
6.00 A. M. 1 
6.00 P. M. , 




Min. 
8.85 

4.46 
2.31 
1.63 
1.33 
1 .20 

LIS 


Min. 
10.00 

5. 04 

2.61 

1.85 

1. 51 

1. 35 

1. 31 


Min. 
II .92 

6,01 
3. II 

2 .20 
1.80 
1. 61 
1.56 


Min. 

14.07 
7.68 
4.00 
2.83 
2.31 
2.07 
2.00 


Min. 
8.87 

4-31 
2.00 
1. 15 
0.67 
0.31 
0.00 


Min. 
9.92 

4.87 
2.26 
1. 31 
0.75 
0.35 
0.00 


Min. 
11.82 

5.81 

2.69 

1. 56 

0.90 

0.42 

0.00 


Min. 
13.56 

6.37 
3.46 
2.00 
1. 15 
0.54 
0.00 



SOLAR MERIDIAN 413 

Stated simply this means that if the observations are taken 
between 9 and 10 o'clock as recommended that for the most 
unfavorable conditions of fast changing declination an error of 
time of 15 minutes will result in an error of 01' of arc on the 
meridian computations. 

It is well to check the latitude by observation unless your loca- 
tion is well fixed on a very reliable map. A simple method of lati- 
tude determination is quoted from the Metro Manual of the Bausch 
& Lomb Optical Co. 

LATITUDE DETERMINATIONS 

" Latitude may be variously determined by observing the transit 
of a star, by a mean altitude of polaris or by a direct observation on 
the altitude of- the sun at apparent noon. 

" Owing to the earth's annual motion in its orbit, the sun changes 
his position along the ecliptic with respect to the stars at a not al- 
together uniform rate; so that some solar days are either longer or 
shorter than others. 

" For the reason that a chronometer could not conveniently be 

I made to change its speed to suit this solar phenomenon, there has 

< been established a uniform system of time called *'mean solar time.'* 
The difference between mean noon, when the sun should be on the 
meridian, and apparent noon when the sun actually is on the 
meridian, is called the '' Equation of Time." 
The tabular corrections will be found in the 
Ephemeris Tables. 

1 "Thus, in early November the sun has passed 

I the meridian more than 16 min. before mean noon. 
It is always well to begin latitude observations 
some 20 min. before local noon, although there 
will be seasons of the year when the sun will not 
attain its greatest altitude until after local noon. 

I " Standard time will also qualify the argument, but this should 
be studied out by reference to the map on page 396. In Western 
Texas, for instance, observations need not begin until nearly i 
o'clock standard time; whereas in Erie, Pa., they should begin 
shortly after 11. 

" Procedure. — Follow up the lower limb of the sun, and when 
the maximum altitude is found add the sun's semi-diameter, as 
given on page 412, to the reading on the vertical circle; subtract 
correction for atmospheric refraction, as figured by interpolation 
from the table, page 412, and correct this result by the sun's de- 
clination: adding if south and subtracting if north. The final re- 
sult is the co-latitude or the polar distance (90° — latitude).'* 

To find the latitude subtract the co-latitude from 90°, i.e., latitude 
= 90° — co-latitude. 

Time. — In case telegraphic standard time is not available de- 
termine the meridian by polaris at elongation and then the mean lo- 
cal time can be obtained by the transit of polaris across the meridian 
by referring to Table 33, page 396 or by the apparent sun time 




414 THE SURVEY 

when it crosses the Meridian at noon connected to Mean time as 
given in the Ephemeris referred to on page 403 which can be ob- 
tained from any instrument maker. 

SOLAR MERIDIAN BY DIRECT OBSERVATION, PRO- 
CEDURE AND EXAMPLE OF COMPUTATION 

Procedure. — An ordinary transit with 3^ vertical circle in good 
adjustment will give satisfactory results although it is convenient 
to have a machine with a full vertical circle and a masked pris- 
matic eyepiece for direct observation. 

When using an ordinary transit remove the cap from the eyepiece 
and then by focusing the eyepiece and objective lenses correctly 
a sharp well-defined image of both cross wires and sun can be 
projected onto a piece of white paper held a few inches back of 
the eyepiece. The vertical and horizontal angles to the sun can 
then be read by bringing the image of the sun tangent to the image 
of the vertical and horizontal wires simultaneously and the time 
recorded. Two, four or six observations are made as rapidly as 
possible with the image of the sun alternately in opposite quad- 
rants and the average time, average vertical angle and average hori- 
zontal angle used in the computations. 



r: 



a. 



Observation No.l., No.2., No.3., No. 4. 

Example. — Solar meridian observations at Lima, Ohio, Jan. 18, 
1918. 

Average time of 4 observations, 2.42 P. M. Central Standard 
time. 

Average horizontal angle (mark to sun) 

Average vertical angle to sun 

Longitude of Lima 

Latitude of Lima 



132° 22' 


00 


16° 37' 


00 


84° 07' 


00' 


40° 4S' 


GO 


i6» 37' 


00' 


— 3' 


00' 


16" 34' 


00' 


40" 45' 


00' 


20^ 34' 


30' 



Observed altitude of sun 

Refraction correction 

Corrected altitude 

Latitude 

Declination at time of observation S. 

Declination Computation. — Observed standard time (central 90th 
meridian) 2.42 P. M. Lima is 5° 33' east of the 90th meridian. 
To get the correct local mean time add to the recorded time 4 
minutes for each degree of longitude east of the 90th meridian or 
4 X 5.9° = 23.6 minutes. (Say 24 minutes.) 

Correct local mean time of observation 3.06 P. M. 



I 



SOLAR MERIDIAN 415 

Take from the Ephemeris the sun's declination at Greenwich 
mean noon of Jan. 18, 1918 = S. 20° 38.9'. 

Lima is 84° of west of Greenwich or its mean local time is 5 
hours and 36 minutes earlier. That is the local mean time of 
Lima at Greenwich mean noon is 6.24 A. M. and the sun's declina- 
tion for 6.24 A. M. Lima local mean time is S. 20° 38.9'. 

The declination is decreasing at the rate of 30" per hour. The 
time of observation 3.06 P. M. local mean time is 8 hours and 
42 minutes later than 6.24 A. M. and the declination for the time of 
observation is therefore: 

Declination at 6.24 A. M. Lima = S. 20° 38.9' 

8.7 hours X 0.5' (30" hourly change) = — 4.3^ 

Declination at time of observation = S. 20° 34.6' 

= S. 20° 34' 36" 
Say = S. 20° 34' 30" 

It should be remembered that a south declination is a minus 
declination. Be careful of your signs in the following formula: 
Applying the formula 

2 i/A = sin [S — (90° — alt.)] sin [S - (90° — lat.)] 
^2 sin 5 sin [S - (90° - dec.)] 

c _ (90° - 16° 34O + (90° - 40° 45O H- (90'' - ( - 20° 34^ 30^0) 



^ ^ 73° 26- + 49° 15^ + 110° 34- 30^^ ^ ^^^o ^^, ^^. 
2 - 

5- (90° -alt.) =43° 11' 45" 
S - (90° - lat.) = 67° 22' 45" 
S - (90° - dec.) = 6° 03' 15" 

log sin 43"" 11' 45" = 9.835 3697 

log sin 67° 22' 45'' = 9.965 2348 

colog sin (180° - 116° 37' 45'') 63° 22' 15'' = 0.048 6988 

colog sin 6° 03' 15" = 0.976 8768 

log tan^ )^A = 2| 2o.826 1801 

log tan J^yl = 0.413 0900 

y2A = 68° 52' 45" 

A = 137° 45' 30" 

As the observation was in the afternoon the angle between the 
sun and true north is 137° 45' 30'' to the west of north. The 
azimuth from the instrument to the sun is therefore 360° — 
137° 45' 30" = 222° 14' 30''. 

The true azimuth from the instrument to the mark is therefore 
222° 14' 30" - 132° 22' = 89° 52' 30". 

To mark the true meridian on the ground turn off an angle 
of 89° 52' 30" to the left from the reference mark used in the 
observation. 



4i6 



THE SURVEY 



The Ross Meridiograph. — If much meridian work is being done 
it will "pay to obtain the Ross Meridiograph which graphically 
solves the solar meridian to the nearest minute. It is quick and 

simple to use and eliminates the one 
drawback of the direct observation 
namely, the extended computations. 



A M 




STADIA MEASUREMENTS 

An expert instrumentman with a 
first-class transit can get more accu- 
rate results in rough country provid- 
ing the atmospheric conditions are 
steady by the use of the stadia method 
of measurement than by the ordinary 
chaining of the average survey gang. 
The author has for a number pf years 
worked under a restriction of a closure 
of less than 5.0 feet to the mile which 
is better than can be attained by ordi- 
nary chainmen in hard topography. 
The method is quick and reliable and 
is to be preferred in open country. 
Chaining is to be preferred in heavy 
cutting or where curves must be run in. 

For an ordinary tangent preliminary survey the stadia method 
is very satisfactory. To get good results however, the observer 
should be expert. The ordinary garden variety of instrument men 
can not use stadia successfully; he should check his main line by 
both back and foresight readings. He must keep his instrument 

Rod: 



Section A-A 



Elevation 

Sketch of circular 
plumbing level for stadia 
rods. 




--> 



r J/////M//////)////////w//w^^^^ 



in first-class shape and must use a rod with a fairly broad face 
with clear distinctive markings; this rod must be held steady and 
vertical which can be accomplished by the use of a small universal 
circular level attached to the rod, and steadiness can be secured 
by a short hand rod (about 4' long) that the rodman uses as a 
shifting brace. 

The transit must be steady, must have a first-class lense and 
must be equipped with fixed stadia wires. Adjustable stadia 



STADIA MEASUREMENTS 417 

wires are worthless if good work is required. Distances between 
hubs should as a rule not exceed 500 to 600 feet for close line meas- 
urements but side slots can be taken up to 1500 feet. 

The essential elements of the theory of stadia measurement are 
briefly as follows : 

The measurement depends on the optical angle of the stadia 
wires. This angle is governed by the distance apart of the stadia 
wires. The rod intervals A and A' subtended between the 
stadia wires are directly proportional to the distances b and b^ 
from the apex of the optical angle. The apex of this optical angle 
is always a certain fixed distance in front of the instrument and is 
different for different makes of transit. Call this distance C which 
can be determined as later explained by test or is generally noted 
in instructions furnished by the instrument maker. The actual 
rod interval as read by the observer is therefore proportional to 
the distance from a point ahead of the instrument and not from the 
center of the transit. For close work this distance C must be 
known and also the rod interval per 100 feet of distance beyond the 
apex of the optical angle. The rod interval per 100' of distance 



' I I 

is desirably i.o' but unless unusual care is exercised in setting the 
vires it is rarely exactly this value. To determine the actual 
value of this interval proceed as follows: 

Case I. — Where the value of C is known. 

(Note. — C generally ranges between 0.75' and 1.25'.) 

Pick out a level line about 800 to 1000' long. Drive a transit 
hub; place a foresight picket. Measure from the transit hub 
toward the foresight the distance C which we will assume in this 
case to be 1.25' and drive a hub. This hub represents on the ground 
the apex of the optical angle. From this hub measure carefully 
with a steel chain 100' and set a hub on line with the foresight and 
continue to set points at intervals of exactly 100 feet until you have 
a test line 800. to 1000 feet long. 

Now level the telescope and read the rod intervals when the 
rod is held on each of the stakes and record this interval to the 
nearest fraction of a foot that you are sure you can actually see. 
As the length of sight increases it becomes less and less possible 
to determine exactly the interval and when you are not certain 
of the reading to a o.oi' stop attempting to lengthen the sight and 
you have practically determined the safe length of sight for actual 
line work that the instrument is capable of handling. To deter- 
mine the rod interval record your readings and take the average 
value. Assume your rod intervals to be as follows: 




4i8 



THE SURVEY 



997 


feet -^ 


•995 


'' -7 






•99 


~ 


•99 


" -T 


.985 


" -7 


97 


" -T 


•95 


'' -f 


.02 


'' -i 



= 0.997 
= 0.9975 

= 0.9967 

= 0.9975 
= 0.997 

= 0.995 
= 0.993 

= I . 002 



This indicates that beyond 500' the readings become uncertain 
and that about 600' is the limit of practical line sight for close 
work. Good stadia work requires that the instrumentman is 
perfectly honest with himself and recognizes his limitation when 
it is reached. The rod interval per 100' is therefore 0.997 in this 
case and every foot on the rod when the line of sight is level means 

an actual distance from the apex of the optical angle of ~ = 

0.997 
100.3 feet. 

To get the actual distance then for a level line of sight rod reading 
of 2.45 feet multiply 2.45 X 100.3 = 245.73 feet. 

Say 245.7 feet from the apex of the optical angle and the distance 
from the center of the instrument will be 245.7 feet plus the constant 
C (1.25) equals 246.95 feet from the center of the instrument. 

The efifect of the inclined line of sight will be discussed later. 




—too ->4< -100" 



W//////////A 



Case 2. — Where the constant C is not known. To determine 
the constant C and the rod interval per 100' of distance beyond 
the apex of the optical angle. 

Measure a base line 800 to 1000' long as previously stated 
placing hubs every 100'. 

Set the transit up over the first hub and with a level line of sight 
read the stadia wire rod interval at each of the stakes on the line 
which are at actually measured known distances from the center 
of the instrument of 100', 200', 300', etc. 

The problem is to determine two unknown quantities, C the 
constant and X (the rod interval per 100 feet of distance beyond 

the apex of the optical angle). According to Case i, -^—:^ — ■* = 



STADIA MEASUREMENTS 419 

the actual distance beyond the apex represented by a rod interval 
of one foot. Therefore we can determine the constant C from two 
equations using the actual rod intervals a^ and a^ at the stakes 
which are 100' and 200' from the center of the instrument thus. 

T on' 

100' — C = observed rod interval a^ X 



X 

1. 00 



/ - C = " " , " ""'^ X 

Suppose the rod interval a^ = 0.0845 
" " " a^ = 1.9815 

lOO.O — C = 0.9845 —y- 



200.0 — C = 1. 9815 -^ 



W) 



call ( -^ I the symbol F. 

loo.o — C = 0.9845 F Equation i, 
200.0 - C = 1.9815F " 2. 

loo.o = 0.997 F Subtract Equation 
I from 2. 
_ 100.00 
0.997 
F = 100.3 feet. 

That is, a one foot rod interval equals 100.3' of distance beyond 
the apex of the optical angle. 

To determine C substitute this value of F in Equation i . 

loo.o — C = 0.9845 X 100.3 

- C = - 100 + 98.75 
C = 100 — 98.75 
C — 1.25 feet. 

Apply this principle to three or four sets of readings and take the 
mean values. 

You now have the basic constants of the instruments for close 
work. 

Effect of Inclined Sight on Stadia Readings. — The previous 
discussion is based on a level line of sight. It should be borne in 
mind that the stadia distance as previously discussed refers to the 
distance along the line of sight when the rod is perpendicular to 
the line of sight. 

In case the line of sight is inclined the rod reading must be 
corrected to a true rod reading perpendicular to the inclined 



420 



THE SURVEY 



line of sight and the distance along the inclined line of sight must 
be corrected to the true horizontal distance. 

Rod interval X cos A (angle of inclination) = corrected rod 
interval. 

(Corrected rod interval in feet X actual distance value per foot 
as determined by test X cos angle A) + (the constant C X cos 
angle A) = corrected horizontal distance. 



CorrecHd ->| 
Horijonfal i 
ProJecHonof /\ , ^,^ 

'r ! L" 



I Correc-hed ^ 

I "Horhotifal ^ ^ ^ 

I Distance, ^^-<\0^3 




Corrected Rodlnfgrval 
Perpendicular fo 
^Line Qf^ighf. 

1 Acfual Rod Interval. 



'Rod held Vert/calftf. 



All standard stadia reduction tables and diagrams similar to 
Table 30, page 335, are based on (100 feet of distance for i.o 
of rod interval) plus the constant of the instrument. 

If much stadia work is to be done all instrument makers will 
set fixed stadia wires guaranteed to measure 100' distance per i.o 
of rod interval for the distance from the apex of the optical angle 
and such wires are generally sufficiently close to this standard 
so that for all practical survey work on which stadia methods are 
desirable no correction for rod interval need be applied. 

The following example of reduction of stadia reading for careful 
line work will show the method. 




fie igh-h of Instrument 
above Hub 5.3' 



;^;>^. 



■hub Elevation 
Top^2^S.26 



^^ub zievafjp.n df top $210.Z 



Case I. — Where the stadia wires are guaranteed to read 100' 
distance per foot of rod interval and the constant C = 1.25 feet. 

Procedure. — Measure the height of the center of the telescope 
axis at the standards above the top of the transit hub; this is called 
the Height of instrument. Assume this for example to be 5.3 feet. 

To get the vertical angle to the next hub sight on the rod with 
the middle horizontal wire set on 5.3 feet on the rod held on the 
foresight hub and read the vertical angle say + 10° 13': level 
the telescope by the large telescope bubble and record the index 
error say -f- o*' 01': the correct vertical angle is then + 10° 12'. 

To get the rod interval reading corresponding to the vertical 



STADIA MEASUREMENTS 421 

angle of +10° 12' sight on the rod with the middle horizontal 
wire on 5.3': then shift the vertical line of sight so that the lower 
stadia wire is exactly on one of the main rod divisions and read 
the rod interval between the two stadia wires. Say in this case 
3.37 feet or ^t,^ feet distance. Look in Table 30, page 337, 
which gives for a vertical angle of 10° 12' the correct horizontal and 
vertical distance per 100' of stadia reading as horizontal distance 
96.86'; vertical difference in elevation 1 7.43'. The total horizontal 
distance for the stadia reading of 337 feet is therefore (337 X 
96.86 = 326.42) + (constant C X cos 10° 12') given at bottom 
of page in table as 1.23) = 327.65 total horizontal distance. 

The Vertical difference in elevation is (337 X 17.43' = 58.74') 
+ ((constant C X sin 10^12') given at bottom of page in Table 
30 as 0.22) = 58.96' total difference in elevation. The elevation 
of the new hub is therefore 5230.3 + 58.96 = 5289.26. 

Case 2. — Where a stadia interval must be corrected for poor 
wire interval. 

Suppose the instrument used measures 100.3' f^i" ^^-ch foot on 
the rod and the rod reading for a vertical angle of 10° 12' is 3.36 feet. 
The correct stadia distance is found by multiplying 3.36 feet X 
100.3 — 2>^7 fe^t in distance. Then proceed as in Case i. 

Stadia Rods. — Stadia rods can be divided in innumerable 
ways and it makes little difference what symbols are used so long 
as they are clear and distinct. The principle of bisection for the 
smallest readings is a good system. The face of the rods should be 
wider than the ordinary level rod; a width of 23^ to 3" is about 
right. They should have a very brilliant white background and 
jet black face markings with large numbers for the even feet marks 
the tenths should not he numbered. 

The practice of special graduations to fit the wire interval of 
the instrument is not desirable particularly in rough country where 
rods are often broken. 

A standard i.o ft. division is safer, as any standard rod can then 
be used. 

The following system of face markings has been used by the 
author and is given merely as an example in case the reader has no 
preference of his own. 

The rods should be as light as possible with a back brace to 
prevent warping and provide hand holes and a length of 10' is 
ample for all practical purposes. 



422 



THE SURVEY 




Stadia rod. 



CHAPTER XII 

PHOTOGRAPHY, CAMP EQUIPMENT AND NOTES ON 
CAMP MEDICINE 

Editor's Note. — Photographs are often as important as survey notes 
particularly on reconnaissance work and the failure of a negative is compar- 
able to the loss of field notes. The following data has been inserted to help 
the inexperienced photographer reduce his percentage of failures. A green- 
hand is puzzled chiefly by diaphram opening and time of exposure and does 
not understand the effect of latitude, altitude, time of year, light, etc., on 
the problem. The following simple notes have been prepared by a man who 
has taken Engineering Photographs all over the world and should be helpful. 
There are a number of very excellent exposure charts and mechanical sensi- 
tized paper exposure meters on the m^arket which consider all these points 
in more detail than we can give in a book of this character. 

NOTES ON PHOTOGRAPHY 

General. — The following discussion of the subject of photog- 
raphy in connection with engineering operations has been prepared 
with the idea of giving to the engineer the foundations and princi- 
ples upon which he may make exposures in the field under most 
all conditions, and secure fairly uniform results. The engineer is, 
in the day's work, required to make exposures under some very ad- 
verse conditions, and it is not rare that the exposure most needed 
or the most important point along the line of survey or construction 
is reached when weather and light conditions are at their worst. 
In many cases the results are failures, poor, or only fair. This fact, 
under the ordinary procedure of having the film developed after the 
point has been passed, or the survey completed, is discovered weeks 
or months afterward, and a return to the point would either bjB 
expensive — so much so as to make it prohibitive — or impossible on 
account of adverse weather conditions. 

Views on preliminary surveys are of more importance and should 
receive corresponding attention. Views on construction and lo- 
cation are important, but the opportunities for making successful 
exposures on location and construction are many. This is due to 
the fact that the engineer is located longer at one camp on location 
than on preliminary, while on construction he is constantly on the 
job. 

It is urged that all work be done in the field at the time of making 
the exposures on preliminary investigations or reconnaissance 
surveys in order that failures may be discovered and additional 
exposures made which will supply the omissions, and assure a 
continuity of views. By so doing the finished view may then and 
there be properly identified and notations made as to its value in 

423 



424 PHOTOGRAPHY 

connection with the surveyed line, and the subsequent report and 
estimate, as explained on page 283. With this end in view the fol- 
lowing equipment is suggested. 
Equipment. 

1. Camera with good stout leather case and tripod. 

2. Tank developing outfit complete. 

3. Films, chemicals, and paper sufficient of photograph length 
of the line. 

This outfit has been used for a number of years by men who have 
had a wide experience, and it has been found to be a convenient 
and complete camp kit to properly care for the picture end of a 
survey. 

Roughly the films should be estimated at three exposures to 
the mile of line. 

Camera. — The best sized camera, that is, the one which produces 
the largest picture in proportion to the bulk of outfit and cost of 
operation, is the 434 X 63^ film camera — Eastman 4A. Cameras 
having smaller dimensions produce views so small as to be of little 
value from an engineering standpoint, while the outfit necessary 
to carry on development is practically the same in size and weight 
as that required for the camera above mentioned. Enlargements 
may be made, but this is an additional expense and delay. What 
is required is speed and accuracy. 

This sized film when properly masked will give a picture 4 3^" 
X6%'' exclusive of legend. If the roll is cut so as to leave the un- 
exposed portions between the exposures, on the bottom of vertical 
views, or the left hand end of horizontal views, space is left for 
filing number and legend. This information is put on the face of 
the film with india ink as soon as it is dry and is a clear but concise 
statement of (a) station from which the view was taken, (b) direc- 
tion of the camera, {c) general description of features shown, 
or purpose for which taken, and (d) index number by which the 
same may be identified. This information is obtained from the 
exposure record which is made and kept at the time of the exposure, 
and regarding which description is given on page 430. 
^ Autographic backed cameras are in use but are not specially 
desirable unless the films are to be developed by some other person 
at a latter date. The writing that may be done while specific, is 
generally so large as to take up all the space between the exposures 
which should be devoted to more detail. If used it is better to 
merely record the roll and exposure number as R 23-2 and depend 
on the exposure record for detail data. 

Lens. — The camera should be equipped with a standard lens of 
known value. In the matter of lenses nothing empirical may be 
said. Generally, however, the regular B. & L. f 16 rectilinear lens 
gives excellent results. As speed is not essential the higher priced 
rapid lenses are not necessary, and the investment of money is 
such a refinement which the work in hand does not call for, is a 
luxury to say the least. Given a well made and flawless lens, an 
equally good picture may be secured, provided the proper time is 
given, as with the more expensive lens. As there are no moving 



COMPOSITION 425 

objects in the class of views that the engineer will photograph, 
exposures may be properly timed. 

Shutter. — The shutter should be of the ordinary variety, operated 
or snapped with a bulb or cable. For rough handling the bulb 
release is considered the best. There are a number of standard 
shutters on the market, anyone of which gives entirely satisfactory 
results. Improvements are being continually made, and it is ad- 
visable to purchase the most durable pattern on the market. There 
is less liability of making errors with the shutter that sets and re- 
leases automatically with a bulb or cable. Those that have to be 
set by hand ofttimes produce no exposure, the photographer for- 
getting to set the shutter. 

Diaphram. — Most all cameras are now equipped with the 
iris diaphram, and this attachment is the best with which to control 
the stop. 

The stop is the technical term for regulating the size of opening 
in the diaphram. There are two systems of indicating the dif- 
ferent stops. The ^'Universal Standard" (U. S.) and "f " for focal 
speed of lens. The following list shows the usual stops for both 
systems that are equal to each other. 

U. S. 1.2 2.0 2.5 4 8 16 32 64 

f 4.5 5.6 6.3 8 II 16 22 32" 

Ordinary kodak stops 123 

Stop . U. S. 1.2 gives the largest opening. 

'' 64 " ''smallest '' . 

Manipulation.— The most important factors that enter into 
making an exposure are : 

1. Composition. 

2. Distance. 

3. Aperture. 

4. Time. 

5. Strength and direction of light. 

6. Phases of views. 

7. Recording all operations in the exposure record. 

Taking up these operations in their order: 

Composition. — A photo should not be looked upon as a miscel- 
laneous lot of black and white spots on a piece of paper; In order 
that the photo should properly show the information required, 
it should in most instances be taken from some station along the 
line of work, or from some point which has been definitely located 
without the line of work. The most desirable position from which 
to make the exposure is one from which professional as well as 
artistic points may be seen. The selection of such a point is made 
after carefully studying the composition of the view as seen in 
the finder. If a view is required along the survey line, select if 
possible, that station where the light will come from behind or 
from the side. Carefully study the composition. 

If on a survey line, along a stream bank, on the edge of a mesa, 



426 PHOTOGRAPHY 

at the shore of a lake or bay, bring the important features into 
the middle of the finder. No picture should be taken that does 
not contain some life, as only professionals can make a good picture 
of still life. Picket a rodman with a level rod or stadia board of 
known length on a station 50 or 100 feet away on line — or more 
particularly at the point it is intended to feature. This not only 
gives life to the view, but provides a medium by which distances 
in the view may be estimated. Have, if possible, one-third of 
your view composed of sky. Balance your picture. Guard against 
having the center view obstructed by a 6 foot tree 15 feet from 
the camera, while the feature you are trying to photograph is 100 
feet away. Such a composition blurs the foreground, reduces 
the field of view, and in general spoils what might have been a 
successful photo. 

Hold or set the camera level. If it is necessary to obtain some 
feature that is below or above the outline as shown in the finder, 
manipulate the shifting front of the camera. Never tip the camera 
up or down, for to do so will produce distorted photos on account 
of the vanishing point lying outside of the horizontal plane. 

Distance. — Ascertain the distance from the camera to the object 
to be photographed. Do this with reasonable care as too many 
poor negatives result from carelessness in estimating distances. 
Set the indicator at the proper point on the scale of distance. 
The nearer the subject is to the camera, the more care should be 
exercised in ascertaining the distance. For universal focus use 
stop U. S. 16, 32 or 64 and set focusing indicator at 25 to 30 feet. 

Aperture and Time. — The aperture (stop) and time of exposure 
are the governing points in making an exposure.' 

For a given condition a number of different combinations of 
aperture and time will give satisfactory results. The larger 
the aperture the shorter the time. The smaller the aperature 
the better the detail of the picture becomes. In general it is 
desirable to use a fairly small aperture to get detail and as long 
a time as conditions permit. 

The correct combination of aperture and time is affected 
by the use of a tripod, movement of objects, speed of plate or films 
used, altitude, latitude, season of the year, intensity of light 
and composition of the picture.- This sounds complicated and is 
for the best results but fortunately considerable variation from the 
best timing will still produce a fairly good negative for all practical 
purposes. 

Effect of Use of Tripod. — It is advisable to use a tripod for all 
engineering photography as it prevents blurring by movements 
of the camera during exposures and makes it possible to use a 
small aperture, with the necessary time of exposure, to get good 
detail. If the camera is held in the hands the time of exposure 
should be J^s of a second or less and the aperture will have to be 
made large enough to allow this speed. 

Effect of Motion of Objects. — As a rule moving objects need 
not be photographed but if necessary the following speeds of ex- ; 
posure will stop motion. ' 



EFFECT OF ALTITUDE 



427 



J^5 of a second will stop wind in foliage. 

J^O of a second will stop pedestrians and slow moving rigs. 

J^OO of a second distant trains. 

Moo to Ho 00 of a second near trains, automobiles, etc. 

The aperture must be regulated to allow these speeds. 

That is, time governs aperture where motion is encountered. 
Under most conditions, however, where a tripod is used aperture 
governs time and a small aperture is desirable in order to obtain 
detail. For most landscape engineering survey work a U. S. stop 
16, 32, or 64 is used and the time is varied to correspond with the 
stop selected. 

Bright sun use stop U. S. 64 or U. S. 32. 

Fair light use stop U. S. 32 or U. S. 16. 

Moderate light use stop U. S. 16 or U. S. 8. 

An aperture of U. S. 8 will give moderately good detail. 

Speed of Plate or Film. — Different makes have different speeds 
but there is no great variation in the speed of the ordinary roll 
films or speed pack films and the follomng exposure chart is based 
on the commercial film in ordinary use. 

Effect of Altitude. — Altitude has a marked effect on time of 
exposure. Exposure charts are worked out for sea level. 

Wilson topographic surveying quotes Mr. E. Deville as stating 
that altitude has practically no effect on timing when the sun is 
near the zenith in the middle of the day but that as the sun ap- 
proaches the horizon the effect becomes evident. He gives the 
following relative time of exposure at sea level and 10,000 feet 
altitude. - 



Altitude of Sun 



Relative Time of Exposure 



At 10,000 ft. Altitude 



At Sea Level 



90 
40° 

25° 
15° 



I second 



I second 



3>^ 



The rule generally used for ordinary engineering photography 
1 is to cut the time of exposure in half when you are working at an 
i elevation of 5000 to 10,000 feet. 

Effect of Latitude. — Exposures at the equator require the shortest 
timing. 

As the latitude increased, the time of exposure increases. 
i For example conditions requiring J^ 5 of a second at the equator 
- requires M of a second in Alaska. 

Effect of Season of the Year. — The summer months require less 
; exposure than the winter months. 



428 PHOTOGRAPHY 

For example conditions requiring an exposure of Mo of a second 
in summer will require 3^ of a second in winter, except that it must 
be remembered that snow on the ground changes the classification 
of ''phase" discussed below. 

The chart on page 429 is prepared for sea level at average con- 
ditions of latitude and season in the United States and the effect 
of latitude and season can be disregarded for all practical purposes 
except for extreme cases as they have a relatively small effect 
for this territory as compared to light intensity and phase of the 
picture. 

The extreme variation from the chart will be approximately as 
follows; for winter months along the Canadian boundary, doublet 
the time of exposure given in the chart. For southern Floridal 
in midsummer use J^ the time given in the chart. 

When it is borne in mind that this variation in relative exposure 
does not ruin a negative it can be seen that unless these extreme 1 
conditions of combined location and season prevail that the chart j| 
time without correction should give reasonably good results. "" 
Altitude should however be considered. 

EFFECT OF LIGHT AND PHASE , 

Light Values. — Judgment and experience are essential if good, 
average negatives are to be secured. However, the following 
discussion of light values of different lights and phases of views 
may be of use. There are five distinct conditions of light that are 
generally taken into consideration when calculating for an exposure. 

(A) Bright Sunlight. — When the sun is shining brightly in a 
cloudless sky. 

(B) Light Clouds, — When a thin film of white clouds partially 
obscures the sun, but fairly well defined shadows are discernible. 

(C) Diffused Light. — An even light but no shadows. 

(D) Dull. — Sky covered with dull clouds with no sunlight 
penetrating. 

(E) Very Dull. — Sky overcast with very dark clouds. Gloomy. 
Phases of Views. — For the purpose of classifying views or sub- 
jects in a view — the five following phases are given: 

1. Landscapes. — This view contains distant landscapes, sea- 
scapes, snowclad hills, or broad expanses of river scenery. Such 
views reflect a large percentage of actinic light, and should be 
short timed or stopped down accordingly. 

2. Light Foreground. — This view contains open fields and woods, 
flocks of live stock, buildings, and small expanses of water. 

3. Strong Foreground. — This view contains a large percentage 
of foliage, buildings close enough to make strong and distinct 
outlines, fences, figures, animals, well defined roadways, rock j 
cliffs, or well defined hill slopes not over 400 feet from the camera, 
urban scenes where the sky line is serrated with buildings, or 
full views of concrete structures. 

4. Very Heavy Foreground. — This view contains close-ups of 
the following: landscapes having dark green foliage and shadows. 



TIME OF EXPOSURE 



429 



bridges and other structures with heavy shadows, and rock cliffs 
which are generally located in canyons where considerable direct 
light is shut out. 

5. Shaded Foreground. — Under this caption comes, ravines, 
wooded hillsides, standing timber, under trees, and small dark 
box canyons where sun light is shut out by shadows. 



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Caution. — Great care must be exercised in making exposures for 
views under conditions for No. 5. Give plenty of time, and should 
doubt exist double the time taken from the chart and make another 
exposure. 

Bearing in mind the five conditions of light "A'' to **E/' and 



430 



PHOTOGRAPHY 



the five Phases of Views i to 5, enter the chart with the view as an 
argument. Along this line a number of combinations for time 
and stop may be had which will give satisfactory negatives. If 
detail is required, select a small stop, and from this get the time 
for Bright Sunlight ^^A." Should light conditions be other 
than "A" multiply the time obtained by the proper factor given 
below the chart. 

For Example. — Condition of light: Diffused "C. " Phase of 
View: Strong Foreground No. 3. Suppose you desire to use 
stop U. S. 8, the time for bright sunlight is given as 3^ second. I 
Multiply this time by 2 the factor for diffused light getting Ji 1 
second as the exposure required. 

Note. — There are a number of meters now published which go 
into detail as to time, aperture, conditions of light and phases of 
view all of which give excellent results. These may be purchased 
from most any photo supply depot. 

Exposure Record. — In order that the photographer may have 
something upon which to check up his failures, identify each view 
in connection with the project in hand, and properly reference them 
in the files, an exposure record should be used and each exposure ^ 
carefully recorded. This record may take any number of forms, f ! 
but from experience the following is suggested, which has been ' 
filled out to show how it is intended the columns should be used. 



Roll No. 36. 



Exposure Made by Bill Jones - 



Sept.- 



No. of 
Film 


Job 


Date 


Hour 


Light 


stop 


Time 


Subject. Descriptive 

Notes 


I 
2 


Rabbit 
Ears 


Vs 


9.00 


A 


16 


Mo 


Sta. 1007+40. Looking 
Az. 170 deg. along tang. 
Rodman on Sta. 1006. 


Rabbit 
Ears 


H 


10.00 


B 


II 


3-1 


Old timber br. at Sta. • 
1020. Camera 60' to 
right of 1019-SO look- 
ing Az. 130 deg. (out of 

. focus). 


3 


Rabbit 
Ears 


H 


10.30 


B 


22 


H 


Sta. 1025 looking Az. 90 
deg., showing proposed 
Xing of river. Solid 
rock in extreme left of 
view. 


4 


Rabbit 
Ears 


% 


4.00 


A 


II 


Ho 


Sta. 1091 looking Az. 
270 deg., showing Ama- 
zon Pass, Hopland and 
Big River Valley. 


5 


Tyeras 
Canyon 


H 


10.00 


C 


8 


I sec. 


Sta. 1 107-45 looking Az. 
210 deg. Dense tim- 
ber along tangent. 


6 


Tyeras 
Canyon 


H 


3 00 


D 


22 


i^^ 


Sta. 1 136 looking Az. 
226 deg. along tangent 
showing houses on right- 
of-way. Close up view. 
Rodman on Sta. 1 137- 



431 



DONTS 



Dont expect good results from snapshots taken before 9.00 
A. M. or after 5.00 P. M. even with sun shining brightly. 

Don't try to make snapshots under trees or in a shadow. Make 

a time exposure resting the camera on a firm base, or better still 

use a tripod. Get the proper time from the chart. ' 

Don't hold the camera in your hand when making exposures 

over 3^5 of a second. 

Don't attempt to make snapshots indoors. 
Never face the camera at the sun unless necessary and then be 
sure to shade your lens from direct rays of the sun. 
Always use small stops if detail is desired. 
Don't give time exposures to distant landscapes. The farther 
away the subject the less time is required. 

Buy only fresh films which will exactly fit your camera, and ob- 
serve the date on same beyond which no guarantee of value is given. 
Always turn the key bringing a new unexposed film into correct 
position after having made an exposure. 

After having exposed a roll take it from the camera, and before 
putting in a new roll, examine the lens, try shutter, and blow out 
any particles of dust that might have worked into the bellows. 
If after having made an exposure, the least doubt arises as to 
whether It was an overexposure, underexposure or double exposure, 
calculate for a stop and time, and proceed to make an exposure 
that will be satisfactory. This advise is of particular value to 
engineers, as it is not infrequent that the picture most needed is the 
one failure on the roll. The second exposure costs but ten cents. 
To secure it after the camp or work has been abandoned may 
cost a hundred dollars. 

Developing.— Fairly good prints may be secured from average 
negatives, but the best prints are obtained from good negatives. 
To obtain good negatives the exposure must be reasonably correct* 
and development must be done with fresh and pure chemicals in 
quantities called for in the respective formulae recommended by 
the makers of the plates or films used. 

The simplest, most convenient, and most certain method of 
development that has been worked out for films, is what is generally 
known as tank development. 

The equipment necessary to properly handle films of the size 
suggested m the beginning of this article is as follows: 
I E. C. Eastman tank No. 5E7 complete. 
15X7 Gutta-percha tray. 
132^ oz. Measuring glass. 
I Stirring rod. 
I Thermometer. 
I or more pairs of film clips. 
I Dripping pan enameled, about 9" X 12". 
The chemicals required for one roll of films are: 
I Tank developing powder for 5 X 7 tank. 
4 oz. of hypo with acidifier. 
Plenty of clear pure water having a temperature of 65° F. 



432 PHOTOGRAPHY 

As no dark room is required the development, may be carried 
on at any time, and the process is as follows: 

Dissolve the developing powder as per directions, using the 
developing tank, testing the same with the thermometer so that 
the solution when ready shall have temperature of 6s°F, Set this 
aside. 

Thoroughly rinse the measuring glass, and in i6 fluid ounces 
of water, dissolve the 4 ounces of hypo and acidifier. Pour this 
solution, know as fixer, into the 5X7 tray. Thoroughly rinse 
the measuring and glass stirring rod. 

Prepare the films as directed in instructions accompanying the 
developing tank outfit, "and wind it onto the opaque curtain. 

This operation takes place in the light proof box. 

Remove the spool containing the curtain and film, and place it 
in the tank containing developing solution, firmly fastening the top 
on the tank. Turn the tank end for end two or three times, holding 
it vertically for five or ten seconds each time, so as to expel all 
air from between the folds of the curtain, and insure complete 
contact between the developing solution and the film. At the 
moment of immersion, record the time, and permit development 
to go on for the specified time given for the temperature of the 
solution. If using Eastman Tank Developing Powder, and solution 
is 65°F., the time of development should be 20 minutes. 
Invert the tank every 5 or 7 minutes so that even development 
may be obtained. 

Development having been completed, fill the dripping pan with 
fresh water, take the spool from the tank, and working rapidly, 
unroll the apron or curtain until the end of the film is visible. 
Firmly clamp a film clip, to this end of the film. Now lift the end 
of the film by this clip, unrolling it from the curtain until the other 
end of the film is free, and clamp another clip on this end. Rinse 
the film in the dripping pan of fresh water, running it through three 
or four times. Change to fixing bath, and run film through rapidly 
three or four times, making sure that the entire surface of the film 
is flooded with the solution, thus insuring that development is 
completely arrested. 

Continue washing in the fixer until the film is clear. This will 
take from 7 to 10 minutes. Rinse in clear, cool, running water 
for one-half hour, or in 20 changes of water allowing the film to 
remain three to five minutes in each change After rinsing, 
suspend the film from a wire or hook, so that the same will hang j 
free and permit it to dry. Do not touch the surface until perfectly | 
dry. If the film has a tendency to curl during drying, leave it ' 
alone. The weight of the clip at the lower end will be suflficient , 
to correct this. ^ ' 

When perfectly dry, trim the ends so as to leave as much un- 
exposed film as there is between the exposures. Before cutting 
the film, place it on a table, back up, and under vertical views, 
or to the left of horizontal views, inscribe the information contained ! 
in the 8th column of the exposure record, together with the index 



FAILURES 433 

or filing number, using india ink. ^ Place the index or filing number 
in a convenient space usually the^upper left hand corner. 

Cut the film, taking particular care that in so doing the legend 
and the view to which it applies, are together. Do not use scissors 
to cut the film, as this unless cleverly done, is apt to produce an 
irregular edge which is difficult to fit into the mask. Use straight 
edge and sharp pointed knife, or better still a trimmer, the latter 
costing about $1.75. 

All operations to this point having been correctly performed, 
films will be uniform, have a neat and workmanlike appearance, 
and bear complete information as to date, subject, station from 
where taken, and index number. The film so labeled will be special, 
specific, and sufficient; special because it applies to a certain project, 
specific because it pertains to a particular point of feature of the 
project, and sufficient because it gives complete information. 

CAUSES OF FAILURES 

Not Sharp. i. Objects moving or moving too fast. 

, 2. Out of focus. 

I " 3. Camera being moved during exposure. 

Under Time. i. Use of too. small stop, 

j 2. Light too weak, 

j 3. Exposures too short. 

j No Exposure. i. Failure to set shutter. 

I 2. Failure to release shutter, 

i 3. Something in front of lens. 

I Double Exposure, i. Failing to wind up film after making 
I exposure. 

\ Fogged. I. Camera leaks light. 

2. Carelessness in loading or unloading. 

3. Taking pictures against sun. 
,; Over Timed. i. Stop too large. 

2. Too much time given. 

Printing. — Equipment additional to that required for film 
developing: 

I Printing frame 5X7. 

I Gutta-percha tray 5X7. 

I Orange light. 

I Dish pan from camp kitchen. 

Developing powders. (One tube of M-Q develops 18 

prints of the size herein mentioned.) 
4 oz. Hypo with acidifier. 
4 oz. Bottle potassium bromide, 10% solution. 
Quantity of 5 X 7 developing out paper, Azo preferred. 

Procedure. — Prepare the developer by dissolving the contents 
of the tube as per direction thereon, and pour the solution into one 
tray, not the one used for fixing bath. In order that no doubt 



434 PHOTOGRAPHY 

may arise as to which tray is for the fixer, take a sharp instrument 
and scratch the letter ^'H" in the bottom, so the same may be 
seen when the tray is in use. 

Prepare the fixing bath by dissolving the 4 ounces of hypo and 
acidifier iti 16 ounces of water. The temperature of the developing 
solution should be normal, or 65 °F. If too cold it retards 
the development, and if too warm the development is too rapid, 
and prints are apt to show streaks. A warm developing solution, 
fixing bath or rinsing bath produces blisters, due to too rapid action 
which produces gas under the filament on the paper. The fixer 
and rinsing water may have a temperature as low as 4o°F. 
In fact the writer has had the best success working with the fixing 
bath and rinsing water at this temperature. Prints may be left 
in running water at this temperature all night without blistering 
or raveling. 

Arrange the pans and trays in a row in the following order: 
from left to right, (i) dish pan of water in which to rinse the hands 
and finished prints, (2) dripping pan of water in which to immerse 
the prints before placing them in the developing solution, (3) 
tray containing developing solution, and (4) tray containing 
fixing bath. 

Provide a towel to dry the hands on bef9re taking up new, 
undeveloped prints. 

Take one sheet of paper and cut the same into strips about one- 
half an inch wide, and keep the same in a light proof box. These; 
strips are for making a trial of the negative, if doubt exists as to the 
length of time to print. Clean the glass of your printing frame 
and provide a mask having a width inside of 43^'', if using 4^^ X 
63^ films. The mask should be open at one end so as to allow the 
legend, which has previously been written or printed on the film, 
to print. The mask should be provided with paper guides of 
about 2" X K" pasted on one side and top at the corner back 
from the edge of the opening — a distance equal to the white margin 
that should surround the print on the top and the two sides. 
These guides are generally the thickaess of medium weight detail 
paper, and serve to hold the paper and film together when the same 
are placed in the frame, and also during printing. Printing frames 
are now made provided with adjustable guides by means of which 
any desired size of mask may be had. These are convenient, 
and their purchase is suggested. 

Working in subdued light only, and with orange light in position, 
place the film and a sheet of paper in the printing frame, and print 
in accordance with the light used and density of the film. 

Printing should be done in accordance with directions contained 
in the container of the paper purchased. Artificial light is pref- 
erable to daylight, and electric, gas or oil lamps may be used. 
The proper time and distance from light is always given by the 
manufacturer of the paper. 

If daylight be used, hang a sheet over the north window so as 
to diffuse the light and by experiment deduce^ correct time for 
printing. Usually medium negatives will print in such a light in 



DEVELOPING AND PRINTING 435 

from two to four seconds. Note the time taken to print, and remove 
the paper, and rinse in pan No. 2, in order to moisten and prepare 
the surface. Immerse in the developing solution, tray No. 3. 
When the desired tone is obtained take the print from the develop- 
ing solution, rinse for a second or two in tray No. 2, and then im- 
merse in fixing bath tray No. 4. Should abrasion marks appear 
on the print, add from 5 to 10 drops of the 10% solution of potas- 
sium bromide to the developer. This will make the development a 
little slower, but will correct this trouble. 

Prints should be left in the fixing bath for 20 minutes. At the 
end of this time, remove them and place in rinsing bath, pan No i. 
If running water is available, rinse the prints for one hour, or longer 
if possible. If no running water is at hand, rinse in a dozen changes 
of water, keeping the prints moving so as to remove all traces of 
hypo. 

When washed, collect the prints as you would a deck of cards, 
and taking not more than a dozen at a time, lay them on one 
fold of a towel placing another fold over them. With an ordinary 
rolling pin, or in the absence of this, a round bottle, roll and press 
out the excess water. Separate, and lay them face down on cheese 
cloth, muslin, or even a clean piece of paper which has been placed 
on a smooth surface, and permit them to dry. When thoroughly 
dry, place on a table face down and drawn them separately back- 
ward and upward under a not too sharp straight edge or triangle. 
This will leave them either flat or slightly convex. The prints 
may now be trimmed as desired. 

Two grades of paper are recommended. One grade for average 
negatives, and one for contrasty negatives. Provide sufficient 
paper based on the ratio of average to contrasty negatives of 6 
to I. There are several grades of paper with a number of finishes. 
The glossy finish generally 'gives the best results for engineering 
purposes, and its use is recommended. To go to the expense of pro- 
viding more grades of paper than above mentioned is an unnecessary 
refinement. 

With practice the operator will soon be able to judge the destiny 
of negatives so that the use of trial strips will rarely be necessary. 
After sufficient practice, and when the operator is able to judge 
his negatives so as to print to within a reasonable degree of cor- 
rectness, printing should be carried on until ail the prints required 
have been made, inserting them in a light proof box or between the 
leaves of a book. Then develop the batch, and perform all opera- 
tions through to the hypo bath. The batch after 20 minutes may 
be taken from this bath and placed in rinsing water. The white 
light may be turned on as soon as all are in the hypo. By this 
method a large number of prints may be handled in a short time. 

Rinse the hands each time after having them in hypo, for hypo 
is a strong restrainer, and should you handle prints without so 
doing white finger prints will appear when development is carried 
on. 

After developing films or prints, wash up all equipment and scrub 
hypo and developing trays with salt — this will remove all traces 
of chemicals. 



436 CAMP EQUIPMENT 

CAMP EQUIPMENT 

We would not have the'^temerity to recommend camp equip- 
ment any more than we would dare advise a woman on cooking 
utensils. It is a delicate subject on which most campers have 
their own pet notions. The following lists are more in the nature 
of reminders than anything else and are based on outfits in ordinary 
use on mountain road surveys in the west where equipment can 
be moved by wagon. 

Outfit for an 8 or lo Man Party on Location Surveys 
Table Ware 

White enamelware dishes unless otherwise noted. 

Item Approx. Vahie 

12 Cups, 3M" diameter $2.00 

12 Saucers, 6" '* i , 80 

3 Salt shakers (large) aluminum 0.60 

1 " shaker (small) " o . 10 

12 Table forks (retinned) i . 50 

24 Tea spoons " 0.60 

2 Meat platters, 16" i .00 

3 Pepper shakers (small) aluminum o. 60 

r " shaker (large) " o .60 

12 Plates, 9" 2 . 50 

12 Table knives (retinned) i . 80 

12 '* si)oons ** o . so 

2 Water pitchers i . 50 

2 Syrup ** '. I . SO 

1 2 Soup bowls, 5" 2 . so 

1 2 Sauce dishes, 5" i • 80 

2 Sugar bowls, 6" 1.50 

Total value tableware $22 .40 

Say $25 . GO 

Cooking Utensils 

Item Approximate Value 

1 Butcher knife 10" $1 . 00 

2 *' knives 8" i.co 

I •• knife 18" (steel) i . 00 

1 Bread board 0.50 

2 Basting spoons, 14" (retinned) o. 20 

2 Berlin kettles, 10 quart (aluminum) 3 .00 

3 " " 6 " " 400 

I " " 5 *' " I 00 

I ** ** 4 " " 1. 00 

3 Bowls, 10" diameter earthenware i . So 

4 Buckets, 10 quart galvanized iron i . SO 

I Coffee boiler, i3^ gallon, gray enamel o. 70 

1 " *' 3 quart (aluminum) 10 . 00 

2 Carving forks, wire (3 prong) 0.30 

I Cake turner (retinned, perforated) o.io 

3 Can openers 0.50 

I Collander, 9" (aluminum) i . 80 

I Dishpan, 17 quart (retinned) 0.7s 

I '* ,14 ** ** o .60 

3 Dippers, i pint " 0.50 

I Drip pan, 9" X 11" " 0.2s 

I " " io"Xi2" " 0.25 

I •* '* ii"Xi6" " 0.25 

12 Dish towels 2 . 00 

1 Egg beater (family size) 0.15 

2 Frying pans, 13" diameter steel , 65 



EQUIPMENT 437 

I Frying pan ii^i" diameter steel o . 25 

1 Flour sieve (tin) 2 quart 0.20 

2 Funnels (large) o . 40 

2 " (small) o . 10 

I Grater . 10 

I Jar for bread yeast, 3 gallon 0.75 

I Iron griddle, 20" X 12" cast iron • 2 . 50 

I Meat saw 1.80 

I " chopper o. 50 

I •• grinder 1.50 

I '• cleaver, 8" 1 . 50 

I Milk pan, 6 quart (retinned) . ,' o. 5© 

3 Paring knives 0.40 

12 Pie tins 2 . 25 

I Quart cup (retinned) 0.30 

I Rolling pin, 2^' X 10^" . o. 15 

I Stove pot 2 . 10 

1 Skimmer (aluminum) 0.25 

2 Soup ladles, 3" diameter 0. 40 

3 Serving pans, 12" diameter white enamel i • 75 

4 " " 7" " " " 1.75 

I Tea pot, I gallon white enamel o. 60 

1 Cook stove, 6 hole range, 18" X 18" X 12" oven, 

top 26" X 31" (30" high), weight approx. 250 lb. 25.00 

Total cooking utensils $77 , 75 

Say $80 . 00 

Hardware 

Item Approx. 

Value 

4 Axes, 3H lb . . $6.00 

4 •* i^i lb. with sheath (hand) _.. 5 . 00 

6 Axe handles 2 . 00 

2 Brush hooks or machetes 3 . 00 

I Cold chisel, small, 6" o . 10 

I Carborundum stone 1.20 

1 Claw hammer, standard. ^6 oz 0.80 

4 Camp beaters with 5 joints nestible pipe (Sibley) 16.00 

2 Files, mill bastard, 8" . 50 

1 Hasp 0.50 

5 Oil lanterns i3<4"-iy^" "wick Stalit" 5 .00 

3 Gasoline lanterns, "Quicklite" 17 .00 

2 Picks, railroad 2 . 50 

2 Pick handles i . 60 

I Pliers, 7" lineman's i . 10 

5 Piece nestible stove pipe for cooking stove i .05 

1 Screw driver, 18" o . 40 

3 Sheath blocks C. I., >4" or >4'' rope 3 . 00 

2 Shovels, sharp pointed, long handles 2 . 50 

1 Saw, 4', one man in case 3 . 20 

2 Sledges, 8 lb 2 . 50 

6 ** handles 2 . 40 

I Saw, 26", 7 point. No. 7 Diston i . 80 

4 Stove pipe protectors, asbestos' 9 . 00 

1 Tool grinder, No. 6 American 

6 Boxes tacks, carpet, 8 oz 0.50 

Nails, 8d and 2od i . 00 

3 Balls twine 0.50 

2 Tubs, 24" diameter galvanized iron 2 . 50 

I Whetstone 0. 10 

I Washboard brass, loW X i iH" • o . 60 

4 Washbasins, enameled ware ■. . . i . 00 

100' Wire baling o. 25 

I Wedge, splitting. No. 5 Truckee i . 10 

I Wrench, monkey, 8" i . 00 

$96 . 70 
Say • . $100 . 00 



43^ CAMP EQUIPMENT 

Tents, Tables and Miscellaneous 

Item Approx. 

Value 

2 Tents, 14' X 16' $180.00 

3 ** 10' X 12' 110.00 

I Tent, 7' X 9' 20.00 

I Kitchen table (see Figure 87, page 442) IS .00 

I Canvas mess table (see Figure 88, page 443) 25 .00 

3 Equipment chests (see Figure 86, page 440) 40 . 00 

I Mess box with padlock 5 . 00 

1 Lantern box (see page 440) , 5 . 00 

2 Lunch baskets 3.80 

6 Canvas chairs 6 . 00 

4 •* saddle bags 16 ! 00 

4 ** note book shoulder bags 6 . 00 

2 •' water bags, 23^ gal 2.50 

3 Canteens, 2 qt. with webbing and strap 5 . 00 

100' 3-^'' rope 1 . 00 

48 Clothes pins 0.20 

1 Alarm clock 2.50 

2 Scrub brushes, i^^" X 4'' . 25 

125' }'i" rope 4.00 

5 Yards oil cloth, white i . 40 

2 Brooms i . 60 

I Spring balance, 50 lb 0.40 

I Sailmaker's palm with needles, twine and wax .... i .65 
I Shoemaker's outfit containing semi-steel, stand, 

2 lasts and pegging awl 2 . 00 

12 Hand towels 2 . 50 

I Medicine chest with remedies 30 . 00 

$486.80 
Say $500.00 

Depreciation on Camp Equipment 

Table ware $ 25.00 

Hardware 100.00 

Cooking utensils ." 80 . 00 

Tents, etc 495 . 00 



Total. $700.00 

AllovMng for ordinary wear, accident, loss, etc.,'^this equipment is 
probably good for three years. Allowing 50 miles of survey per 
season for each party which is a fair average, the equipment is 
good for 150 miles of survey or at the rate of $4.50 per mile which 
is a reasonably close charge for the use of camp equipment on survey 
work of this character. 



TENT LAYOUT 



439 






QuySfake 

MATERIAL LIST. 

( I- 14x16 'Tent 
4-l2-'x4 "(p Ceni-er Poles . 
d-5^'x2"(p Side Poles, 
le-Z^xd" <p Sfakes. 
l4-i-xZ'4> Pegs. 




Fig. 85. — Layout diagram. 



440 



CAMP EQUIPMENT 



Y^-e"^ g "Mei-a/^ Hasp ^-e'-^ \ 




3'^' Metal Strap Hinges 
oh each Box. 






\4-' Metal Handles 
Hinged. 



E 



» 



.z:^ 



■iHf<-2 



E a u i p m e rrf B o 
■ -^V- S' Metal Hasp j^V '^ "^"^^ 



End View: 

/'/4// Timber to be Fir&f 
I Qrade Native Pine. 
I All Joints to be set 
I ff'ith 2V Countersunk 



Fron-t- View. 
-3^' 



r-5- 



_^^_ ; jp ,j EL I y^ood Screws. 

3 -^'^-f nt ^il— -."Tjl I Eac h Box -to receive 

Coat 
Coatof 



3-6' Metal Strap Hinges on each Bok M W * jL ^.'' Wl ^^^ Priming 
Fron+ View. ^""-IT-'-i"^ "Tl-'^ir^.l ^''C/ One Coa. 



[ Varnish. 



C-3V 



End View. 



T-S-, 

j(^,: -^^« i 



La n + ern Bo x . 






Plan wi+h Top Removed . 



Fig. 86. 



TENT HEATER 



441 




— 2a" "^ 

3- J Rivets on each 5ide 
foeach Sfnap- Rivet Heads 
[to if e Flat 

fl"5traps extend 
all around Inside, 



WStraptrohfo 
^xUnd ait the waif 
around the doifoni, one 
Continuous. Piece on Outside 
No.ie Qage, 

(Each Srtpve to be supplied with 5 Joints^ 
of Stove Pipe, One Joint to contain a 5 Damper. 



I Ends to be cut' 
Large enough to 
Lap over and 
Rivet under End 
Straps 



(e^ove made of 2Z6age 
Blacl^ Ironsides and Tops 
of 3 Stoves mag be cut Prom 
One Sheef 28 x lOS". fop and ' 
Sides all in One Piecp. 



Tent heater. 



442 



CAMP EQUIPMENT 



{4- Hole S+rap Hinges. 
A Use ScretY-headecf 
f (BoJt wjfh CI. Nut. , ^ J 

p'^'V^''^ "_ .^ "'"_" K^"' .d 




— ^r-i-' r 



-j: *: 



'c irasfeners-foh 
i^\Iron Braces 
^ Mr/re/? 7b^/<? /5 

fiscreyy m'ffr 
Washer. 



Siole View. 



iter Wing-'nuf 

on Bolts --.aI^' 



/;7\ f C. 5. Bolt Head leaving I C 
iiotfHofes-^/ V-l^'^'- WoodPluq(3\4f'Bi 
^ ^ y L-^ X^A Square Head. ° 




Clearance 
'Bolf with 



k:^ >*• ::^=rf:^/ 



2'>-f"-'' *ii; Use 1^ F.WH. Screws. 

Ertd View. Detail No.3. 

Pig. 87. — Folding kitchen camp table. 



MESS TABLE 



443 



ki* •^'?' ^5' 



Ltg$ to^ Securelij Screwed on Ont 
Side only. 

lSeeDefailNo.2. 






Ix4--' 



Side View. 



M o r s e a End View. 



'Iron Strap 



Each Strip to be rivefed" 
I ..- as shown. 

t:^''^ 



->iV I 



V 



'strips to be of Oak. 
rx3'on4"Centers. 



Use Z4 or. White Canvas 



OJJi 



^ '*\'^' f AH Edges (rf Canvas to be turned under Plan of Table. ^\ 

I 1-inch and Semd. 
HOTE I 2- Z" Leather Straps 60 inches long wHh 

J Buckles to be attached to Under Side of 

\Canvas fo bind Top when Pol led. 

5' .^, L 

e--"^'l-^---i:v,,^ _^ (JobeBevelled ^il^ jL'tlil 

^. ^^fe horijonial/y ••' ^^ JL^illl 

\ — ==~^> [for Seat. ^ ^^ ,, /'' 



^Cenfers p: 



Pin Holes to be Lined { (Z Extra Holes to be made '2 

mth^ "das Pipe "^ | on one End onig to alhrf 

[for^rinkagi in Canvas,^ 

Detail No. 2, |>etoU No.l 

Pig. 88. — Portable mess tables. 




Width of iron f L 



444 



CAMP KQUTPMENT 



Survey Party 
Ration — (one man one day) 



Article 



Unit 



Quantify 



Fresh meat 

Cured meat 

Lard 

Flour. 

Corn meal. 

Baking powder 

Sugar 

Coffee 

Tea 

Butter 

Dried fruit 

Rice, beans or hominy 

Potatoes 

Salt 

Flav. extracts 

Spices 

Milk, condensed 

Canned fruits 

Vegetables (fresh or canned) . 

Syrup ! 

Pickles 

Eggs 

Breakfast foods 

*Miscellaneous cost 



pounds 


o. 70 




0.30 




0.14 




0.70 


it 


0.05 
0.02 


u 


0.35 
0.05 




O.OI 


n 


0. 14 
0. 10 


i( 


0. 10 




1. 00 




0.04 


ounces 


0.03 


u 


0.05 


cans 


0.40 


a 


0.18 


pounds 


0.50 
0.06 


nos. 


0.03 


pounds 


0.08 




2>ic. 



* Miscellaneous includes, crackers, yeast, chile powder, soda, salad, oil, 
catsup, chocolate, 'lemons, soap, sapolio, candles, matches, oil and wood. 
An allowance of 2^c. per ration should easily supply these items. 

Note. — Fresh milk may be substituted for condensed at a rate of i quart 
for one can. 

Cost of Ration. — The cost of feeding one man per day including , 
cook's salary based on 5000 man day rations in 1918 on Western j 
Mountain Location Surveys averaged $1.30. I 

Preliminary Investigation Outfit 
Where one man is traveling alone on foot and will be out of 
touch with habitation for a day or so at a time a simple outfit 
carried in a knapsack or^pack basket will serve very satisfactorily. 

I Waterproof canvas sleeping bag $15 . 00 

I Light belt axe i . 00 

I Small fry pan o. 25 

I Cup with long handle for heating water o. 25 

Knife, fork and spoon o. 50 

Matches in bottle or waterproof case o. 10 

Small emergency food supply 2 .00 

Personal supplies 

Canteen in arid regions 

This whole pack will not weigh over 30 lb. and can be easily 
carried. 



PERSONAL HYGIENE 445 

NOTES ON PERSONAL HYGIENE AND CAMP MEDICINE 

General Note. — Anyone responsible for a party of men in the field should 
make a careful study of this subject. Miscellaneous Publication No. 17 
of the United States Health Service on the ' ' Prevention of Disease and 
Care of the Sick" can be obtained by anyone free of charge and covers in a 
very thorough manner the points that we can only touch on in a book of 
this character. Much of the data following is quoted or briefed from this 
source supplemented by the author's personal experience. The material on 
First Aid is quoted verbatim from Bulletin No. 17 of the U. S. Public Health 
Service by courtesy of that department. 

Personal Hygiene. — Camp life is at its best a dirty proposition and 
every care should be taken to retain as far as possible the ordmary regular 
and cleanly personal habits. Proper clothing should be worn, excess in 
eating or drinking should be avoided, the bowels should be kept regular, the 
body clean and the teeth and feet well cared for. Many a novice in camp- 
ing goes without the ordinary personal toilet articles either because he 
thinks that under the circumstances they are not in good form or because 
he forgets them, but it should be remembered that for anyone accustomed 
to their use, the lack of a tooth brush often causes sore mouth or gums; 
the lack of toilet paper often causes piles and that a razor adds wonderfully 
to the enjoyment of the Sunday in camp. 

Clothing. — In high altitudes heavy woolen underwear should be worn 
even if the midday temperature is high as the rapid cooling at night is 
injurious unless this precaution is taken. Mountain fever is often brought 
on by overheating and chilling caused by the rapid cooling at night. If 
the work involves wetting by fording cold streams or intense rain, woolen 
clothing is essential. Under these conditions if the air temperature is low 
the woolen clothes should be worn until dried at a fire and never removed 
while wet. If the air temperature is high particularly in the tropics wet 
clothing should be removed immediately and dried. 

In the tropics silk or silk wool light underwear next to the skin adds to 
the comfort. Flannel about the abdomen must be worn at all times. 

The army campaign hat of the heavy felt sombrero type is very com- 
fortable for all ordinary work. The close fitting canvass fur lined caps for 
cold weather and the pith helmet for tropical conditions. The more intense 
the sun the heavier the head covering should be. 

In intense light, colored glasses with side flaps fitting closely to the temples 
add greatly to the comfort and prevent eye troubles such as snow blind- 
ness, etc. 

Where much walking is done heavy cotton socks are desirable in warm 
weather and heavy woolen socks in cold weather. Socks should be free 
from holes or lumpy darns and should be frequently changed. 

Rubber boots should not be used. 

Leather shoes with heavy extension soles are the most satisfactory even 
in snow or water. Four buckle arctics may be worn over them in snow. 
For intense cold German felt socks and felt boots are desirable. 

For ordinary summer conditions kaki trousers and a light flannel shirt 
is a satisfactory outside rig. For cold weather a tight woven canvas trouser 
worn oyer a warm woolen trouser keeps the wind out and the heat in and a 
sheep lined or blanket lined leather or moleskin pea jacket makes a suitable 
body covering. In rain an oilskin slicker is better than a rubber coat. 

In steep wooded side hill work in a rattlesnake county stiff canvas leggins, 
tight woven canvas trousers and leather gauntlet gloves are desirable. 

Bedding. — jThe most satisfactory portable camp bed is the waterproof 
canvas sleeping bag lined with woolen blankets. In this connection it 
should be n9ted that if it is possible to do so avoid sleeping on wet ground. 

Diet. — Stick to your normal diet but avoid overeating or drinking. In 
extremely hot weather avoid heavy meats. On a long tramp in hot weather 
do^ not drink water freely. ^ More endurance results from controlling your 
thirst. Do not use alcoholic liquors except for medicinal purposes. 

Be very careful of the drinking water; impure drinking water causes 
typhoid fever, dysentery and malarial complaints. Boiling is the surest 
method of treating doubtful water. Muddy water should be filtered. 

A bath should^ be taken once a day but prolonged immersion particularly 
in cold water is injurious and lowers the vitality. Soaking the feet in cold 
water tends to toughen them. 

Care of Mouth and Teeth. — Before going on a camping trip get a dentist 
to put your teeth in perfect condition. There is nothing more annoying 



446 



CAMP MEDICINE 



than a bad toothache under conditions where expert treatment is not 
available. ^ If toothache develops accompanied by swelling locate the cavity 
and break into it allowing the gases to escape. If the toothache is a sharp 
shooting pain with no swelling it is probably an exposed nerve. Pack the 
cavity with cotton saturated with clove oil, laudanum or chloroform. If 
toothache develops w;ithout an apparent cavity the application of heat to 
the seat of the pain will often cause relief. 

The teeth should be brushed at least twice a day using a good tooth 
powder or castile soap. 

An unclean condition of the mouth renders a person more liable to attacks 
of influenza, bronchitis and pneumonia. 

Care of the Feet.i — i. A good marching shoe should be large enough in all 
directions, but not too large. If the foot moves in the shoe it is liable to 
chafe and blister. A common defect in shoes is that they are too tight over 
the instep and too loose across the ball of the foot. If the leather forward 
of the instep is too slack, wrinkles will form. Folds of leather and rough 
inner seams should be avoided. ^ The inner edge of the shoe should be almost 
straight, the sole thick and wide, projecting beyond the upper leather. 
The heel should be low and broad, and the toe of the shoe should be of such 
a length that there will be no pressure on the ends of the toes or toenails. 

2. The toenails should be cut straight across, a little behind the end of 
the toe, and should not be rounded. Any tendency to ingrowing should 
receive treatment at once. 

3. Corns and callosities are due to pressure and friction from unhygienic 
shoes. When between the toes they are soft; on other parts they are dry 
and hard. They often render men unfit for duty. 

Treatment. — (a) Remove the cause by wearing hygienic shoes. Soak 
the feet well in hot water, thoroughly disinfecting them with bichloride 
(i part bichloride of mercury to 2000 parts water) or other disinfectant 
and then pare the corn or callus down with a sharp knife without wounding 
the skin. The hands of the person and the knife should be sterilized before 
the operation is performed. Fragments of glass and sandpaper should 
not be used on corns. Persons should be cautioned about the care and 
treatment of corns as a slight wound of the foot may lead to lockjaw or 
blood poisoning. Soft corns should be treated by applying a dusting powder 
like aristol on cotton or gauze between the toes. 

(b) Apply the following collodion paint with a camel's-hair brush, night 
and morning, for several days, then soak the feet in hot water, and the corn 
will come away painlessly: 

Acid salicylic i dram 

Extract cannabis indicae 10 grains 

Collodii I ounce 

M. C. Corn paint. 

4. Blisters. — Save the skin; drain at the lowest point with a clean needle. 
Protect with adhesive plaster. 

5. Excessive and Foul Perspiration. — Excessive perspiration often leads 
to foot soreness, blisters, fissures, and corns and may be offensive. 

(a) Mild cases will be relieved by dusting into the shoe and onto the foot 
the following "foot powder." 

Acid salicylic 3 parts 

Pulverized amyli. ; "10 parts 

Talci 87 parts 

This foot powder may be used with benefit before a march, especially 
in case of sore or tender feet. . 

(b) Severe cases will be relieved by soaking the feet, after a prelimtnary 
scrub with soap and water, in a solution of permanganate of potassium. 
The stain should be left on the feet. The solution should be gradually in- 
creased from I per cent, to 6 per cent, and the treatment continued nightly ; 
for three weeks. The foot powder should be used during the day. 

(c) Another method of treatment is to sprinkle a few drops of formalin 
into the shoe each morning. 

6. The feet should be well greased with tallow or neat's foot oil before a 

1 Quoted from the Landing Force and Small Arms Instructions of the i 
U. S. Navy. 



VERMIN 447 

march, or the inside of the stockings should be covered with a stiff lather 
of common yellow soap well rubbed in, or the foot powder may be freely used, 

7. Should the stockings cause pain, the pressure is sometimes relieved 
by shifting them to the other foot or by turning them inside out. Within 
two hours after reaching camp the feet should be wiped off with a wet 
cloth, clean stockings put on, and those which are removed washed for the 
following day, if possible. 

8. Men unaccustomed to marching may toughen their feet by soaking 
them in strong, tepid, alum water (a teaspoonful to a pint.) 

Fly and Mosquito Dopes. — During certain seasons field work is made very 
annoying in thickly wooded county by flies and mosquitoes and unless some 
relief is obtained a man taking notes gets nervous and makes mistakes. 

Small flies such as punkies and mosquitoes will not bite if the face and 
hands are covered with oil of citronella or a mixture of 3^ wood tar oil and 
}r^ sweet oil. The citronella evaporates rapidly and has to be renewed at 
short intervals but it does not stain a notebook and has a rather pleasing odor. 

The tar oil is more lasting and is more effective but is rather of a dirty 
looking mess although the odor is not unpleasant. It will stain a notebook 
or plain table sheet and can not well be used on the hands of a man doing 
this class of work. 

Insect Bites and Stings. — Spider bites and bee stings can be relieved by 
moistened baking soda applied on the bite or Hartshorn and water half 
and half. Ice cold water will reduce the swelling after the pain has been 
relieved. 

Vermin and Insect Pests. — Accidents will happen in the best regulated 
families and the author has often frantically hunted for a cure for these 
evils that are encountered in logging camps and picked up in all sorts of ways. 

Fleas. — A house may be rid of fleas by sprinkling flaked naphthalene on 
the floors and leaving the rooms closed for a number of hours. Kerosene 
will kill them. Chloroform is useful in killing fleas on the body as it can 
be poured through the clothing directly on the spot where the flea is located. 

Lice. — There are three kinds of lice, head lice, body lice and crab lice. 

The following data on vermin is quoted from the Health Service Bulletin 
No. 17- 

" Every effort should be made to free the body from lice and their eggs if 
one should be so unfortunate as to become infested with these insects. 
The head louse is destroyed by washing the hair with a mixture of equal 
parts of kerosene and vinegar, care being taken that it does not run down 
over the face or neck. The vinegar dissolves the sticky substance which 
binds the nits to the hair, and the kerosene kills the lice. Gasoline is as 
effective as kerosene, but- it should not be used as its inflammability is much 
greater than kerosene. The danger of burning a patient in case either of 
these preparations is employed should be borne in mind, and the patient 
should be outdoors at the time of application and remain outside until the 
hair becomes dry. Several applications at intervals of two or three days 
are required, as the nits, or eggs, are hard to kill. These may sometimes be 
combed from the hair with a fine-toothed comb. The body louse lives in 
the clothing, so this should be boiled or baked. If this is impossible the 
clothing, and especially the seams, should be ironed with a hot iron. An 
efficient method is to soak the clothing in gasoline, or the vapor of gasoline 
may be forced through them. Another less expensi\e method is to put the 
clothes for half an hour in a soapy solution to- which 2 per cent, of tri- 
chlorethylene has been added. A good application to the body is a solution 
made by mixing i part of gasoline with 3 parts of vaseline. This prepara- 
tion is noninflammable under working conditions.^ An ointment made by 
mixing 5 parts of naphthalene with 95 parts vaseline is also useful for this 
purpose. Pubic lice, commonly known as "crabs," are destroy-ed by the 
application of white precipitate « or mercurial ointment. 

** Lenz found that he could eradicate lice frpm prisoners at Pucheim (near 
Munchen) by means of finely powdered naphthalene. A handful of this 
material is put into the patient's clothing, introduced through the opening 
at the neck. He is made to sleep at night with all his clothes on. The body 
heat causes the naphthalene to evaporate, the vapor killing not only the 
lice but also most of the eggs. This treatment should be repeated every 
four days for a period of twelve days. 

** In the British Army a powder composed of naphthalene (96 parts) , 
creosote (2 parts), and iodoform (2 parts) is used. About two-thirds of 
I ounce is required for each man. Two tablespoonfuls of an ointment made 



448 



CAMP MEDICINE 



ne 
scg 



of crude mineral oil (9 parts), soft soap (s parts), and water (i part) is 
rubbed into the interior seams of the clothing. Articles of underclothing 
are treated by dipping and wringing them out in a solution of i per cent, 
each of naphthalene and sulphur in benzene or gasoline. 

*' Itch Mite. — The itch mite is a small parasite which burrows into the 
skin and produces a disease known as the itch or scabies. ^ The irritation 
produced by the mite causes scratching, which results in excoriations, 
papules, and postules at places where the mite has entered. 

** Prevention. — A person with the itch should be careful not to shake hands ■ 
with other persons. He should use separate towels and sleep in a bed by 
himself. He should, as far as possible, keep away from other people, par- 
ticularly children, as they are especially susceptible to the disease. 

** Treatment. — The patient should take a hot bath, using plenty of soap, 
and an ointment composed of powdered sulphur (2 ^ teaspoonfuls) and 
vaseline (8_ tablespoonfuls) should then be well rubbed into the skin. The 
treatment is continued for three nights, and on the morning of the fourth day 
the patient takes a bath and puts on clean clothing. If there is burning of 
the skin, a Httle zinc ointment may be rubbed m. The underwear and 
bed clothing should be boiled and the outerclothing ironed or baked. The 
treatment should be repeated after an interval of three or four days i 
itching is still present. Another method of treatment is to rub the bod^ 
with powdered sulphur every night for a week after taking a bath and als( 
sprinkle it between the bed sheets at night, and on the underwear during' 
the day. The sheets and underwear should be changed each day. 

" Ticks. — Ticks are believed to feed upon blood alone. ^ They attach 
themselves to the skin of man and animals and partly burrow into it. They 
hold on tenaciously. If carelessly pulled off, the head may be torn from the 
body and remain in the skin. The eggs of ticks are deposited upon the 
ground. The larvae are six-legged creatures which catch hold of any animal 
within their reach. After becoming engorged with blood the larva drops 
off and changes to the third or nymph stage. The nymph, after obtaining 
more blood and shedding its skin, changes to the adult insect. The tick is 
instrumental in spreading Rocky Mountain spotted fever throughout some 
parts of the country. It should be removed from the skin by means of 
hartshorn, kerosene, turpentine, or carbolized vaseline, which prevent the 
head remaining in the skin. Persons traveling through woods or other 
places in a tick-infested country should stop and search their bodies every 
two or three hours and remove any ticks that may have attached them- 
selves thereto. 

" Bedbugs. — The presence of bedbugs in dwellings is indicative of want 
of care and cleanliness as to bed, bedclothes, etc., and means should be 
taken to exterminate them when they appear. A liberal application of 
kerosene oil to the places infested is probably the best means of killing them. 
There are preparations of gasoline or naphtha sold which leave no stain 
when sprayed on painted or papered walls. Badly infested rooms may be 
freed from bedbugs by fumigating with sulphur, using 2 pounds of sulphur 
to every thousand feet. 

** Roaches.- — Roaches are believed to be responsible for the conveyance of 
tuberculosis, diphtheria, typhoid fever, tonsillitis, and possibly some other 
disease. They spread these diseases by carrying the organisms on their 
feet and in their intestinal canals and disseminating them over food suipplies, 
books, and other articles in daily use. They are especially abundant in the 
galleys of vessels and in damp kitchens. They appear at night after the 
ights have been turned off and overrun everything in the room. Roaches 
can be quickly, cheaply, and completely exterminated from ships and 
houses by the use of sodium fiuorid. This should be spread with a rubber 
powder blower on the floors near the walls and on shelves in closets. The 
powder does not suffocate the insects, but sticks to their feet. They clean 
it off with their mouths, some of it being swallowed and causing the death 
of the insect. As sodium fiuorid is poisonous to man in doses of a table- 
spoonful or more care should be taken not to spread it over articles that | 
are to be eaten." 



Ill 



SUPPLIES 



440 



List of Medical and Surgical Supplies for Medicine Chests 
Medical Supplies (U.iS. Health Bulletin, No. 17) . 





For Homes 




For Vessels 


and 
Factories 


Item 


I pound 


I pound 


Absorbent cotton. 


I pint 


yi pint 


Alcohol. 


2 ounces 


2 ounces 


Argyrol, 10 per cent, solution. 


}4 pint 


4 ounces 


Aromatic spirit of ammonia. 


100 


100 


Aspirin, 5-grain tablets. 


I yard 


I yard 


Belladonna plaster (i year). . 


4 ounces 


4 ounces 


Bicarbonate of soda (baking soda). 


100 


100 


POISON. Bichloride of mercury. Anti- 
septic tablets of 7.3 grains each. One 
tablet to a pint of water makes solution i 
part of bichloride to 1000 of water. 


100 


100 


Bismuth subnitrate, s-grain tablets. 


H pound 


4 ounces 


Borax. 


I pound 


yi pound 


Boric acid (boracic acid) powdered. 


100 


100 


Bromide of potash, 5-grain tablets. 


100 


100 


Brown mixture lozenges. 


100 


100 


Calomel and soda tablets, each Ho grain of 
calomel and Ho grain of bicarbonate of 
soda; amber-colored bottle (i year). 










Calomel and soda tablets, each H grain of 






calomel and i grain of bicarbonate of 






soda; amber colored bottle (i year). 


100 


100 


POISON. Camphor and opium pills. 


yi pint 


4 ounces 


Camphorated oil. 


I pint 


>^ pint 


POISON. Carbolic acid, liquid, pure. 


I pint 


M pint 


Castor oil. 


100 


100 


Chlorate of potash, s-grain tablets. 


100 


100 


Compound cathartic pills, vegetable. 


I pint 


I pint 


POISON. Compound solution of cresol. 


100 


100 


Copaiba, S-minim capsules. 


I ounce 


}4 ounce 


POISON. Creosote, beechwood. 


I pint 


}^i pint 


Dobell's solution. 


I ounce 


I ounce 


Ear drops, formula: Carbolic acid, i fluid 
dram; glycerin, 7 fluiddrams; well mixed. 


2 pounds 


I pound 


Epsom salt. 


]4 pint 


4 ounces 


Essence Jamaica ginger. 


4 ounces 


2 ounces 


Essence of peppermint. 


I pound 


}4 pound 


Flaxseed meal (linseed meal). 


I pint 


I pint 


POISON. Formalin (i year). 


I pint 


}.i pint 


Glycerin. 


100 


100 


Iodide of potash, 5-grain tablets. 


4 ounces 


2 ounces 


POISON. Laudanum (i year). 


I pint 


J-i pint 


POISON. Lead and opium wash. Shake 
well before using. 


yi pound 


4 ounces 


Magnesia, calcined, heavy. 


2 ounces 


2 ounces 


Menthol solution; Menthol, 3 grains liquid, 
petrolatum, i ounce. 


>^ pound 


4 ounces 
yi ounce 


Mustard. 


I ounce 


POISON. Oil cloves. 


I pint 


I pint 


Olive oil (sweet oil). 


H pint 


H pint 


POISON. Oil of wintergreen (methyl 
salicylate). 


H pint 


4 ounces 


POISON. Paregoric. 


100 


100 


Permanganate of potash, 5-grain tablets. 


I pint 


I pint 


Peroxide of hydrogen solution (i year). 


I pint 


H pint 


POISON. Picric acid, H per cent, solution; 


100 


100 


Quinine sulphate, 5-grain tablets. 


100 


100 


Salicylate of soda, 5-grain tablets."' 



450 



CAMP MEDICINE 

Medical Supplies — (Continued) 





For Homes 




For Vessels 


and 
Factories 


Item 


100 


100 


Salol, 5-grain tablets. 


H pint 


4 ounces 


Syrup of ipecac. 


I quart 


I pint 


Soap liniment. 


100 


TOO 


POISON. Strychnine sulphate, Ho-grain 

tablets. 
POISON. Sun cholera mixture, i^-minim 


100 


TOO 






tablets. 


H pint 


4 ounces 


Sweet spirit of niter, dark colored bottle 
(I year). 


>^ ppund 


4 ounces 


Tannic acid. 


I pint 


}i pint 


Tincture of green soap. 


H pint 


4 ounces 


POISON. Tincture of iodine (i year). 


>^ pint 


4 ounces 


Tincture of iron. 


}i pint 


4 ounces 
'}^i pint 


Tincture of myrrh. 


I pint 


Turpentine. 


I pound 


}'i pound 


Unguentine (for burns, scalds, etc.). 


I pound 


I pound 


Vaseline. 



These medicines will remain serviceable until used if kept in glass-stoppered 
bottles, with the exception of those marked "i year" which should be re- 
newed after that interval. The containers of all articles marked "i year" 
should be plainly marked with the date on which such articles are received. 

For bulky articles not over a pint of each need be kept in the medicine 
chest. 

Special bottles with a rough surface must be used for poisonotis medicines. 
These bottles must be plainly marked POISON. 

Gauze and bandages should be in paraffin-paper packages, sealed after 
sterilization. 

Catheters and other rubber goods should be in sealed paraffin packages or 
envelopes, slightly dusted with sterile talcum on the inside of the package. 

Scissors and instruments, if not in cases, may be coated with paraffin, 
which will come off when dipped in hot water. 

Articles marked "i year" should be discarded after that interval and 
new ones obtained. The containers of all articles marked "i year" should 
be plainly marked with the date on which such articles are received. 



i 



SUPPLIES 

Surgical Supplies, Etc. 



451 





For Homes 




For Vessels 


and 
Factories 


Item 


2 


I 


Adhesive plaster, lo-yard reel, i inch wide. 


2 dozen 


I dozen 


Applicators, small, wooden. 


I 


I 


Atomizers, DeVilbiss. 


I dozen 


I dozen 


Bandages, 2 inch by 3 yard (>^ dozen gauze 
and H dozen muslin). 


I dozen 


I dozen 


Bandages, 2 inch by 5 yard, (H dozen gauze 
and \i dozen muslin). 


4 


2 


Bandages, plaster of Paris, 3-inch. Each 
contained in an air and moisture proof 
container. 


I dozen 


I dozen 


Bandages (4 inch by S yard muslin). 


6 


6 


Bandages, triangular (Esmarch's bandage), 
with figures printed on them showing the 
various ways they can be used. 


I 


I 


Bistoury. 


6 


3 


Camel's-hair brushes. 


I 


I 


Catheter, rubber, No. 20 P (i year). 


I 


I 


Corkscrew. 


I 


I 


Forceps, artery (hemostatic forceps). This 
can be used to grasp a bleeding vessel until 
it can be tied, or until the doctor arrives. 
A catch holds the grip of the forceps. 
Sterilize by boiling. 


I 


I 


Forceps, dressing or dissecting. Will be 
found convenient in cleaning up a wound 










and applying dressing; also in removing 






splinters, etc. Sterilize by boiling. ' 


I 


I 


Fountain syringe, 2 quart (i year). 1 


6 


6 


Urethral syringes, glass. 


10 yards 


5 yards 


Gauze, picric acid. Good dressing for 
wounds and scalds. 


10 yards 


5 yards 


Gauze, plain, sterile. 


I 


I 


Hot water bottle, rubber, 2 quart (i year). 
Metal bottle preferred. 


6 


6 


Medicine droppers. 


I 


I 


Medicine glass. 


2 


2 


Nail brushes. 


2 dozen 


2 dozen 


Safety pins, large. 


I 


I 


Scissors, dressing, surgeon's, for cutting 
gauze and bandages. Sterilize by boiling. 


I 


I 


Shears, for cutting cotton and muslin, etc. 


6 


3 


Splints, wooden. Straight and angular 
splints made of this board, as described in 
chapter on "Fractures." 

Spool of silk ligature, medium size. 






I 


I 


2 


2 


Surgical needles, in glass-stoppered bottles. 


2 


2 


Thermometer, clinical, Fahrenheit. 


I 


I 


Tooth forceps, incisor. 


I 


I 


Tooth forceps, molar. 


4 pieces 


2 pieces 


Wire gauze, made of heavy mesh malleable 
wire. When well padded can be wrapped 
around a fracture for temporary dressing. 


4 sheets 


2 sheets 


Yucca palm (a thin fiber board). Can be 
wrapped around a fracture for temporary 
dressing. 



452 CAMP MEDICINE 

LIST OF REMEDIES MENTIONED AND THEIR USES 

(U. S. Health Bulletin No. 17) 

Doses. — Unless otherwise stated, the doses mentioned in this book are 
intended for adults. To determine the dose for children, add 12 to the age 
of the child and divide the age of the child by this sum. This fraction 
will represent the size of dose compared with that for an adult. For example, 

a child 6 years old will require z — ; = -77 or one-third of the adult dose. 

6 + 12 18 

Caution. — Preparations containing opium, such as laudanum, paregoric, 
camphor and opium pills. Sun Cholera Mixture tablets, etc., should not be 
used except where absolutely necessary, as their continued use is liable, to 
produce the drug habit. 

Alcohol. — Externally is useful as a mild .antiseptic wash for wounds. 
As a liniment, pure or diluted with from i to 3 parts of water, is cooling and 
stimulating. 

Argyrol. — Useful, in 10 to 20 per cent, solutions, as drops for sore eyes, 
also as injection for gonorrhea. 

Aromatic Spirit of Ammonia. — Useful in hysteria, faintness, headache, 
flatulent colic, nervous debility, and as a stimulant in shock. Dose: 3'^ to 
I teaspoonful in water every half hour until three doses are taken. 

Aspirin (5-grain tablets). — Useful in rheumatism, neuralgia, and head- 
ache. Dose: i to 2 tablets with hot water or tea every three hours. 

Belladonna Placer. — Useful in coughs, colds, rheumatism in joints and 
arms, lumbago, and pains in small of back. Should be worn only long 
enough to have the desired effect. If the throat becomes dry or the pupils 
dilated, indicating belladonna poisoning, the plaster should be removed. 

Bicarbonate of Soda (baking soda). — Internally useful in sour stomach 
and heartburn. ^ Dose: }r^ to i teaspoonful in half tumlDler of water. Repeat 
in half an hour if necessary. 

Bichloride of Mercury Tablets (poison, 7.3 grains each). — One tablet 
dissolved in from 2 to 5 pints of water makes a powerful and efficient solu- 
tion for washing and dressing wounds, sores, and boils. Do not use internally. 

Bismuth Subnitrate (s-grain tablets). — Useful in dysentery, diarrhea, and 
heartburn. Dose: 2 to 4 tablets every three hours. (C^rush before taking.) 

Borax. — Useful in sore mouth. One tablespoonful dissolved in a pint of 
water and used as a mouth wash several times a day. 

Boric Acid (boracic acid). — One-half teaspoonful may be dissolved in a 
glass of water and used as a lotion for the eye or ears. 

Bromide of Potash (5-grain tablets). — Useful in neurasthenia, con- 
vulsions, and delirium tremens. Dose: 3 to 5 tablets, dissolved in water, 
three times a day. 

Brown-mixture Lozenges. — Useful in bronchitis, coughs, and colds. 
Dose: i lozenge allowed to dissolve slowly in mouth, to be repeated as 
required. 

Camphor and Opium Pills (poison). — Useful in relieving pain in diarrhea 
and dysentery. Dose: i pill every three hours until 4 are taken. 

Calomel (Ko-grain tablets). — Useful in constipation and dysentery. 
Dose for adults and children: Take 2 tablets every 15 minutes until 20 
tablets are taken. When from 4 to 6 hours have elapsed a Seidlitz powder 
or a dose of Rochelle or Epsom salt should be taken. The dose of the 
Seidlitz powder or salt should be proportionate to the age of the patient. 

Camphorated Oil (for external use only). — In sprains, bruises, neu- 
ralgia, rheumatism, and pains and swellings of the breasts or joints it should 
be gently rubbed on the painful part. Applied on hot flannel to chest and 
neck for colds. 

Carbolic Acid, Liquid (poison). — Useful as an antiseptic and disinfectant 
when mixed in the proportion of i part of acid to 100 parts of hot water. 
Useful without dilution to arrest the development of boils and carbuncles 
and as an application to ulcers and venereal sores. _ Should be applied 
cautiously. The surface should be merely touched with a small piece of 
cotton moistened with a drop of the acid, care being taken not to burn the 
surrounding skin. Do not use internally. 

Castor Oil. — Useful in constipation. Dose: i to 2 table'spoonfuls. 

Chlorate of Potash (5-grain tablets). — Useful in sore throat and sores 
in mouth. Directions: Dissolve 5 or 6 tablets in a wineglass of water and 
use as a gargle or mputh wash* ^ 



REMEDIES 453 

Compound Cathartic Pills, Vegetable. — Useful in constipation. Dose: 
I to 3 pills at night. 

Compound Solution of Cresol. — Useful as antiseptic and disinfectant 
when mixed with water in from i to 3 per cent, solutions. Do not use 
internally. 

Copaiba (s-minim capsules). — Useful in gonorrhea and inflammation 
of the bladder. Dose: i to 2 capsules three times a day. 

Cream of Tartar. — In small do^es (i to 2 teaspoonfuls in sweetened 
water) acts as a cooling aperient, gently opening bowels. In large doses 
(i to 2 tablespoonfuls) is a hydrogogue cathartic, causing free, watery stools. 

Creosote, Beechwood (jjoison). — Useful in toothache; i to 2 drops on a 
piece of absorbent cotton introduced into the clean cavity, care taken that 
It does not come in contact with the gums, tongue, or cheek. Do not use 
internally. 

Dobell's Solution. — Useful as an antiseptic wash or spray for nose and 
throat in nasal catarrh and bronchitis. ^ 

Epsom Salt. — Useful in constipation and dysentery. Dose: i to 2 
tablespoonfuls dissolved in as little water as possible. A little lemon juice 
and sugar may be added to disguise somewhat its bitter taste. 

Essence Jamaica Ginger. — Useful in cramps, colic, indigestion, and gas 
in stomach. Dose: i teaspoonful in sweetened water. 

Essence of Peppermint. — Useful in cramps, colds, gas in stomach, and 
colic. Dose: 10 drops to '^'2 teaspoonful in sweetened water or on sugar. 
Externally is useful in rheumatism, neuralgia, and toothache. 

Flaxseed Meal.-;-Useful as hot poultice to apply to boils and felons. 
Compresses wet with hot bichloride solution, i tablet to 5 pints of hot 
water, are better. To prepare flaxseed poultice a receptacle containing 
boiling water should be placed on the fire, the flaxseed meal should be 
gradually added and constantly stirred until the batter is j'ellylike. This 
should be evenly spread, with a thickness of from }/i to 3^^ inch, to within 
2 or 3 inches of the border of a cloth prepared for that purpose by folding 
in two or three layers. To prevent the poultice from adhering to the skin 
any of the following may be placed on its surface: Gauze, mosquito netting, 
cheesecloth, vaseline, or sweet oil. 

Formalin (poison). — Used as a disinfectant generally in connection 
with permanganate of potash, as follows: For every 1000 cubic feet of room 
space to be disinfected use \i pound of permanganate of potash, powder or 
crystals, and from i to i^i pints of formalin. Add the permanganate 
of potagh to the formalin contamed in a deep tin pail. Effervescence begins 
at once, the room is tightly closed, and the operation is over in about 10 
minutes. After 12 hours the room is opened and the odor removed by 
sprinkling ammonia. 

Glycerin. — Is a mild and healing application for sores, chaps, etc. When 
mixed with an equal quantity of water is useful in earache, hard, irritated, 
or feverish skin, chapped face or hands, split lips, and chafing. 

Iodide of Potash (s-grain tablets). — Useful in syphilis. Dose: i tablet 
dissolved in water three times a day after meals. 

Laudanum (poison). — Useful in easing pain in dysentery and cholera 
morbus. Dose: 5 to 30 drops. 

Lead and Opium Wash (poison) (shake well before using). — Soothing 
external application in sprains and bruises. 

Lemon Juice.-;-Useful in fevers _ and inflammatory complaints. Hot 
lemonade on retiring is useful to aid in the relief of a cold in its first stages. 

Lime Water. — Internally is useful in soothing sick stomach, heartburn, 
diarrhea, and in dyspepsia attended with acidity of the stomach. Dose: 
I to 3 tablespoonfuls. For sick stomach, to be repeated after each effort 
to vomit. Externally as liniment (mixed with an equal quantity of linseed, 
cottonseed, or olive oil) for burns and scalds. 

Magnesia, Calcined, Heavy. — Useful in sick headache, dyspepsia, sour 
stomach, and heartburn. Dose: ^ to i teaspoonful one hour after meals, 
and, being mildly laxative, for constipation in doses of ^i to i teaspoonful. 

Menthol. — Useful in oily solutions (menthol 3 grains, liquid petrolatum 

1 ounce) as cooling drops in nose in colds in the head. Ten drops should be 
placed in each nostril with a medicine dropper. 

Mustard. — Externally is useful to draw the blood to the surface in case 
of pain where skin is not broken. Should be employed as a plaster or 
poultice, made as follows: i part of mustard is thoroughly mixed with from 

2 to 4 parts of flour and made into a paste by the addition of a small amount 



454 • CAMP MEDICINE 

of tepid water. This is then spread thinly to within I or 2 inches of the 
border of a cloth prepared by folding in two or three layers of old cotton 
cloth. The amount of mustard depends upon the degree of pain, the age 
of the patient, etc. Care should be taken that the mustard does not blister 
the skin. As a rule, mustard plasters or poultices should not be applied to 
children and old people, as they may blister the surface. Internally given 
to produce vomiting, i tablespoonful stirred to a cream with a cupful of 
tepid water. 

Oil of Cloves (poison). — Useful in toothache, being applied the same as 
creosote. (See above.) 

Olive Oil (sweet oil). — Internally is useful in constipation. Dose: 
2 to 3 tablespoonfuls. Externally is a soothing application to blistered, 
burned, scalded, or other injured surfaces, also to piles. 

Oil of Wintergreen (methyl salicylate). — Useful when mixed with an 
equal amount of olive oil, as an application for the relief of neuralgia, rheu- 
matism, and painful joints. The oil should be gently rubbed on the painful 
area. If used about the head care should be taken that none gets into 
the eyes. 

Paregoric (poison). — Useful in quieting cough and relieving pain in the 
stomach and bowels and to check diarrhea. Dose: i to 2 teaspoonfuls. 

Permanganate of Potash. — Useful in gonorrhea as an injection; 3^ tea- 
spoonful dissolved in 2 quarts of water. ^ One teaspoonful to a quart of 
water makes an efficient wash for perspiring feet. Useful in snakebites 
in the form of a concentrated solution which should be injected freely and 
immediately into and around the part which has been bitten. Useful as 
a general antiseptic in solution (i tablespoonful dissolved in a quart of 
water). ^ As a disinfectant, see "Formalin." 

Peroxide of hydrogen solution is cleansing and slightly antiseptic. Useful 
as a gargle in sore throat, diluted with an equal quantity of water. Useful 
to apply to wounds, boils, and abscesses, after diluting with from i to 3 
parts of water. 

Picric Acid (poison). — Dissolve in water (}4 per cent, solution). Useful 
to wet dressings with, as an application to burns. 

Quinine Sulphate (5-grain tablets). — Useful in malaria, colds, and as a 
general bitter tonic. ^ Dose: i tablet three times daily. Dose as tonic: 
J^ of a tablet three times a day. 

Salicylate of Soda (5-grain tablets). — Useful in rheumatism, neuralgia, 
and headache.^ Dose: i to 2 tablets every three hours. 

Salol (5-grain tablets). — Useful in diarrhea, dysentery, rheumatism, and 
fermentative dyspepsia. Dose: i tablet three times a day. 

Syrup of Ipecac. — Useful in croup, bronchitis, cough, and hiccough. 
Dose: 10 drops every three hours. Also used to produce vomiting in doses of 
I to 2 tablespoonfuls. 

Soap Liniment (for external use only). — Useful in rheumatism, sprains, 
and bruises. 

Spirit of Camphor. — Internally is useful in nervous diarrhea, colic and 
cramps. Dose: 5 to 30 drops, first added to sugar and then mixed with 
water. 

Strychnine Sulphate (poison) (3^o grain tablets). — Is a bitter tonic and 
stimulant and is useful in anemia and dyspepsia. Dose: i tablet three 
times a day. 

Sun Cholera Mixture (poison) (15-minim tablets). — Useful in diarrhea, 
dysentery, and cholera morbus. Dose: i tablet. 

Sweet Spirit of Niter. — Useful in fevers, flatulent colic, and colds. Dose: 
3'^ teaspoonful in sweetened water every four hours. 

Tannic Acid (tannin). — Useful in hemorrhages from external surfaces 
or from mucous membrane which can be reached from without. Applied 
either pure or in solution in water or glycerin. Useful as an application 
wherever powerful astringent action is needed. 

Tincture of Green Soap. — Cleansing hands. 

Tincture of Iodine (poison, for external use only). — Useful to disinfect 
wounds; should be diluted with an equal quantity of alcohol or water. If 
painted over inflamed surfaces, will sometimes be of value. 

Tincture of Iron. — Useful as a tonic. Dose: 10 drops largely diluted 
with water, three times a day. Rinse mouth after taking. Should be 
taken through a straw. 

Tincture of Myrrh. — Useful in diseased gums and sore throat. Direc- 
tions: For spongy and bleeding gums, apply with a sponge or soft brush. 
For sore throat, use as a gargle, i teaspoonful in a cupful of water. 



SICKNESS 



455 



Turpentine. — Used in the form of hot turpentine stupes in typhoid fever, 
pneumonia, colds, bronchitis, lumbago, pleurisy, and inflammation of the 
bowels. The stupes are prepared by wringing a double layer of thin flannel 
out of a pint of hot water with which a teaspoonful of turpentine has been 
mixed. These applications should not be prepared too close to a fire on 
account of the inflammability of the turpentine. 

Unguentine. — Useful in burns, scalds, and inflammation. Spread on 
linen or cotton cloth and apply. 

Vaseline. — Internally and externally useful for the relief of cold in the 
chest. Externally useful in cold in the head, soothing irritated surfaces, 
burns and scalds, and as a protective dressing. 

Zinc Sulphate (poison). — Useful in gonorrhea as an injection, made in 
the proportion of 34 teaspoonful to i pint of water. Is given internally 
in doses of 34 to 3^^ teaspoonful dissolved in water to produce vomiting. 



COMMON SICKNESS 



Stomach and 
Bowels 

Constipation 
Stomach ache 
Diarrhea 
Dysentery 



Fevers . 
Typhoid fever 
Marlarial fever 



Throat and 

Lungs 
Sore throat 
Pneumonia 



Miscellaneous 
Headache 
Sunstroke 
Rheumatism 
Influenza 
Gonorrhea 
Nephritis 
Piles 
Poison ivy 

In case of serious sickness get the Patient to a settlement where he can receive 
proper nursing and medical care. 

CONSTIPATION 

Constipation should be promptly corrected. Mild cases will generally 
respond to cathartic pills. Epsom salts can be used or a couple of table- 
spoonfuls of castor oil. ... 

Obstinate cases require injections of warm water with olive or castor oil 

COLIC (STOMACH ACHE) 

Mild cases can be treated with lo drops essence of peppermint or a tea- 
spoonful of Jamaica ginger in hot water. 

Obstinate cases often require an injection to clear the bowels and a dose 
of 10 drops of laudanum in water taken internally; if the pains persist a 
second dose of laudanum can be repeated in two hours. 

DIARRHEA AND DYSENTERY 

Mild diarrhea caused by poor diet will generally respond to a mild laxative 
(cathartic pills or castor oil). The diet should consist of light articles such 
as weak broths, soft boiled eggs, milk and thoroughly toasted bread. The 
patient should remain in bed if the attack is at all severe and in this case 
after the bowels have moved freely in response to the cathartic if the diarrhea 
or pain continues give one camphor and opium pill repeated after three hours 
if necessary. 

DYSENTERY 

Dysentery occurs in its most dangerous form in the tropics but will respond 
as a rule to immediate treatment. 

Cause. — Bad food, unripe fruit, impure drinking water, exposure to cold 
and dampness while probably not the direct cause are contributary to the 
disease. 

Prevention. — Boil all drinking water and be careful of diet. Avoid ex- 
treme exposure. 

Symptoms. — May or may not be chills. Some fever. Tongue furred and 
rnoist, then red and dry or brownish and glazed. First stools like simple 
diarrhea. Soon are sirnple mucus or a mixture of blood and mucus. 
Patient complains of colicky pains in his belly and a burning sensation in 
the rectum and constantly desires to go to stool. 

Treatment (Health Bulletin No. 17). — Rest in bed. Stop all solid food. 
Give 2 tablespoonfuls of castor oil and 15 drops of laudanum in one dose 
and if necessary repeat the dose in six hours. After the bowels have been 
thoroughly cleared out, give a pill of camphor and opium every three hours. 



4S6 



CAMP MEDICINE 



Hot applications should be placed on the abdomen. Washing out the 
rectum with a pint of warm water and then injecting 2 ounces of thin starch 
containing 25 to 30 drops of laudanum will relieve the burning sensation. 

After two or three days if the disease continues the castor oil may be 
again given, the treatment repeated. 

Diet should be limited to thin porridge milk and broths. Patient must 
be kept warm in bed in even light cases. 

TYPHOID FEVER 

Cause. — Typhoid fever is a contagious disease. It is generally con- 
tracted by drinking infected water or milk or eating food that has been 
prepared by a person just recovering from the disease. 

Prevention. — Care in regard to water and milk supply. 

Symptoms. — Headache, diarrhea, cramps in the abdomen, nosebleed, 
loss of appetite, coated tongue, dry mouth and fever which is higher each 
day than on the day previous. The stools are foul smelling and of the con- 
sistency of pea soup. 

Duration. — Four to seven weeks. Convalescence is slow. 

Treatment (U. S. Health Bulletin No. 17). — Place the patient in bed and 
do not let him get up. When he desires to have an action of the bowels, the 
bedpan should be used. He should have a liquid diet, plenty of water, milk, 
and thin soups, which should be given in liberal quantities, a cupful every 
two hours; no solid food should be allowed until 10 days after the fever has 
subsided. The temperature should be watched and the patient bathed with 
cold water whenever the fever rises above 39° C. (102.2° F.). Ice-bags, 
if obtainable, applied to his abdomen and chest will assist in keeping the 
temperature down. ^ One should also be applied to the head if there is 
delirium. If there is distension of the abdomen hot turpentine stupes 
should be applied. ^ This is done by wringing a double layer of thin flannel 
out of hot water with which a teaspoonful of turpentine per pint of water 
has been mixed. An injection of a pint of warm water containing a tea- 
spoonful of turpentine is also beneficial. The bowels should be kept open by 
injections of warm soapy water. In case of collapse give coffee or inject 
hot coffee or salt solution (one teaspoonful of salt to a pint of water) into 
the bowel, 

MALARIAL FEVER 

Cause. — Malarial fever is caused by germs generally transmitted by the 
bite of mosquitoes. 

Prevention. — Protect bed by mosquito bars. Avoid location of camp 
near stagnant pools or other features favorable to mosquito breeding. In 
localities where malarial fever is prevalent take 6 grains of quinine every 
day. This is an important preventative measure. 

Medical authorities state that the use of quinine as a preventative has 
reduced the number of cases per 1000 men per year from 275 to 50. 

Treatment (Health Bulletin No. 17). — When a chill occurs, the patient 
should at once be wrapped in blankets and be given hot drinks. Hot-water 
bottles, heated bricks or stones wrapped in cloth or in a separate piece of 
blanket, should be placed at the feet. Mustard plasters may also be applied 
to the extremities and over the region of the heart. 

During the hot stage cold drinks may be administered; if it is severe a 
tepid bath in a tub .or by means of a sponge may be given. If the tem- 
perature is very high, 105" or 106° F., a cold bath should be given. 

As soon as the sweating stage begins 10 or 15 grains of quinine should 
be taken, and along with this, if the bowels are not freely open, a calomel 
tablet, one-tenth grain each, should be given every 15 minutes until 10 
have been taken. Every six hours thereafter the patient should take 5 
grains of quinine for two or three days and then 5 grains three times daily 
for the next two weeks. 

If vomiting occurs, a mustard plaster may be placed over the region of 
the stomach, above the navel, and cracked ice may be given by the mouth. 
Headache may be relieved by cold applications or by 10 grains of aspirin 
taken with a cup of hot tea. 

In pernicious types of malarial fever the treatment should be more active. 
No time should be lost in giving the quinine; 20 grains should be given 
immediately, with 2 grains of calomel. A physician should be summoned 
if the services of one can be obtained, as dilute solutions of quinine may have 
to be injected into the patient's veins in order to save his life. 



SICKNESS 457 

SORE THROAT (TONSILLITIS, QUINSY) 

Sore throat is a common disease. It is usually the result of exposure to 
wet and cold. Talking, laughing, or shouting in a damp, cold atmosphere 
is sometimes the cause of it. It may accompany or be an extension from 
an ordinary "cold in the head." It is a complication of diphtheria, scarlet 
fever, smallpox, tuberculosis, and syphilis. It is caused also by drinking 
milk drawn from cows with sores on their teats. Sometimes the inflamma- 
tion is limited to the mucous membrane of the pharynx and soft palate; it 
is then known as pharyngitis or acute catarrhal sore throat. More fre- 
quently the tonsils are affected, and the inflammation is then called ton- 
sillitis. When the inflammation is more deeply seated behind the tonsil and 
tends to suppurate or form an abscess, the term "quinsy" is applied. An 
attack of sore throat may last from 2 to lo days, or longer. 

Symptoms of acute sore throat are chilliness and feverishness, pain or 
soreness on swallowing, dryness, or a tickling or scratching sensation in 
the throat. 

There is liable to be stiffness and some tenderness along the side of the 
neck. If one or both tonsils are involved, as they usually are to a greater 
or less extent, the symptoms are more severe. In marked cases examination 
shows redness and swelling of the parts affected — swollen tonsils (tonsillitis) 
and white or cream-colored spots may be seen on the surface of one or both 
tonsils. (This form of the disease is frequently mistaken for diphtheria.) 
There may be high fever and great prostration. 

In the severest form of tonsillitis (quinsy) the tonsil is hard and swollen 
to twice or three times its natural size, and the patient is unable to swallow 
or to open his mouth beyond a fraction of an inch. The saliva dribbles 
away; if suppuration occurs the tonsil gradually softens until the abscess 
breaks. With the discharge of pus the severe pain is relieved and the 
patient rapidly recovers. If the abscess is large, and if the pus is discharged 
in a backward direction, there is danger from suffocation, particularly if 
the abscess breaks during sleep. Fortunately the abscess usually points 
toward the mouth, and the pus runs out. 

Treatment. — Persons who are subject to attacks of sore throat should 
keep their feet dry and be careful not to catch cold. If a case develop, 
give a gargle of salt water or potassium chlorate and water (saturated solu- 
tion), or boric acid and water may be applied to the tonsil. Dry bicarbonate 
of soda (baking soda) is highly recommended as a local application, a small 
quantity to be applied every hour^ Apply cold water or a light ice-bag to 
the neck, or a thick piece of flannel saturated with ice water may be placed 
around the neck and covered with muslin. Small pieces of ice placed in 
the mouth are usually agreeable. The bowels should be kept open by means 
of Epsom salt. 

If the cold application^ to the neck do not give relief, or if they are not 
agreeable to the patient, apply hot water or poultices and give hot gargles, 
or let the patient gargle with hot tea. If the swelling is very great, he can 
not gargle. If practicable, send for a physician. 

INFLUENZA 

The disease begins like a cold. There are pains in the head, eyes, an 
limbs; a watery discharge from the nose, chilly sensations, sore throat, 
cough, and extreme muscular prostration. The sputum is of a dirty yellow- 
ish color. There may be abdominal symptoms such as nausea, diarrhea, 
vomiting, and cramps. There is fever, which varies according to the in- 
tensity of the disease. There are many varieties of the disease, and any 
organ of the body may be attacked. Pneumonia is a frequent complication. 

Prevention. — C^are should be taken that no one suffering from the disease 
coughs in your face. Keep away as much as possible from such persons. 
A cold in the head or on the chest may be due to the influenza bacillus, so 
do not sleep with persons suffering from these conditions. 

Treatment.— Aspirin, 5 grains every three hours, often relieves the pains. 
A mild purgative such as a Seidlitz powder should be given. The tendency 
to diarrhea should be remembered, so strong purgatives such as salts should 
not be administered. When there is pain m the abdomen a camphor and 
opium pill is of value. A light diet such as milk and soups should be taken. 
Steaming the nose and throat by inhaling steam from a teapot filled with 
hot water into which a small lump of camphor has been dropped will relieve 
tQ some extent the congestion of those structures, 



458 



CAMP MEDICINE 



PNEUMONIAi 

Cause. — The germ responsible for the disease is generally conceded to be 
present in the bodies of all healthy people but only causes sickness when 
the resistance of the victim is lowered for some reason. Chilling after 
extreme exertion and long-continued exposure to cold often bring on the 
trouble. 

Symptoms. — Severe chill, high fever, difficult breathing and pain in the 
chest. The sputum is abundant, and is a rusty brown. The pulse is at 
first full and later weak and rapid. The fever in typical cases lasts for 
7 to 9 days and then in favorable cases drops to normal in a few hours. 

Treatment. — ^^The essential feature of the treatment of pneumonia is to 
see that the patient gets plenty of cold fresh air. Oftentimes no other treat- 
ment is necessary. The bed should be placed upon a porch, or, if this is 
impossible, all the windows of the sick room should be wide open. The 
patient should be well covered, and hot-water bottles or hot bricks should be 
placed near his feet to keep them warm, care being takea not to burn him. 
Once a day the patient should be moved to a warm room and given a sponge 
bath. The pain in the side can be relieved by a mustard plaster (p. 453) 
or by the administration of one-fourth of a grain of morphine sulphate. 
Two grains of calomel and four grains of sodium bicarbonate followed, in 
about six hours, by a Seidlitz powder should be given on the first day, and 
the bowels should be kept open thereafter by a small dose of salts given each 
day. The patient's strength should be conserved by giving him a glass of 
milk or a bowl of soup every two hours during the day, and also at night 
when he is not sleeping. Solid food should not be given, as it will cause 
gas in the stomach, which may press against the heart and seriously inter- J" 
fere with its action. Milk is the best food, but sometimes it produces gas, | 
in which case soups alone should be used. 

HEADACHE 

Headache is not a disease in itself; it is the symptom of some other disease! 
and if it occurs frequently a physician should be consulted. ^ f 

Treatment. — Temporary relief can often be obtained by taking 10 grains ] 
of aspirin repeated in three hours if necessary. Open the bowels with a 
cathartic. 

POISON IVY 

Treatment. — Bath with salt water or a boric acid solution, i teaspoonful j 
in a glass of hot water. Open the large blisters and let the water out. \ 
Every day bath the infected areas with warm water, dry without rubbing 
and apply the boric acid solution. 

SORE EYES 

Inflammation of the Membrane Covering the Eye. — Caused by grit, 
dust, exposure to cold, etc. ^ ^ . 

Symptpms. — Eye painful. Eyeball red and lids swollen. Pain increased j 
by exposing eyes to light. Water runs from eyes. _ ^ .1 

Treatment. — Wash eyes out every two hours with boric acid solution (r 
teaspoonful of acid in a glass of warm water) . A few drops of zinc sulphate 
solution m grain to i ounce of water) should be placed in the eyes every 

three hours. _^„ 

SUNSTROKE 

Cause. — Prolonged exposure to strong rays of the sun or high humid 
temperature. . . - . - 

Prevention. — Proper head and spme protection under tropical sun and 
avoidance of travel under extreme conditions of heat. Drink water 
sparingly. Oatmeal water quenches thirst in small quantities. 

There are two varieties of trouble. 

No. I. — Heat stroke (heat fever) in which the body temperature is high. 

No. 2. — Heat prostration in which the surface of the body is cool sometimes 
below normal. 

The difference is very important as the treatments are radically different. 

Symptoms and Treatment 
No. I Heat Stroke. — Severe cases the victim may fall unconscious and 
die instantly. The usual case manifests intense headache, dizziness, nausea, 

1 Briefed from Health Bulletin No. 17. 



SICKNESS 459 

vomiting and hot skin. Temperature may reach 105° F. Pulse full and 
may be either slow or rapid. Patient sinks into stupor and unconsciousness. 
They may recover under treatment or die within twenty-four hours. 

Treatment (heat stroke). — Reduce temperature of body at once by 
cold water bath, ice pack on head till temperature of body as shown by a 
thermometer in the rectum is reduced to 100° F. If the temperature rises 
again repeat the treatment. 

If the patient is exhausted after the reduction in temperature give strych- 
nine sulphate ^40 grain. ^ ,.,,., 

No. 2 heat prostration with a cool skm and weak rapid pulse stimulants 
are required. Wrap patient in blankets, hot-water bottles at feet and 
around abdomen; give }io grain strychnine sulphate. If head is hot, 
cold-water pack can be applied to head only. If vomiting occurs inject hot 
salt water solution into rectum (i tablespoonful of salt to i pint of water). 

MUSCULAR RHEUMATISM 

In this disease the muscles most frequently affected are those of the back 
(lumbago), side of neck (stiff neck or wry neck), and side of chest (pleuro- 
dynia). Exposure to cold, sudden cooling of the body — especially after 
active exercise and sitting in a draft of air — are the chief causes or exciting 
causes. 

As a rule there are no symptoms other than the stiffness and pain on 
motion. The muscles may be slightly swollen and very sensitive. Some- 
times the attacks come on suddenly and apparently without cause, or follow- 
ing a slight twist or strain, as a "kink in the back," or patient may wake up 
in the morning with a stiff neck. 

In treating acute cases salicylate of soda or aspirin may be given in 5- or 
lo-grain doses every three hours until four or six doses are taken. Apply 
hot applications, dry heat, hot-water bag, or a hot poultice locally, or the 
heat may be applied by a fiatiron over folds of flannel or a piece of blanket 
and the rheumatism "ironed out." Later apply liniment, with friction 
(massage). Keep the affected muscles at rest. If the muscles of the chest 
are affected, apply strips of adhesive plaster, the same as for fractured rib. 
Acute attacks are of short duration, but relapses are not uncommon, and 
chronic forms are frequently met with. Good f9od, fresh air, and attention 
1 to the general health are especially important in the treatment of chronic 
muscular rheumatism. 

I ACUTE RHEUMATISM (RHEUMATIC FEVER) 

This is a comparatively common disease in all climates within the Tem- 
perate Zone. It occurs chiefly during the winter and spring. ^ Exposure to a 
' cold, damp atmosphere is the most frequent exciting^cause in persons pre- 
disposed to the disease. 

It may or may not begin with a chill or with a sore throat. The larger 
joints are usually affected. Swelling, heat, redness, tenderness, and pain 
are the chief symptoms. The inflammation is apt to shift from one joint 
to another. The pain and fever are usually increased in proportion to the 
, number of joints involved. The majority of cases are attended with pro- 
fuse perspirations, scanty, highly acid urine, coated tongue, and constipa- 
tion. The heart is frequently involved. 

In treating, wrap the joint in cotton or flannel; keep it very quiet — 
I the slightest movement aggravates the pain. Flannel wrung out of hot 
I water and applied to the joint sometimes affords relief. _A liniment com- 
I posed of 10 to 50 per cent, of oil of wintergreen in olive oil may be applied 
I on a piece of flannel if the pain is severe, or cold applications may be em- 
ployed if agreeable to the patient. 

Place the patient in a good bed, and let him wear flannel next to his 
J skin. Change the flannel frequently, and bathe the body with tepid water. 
I For internal medication give salicylate of soda or aspirin in doses of 
' 10 grains every two hours until about eight doses are taken or the pain is 
I relieved; then give it in smaller doses of from 3 to s grains every six hours. 
The food should be soft and nourishing and given every three hours. 
I Epsom salt should be given to keep the bowels open. The patient should 
j be kept in bed for a few days after the symptoms have subsided. The 
; duration of the disease is very uncertain. The acute symptoms may subside 
, in a few days and the patient may be up and about in a week or 10 days, but 
^ relapses are common, and the acute may pass into the subacute or chronic 
I form. 



46o 



CAMP MEDICINE 



GONORRHEA (CLAP) 

Treatment (Health Bulletin No. 17). — Rest in bed, light diet, plenty of 
water to drink, regularity in eating and sleeping. Keep the bowels open by 
taking a moderate dose of Epsom salt in the morning. Avoid strong coffee 
and tea, all stimulants, and greasy articles of food. Keep the body and 
mind at rest. Bathe frequently in hot water. Be very careful not to carry 
any of the pus from the urethra to the eyes. (Gonorrheal inflammation of 
the eyes is a serious disease, which not infrequently results in total blindness.) 

Give a copaiba capsule three times a day. If much pain in the back 
or over the region of the kidneys follows the use of the copaiba, it must be 
discontinued for a time or the dose lessened. 

Injections of silvol 5 parts, water 90 parts; argyrol, 10 per cent, solution; 
permanganate of potash i part, water 5000 parts; or sulphate of zinc i 
grain, water i ounce, into the urinary canal may be used. They should be 
employed as follows: The patient first passes his water, the urinary canal 
is then washed out with several syringes full of warm water. One of the 
above solutions is then injected slowly into the canal and held there five 
minutes by the watch. The best syringe for this purpose is one made of 
glass, having a plunger wrapped with cotton thread. If a testicle swells, 
ajjply cloths wrung out of cold water, or an ice-bag. Rub the affected part 
with the following mixture: Oil of wintergreen (10 drops) and olive oil (i 
teaspoonf ul) . If chordee is troublesome, apply cloths wrung out of cold 
water. 

PILES 

Cause. — Often due to chronic constipation. _ 

Prevention. — Keep bowels regular and easy. m 

Treatment (U. S. Health Bulletin No. 17). — In acute attacks, if the bowels« 
are constipated give a full dose of Epsom salt; put the patient on light, soft 
diet. Apply ice to the anus or inject cold water into the rectum. An oint- 
ment composed of 5 grains of menthol rnixed with 2 tablespoonfuls of 
vaseline often affords great relief. If the piles protrude, especially if they 
become strangulated, they should be pushed back with the finger; olive oil, 
or vaseline may be applied. If the piles are large and persistently painful, 
see a surgeon and have them removed by operation, which is the only sure 
cure. 

KIDNEY DISEASE (ACUTE NEPHRITIS) 

Cause. — Expose to cold and dampness. 

Symptoms. — Amount of urine is materially reduced. Generally the 
color is dark red or brown and contains albumen which can be detected by 
boiling a teaspoonful with a few drops of vinegar. The presence of albumen 
is shown by a cloudy precipitate in the boiled urine. Other symptoms may 
be headache, vomiting, diarrhea, convulsions and unconsciousness. 

Treatment. — Put patient to bed, keep him warm and in acute cases in- 
duce sweating by hot blankets, etc. Put him on a milk diet and give him 
all the water he wants. Keep the patient as quiet as possible and after 
the albumen has disappeared from the urine avoid cold, dampness and 
excessive exercise for some time as convalescence is slow. During con- 
valescence avoid eating red meats. { 

FIRST AID FOR ACCIDENTS ? 

As mentioned on page 445 all the data on First Aid are quoted fromf 
Bulletin No. 17 by the courtesy of the department which was glad to co- 
operate to make the data available for emergencies. 

CONDENSED INDEX 

Bruises 461 

Sprains 461 

Foreign Matter in Eyes, Ears, etc.. . , 462 

Snake Bites . 464 

Bleeding 464 

Bums and Scalds 471 

Wounds 474 j 

Drowning 476 

Electric Shock 479 

Poisons 481 

Fractures 483 I 

Dislocations . 496 



FIRST AID 461 

U. S. HEALTH SERVICE BULLETIN NO. 17 
By Surgeon R. M. Woodward 

Rtiles to be Observed in Time of Accident 

1. Give the patient air. 

2. Lay the patient down, head lower than the body. 

3. Rip the clothes off the injured part. 

4. In removing a coat or shirt, first release the good arm, then the injured 
one. 

5. Turn the head to one side to allow vomited matters to escape from 
the mouth. 

6. Do not give whisky to the patient. If he can swallow, and needs a 
stimulant, give coffee, tea, hot milk, or hot water. 

7. Then follow directions given elsewhere in this book. 

A LIST OF DON'TS 

Don't fail to send for the doctor. He knows best. 

Don't leave the patient in order to go for the doctor if there is any, one 
you can send. He may need your moral encouragement if nothing more. 

Don't get excited. An appearance of agitation on your part will dis^ 
courage the patient. 

Don't hold an injured person on his feet, nor require him to sit in a chair. 
He will be better off and less apt to faint if he lies down, preferably with the 
head low. 

If you have a first-aid chest, and a bottle of medicine is exhausted, don't 
wait until you need it again before having the bottle filled. 

Don't put your fingers on a wound. They are covered with germs, and 
you will almost surely infect the wound. 

Don't use a spider web or a quid of tobacco on a wound. They are 
filthy, do no good, and are very apt to infect the wound. The same thing 
is true to a less extent in regard to salves of various kinds. 

Don't place cotton next to a wound. Always keep at least one layer of 
gauze or boiled cloth between the cotton and the raw surface. The cotton 
sticks to the wound and is very difficult to remove. 

Don't apply bandages too tightly. 

Don't remove a dressing to see how a wound looks. Let the doctor 
do that. 

Don't sit down at the bedside and discuss with the callers all of the 
horrible accidents you ever heard of. Your conversation will not be ap- 
preciated by the patient. 

MINOR ACCIDENTS 

Bruises, sprains, foreign matter in eyes, ears, nose and throat. 

BRUISES AND CONTUSIONS 

A bruise or contusion is an injury where the tissues beneath the skin have 
been torn but the skin itself has not been opened. ^ Blood oozes out of the 
injured vessels, but can not escape, as the skin is still intact. The symptoms 
are swelling, tenderness, and a feeling of soreness or pain. Discoloration of 
the skin occurs quickly in superficial contusions and in places where loose 
tissue abounds, but only after days when the injury is deep-seated. This 
discoloration is at first red and then, successively, purple, black, green, and 
yellow. This play of colors is due to the changes which take place in the 
blood while undergoing absorption. 

Treatment. — A pad of gauze or soft towel should be tightly bandaged 
over the injured part to stop hemorrhage, after which cold should be appUed 
except in old or feeble persons or where the contusion is extensive. In 
the latter case heat is best, as cold might cause gangrene. Evaporating 
solutions, such as witch-hazel, a 15 per cent, solution of alcohol in water, 
or a saturated solution of Epsom salt, are often found of great benefit. A 
contusion should never be opened except in rare cases when it is necessary 
to stop persistent bleeding. If an opening is made through the skin, germs 
are liable to enter and cause severe inflammation, resulting in the formation 
of pus. 

S|»'ains. — A sprain in a stretching or wrenching of a joint. The joints 
most frequently affected are the ankle, wrist, knee, and shoulder. 



462 



CAMP MEDICINE 



The symptoms and signs are pain, swelling, impairment or loss of motion, 
and discoloration from effusi9n of blood. When there is much swelling 
it may be difficult to determine whether sprain or fracture, or both, are 
present. 

As explained under "Broken Bones," page 484, it is sometimes very 
difficult to determine whether an injury near a joint is a sprain, a bruise, a 
broken bone, or all combined; and if there is doubt, the case should be 
treated as a broken bone. Injuries about the ankle-joint are especially 
confusing, and sometimes the :v-ray shows a fracture that could not have 
been detected in any other way. It should also be understood that a 
sprain, particularly if some of the soft parts about the joint are torn, may be 
much longer in being restored to a norrnal condition than if a simple break 
of the bone had occurred without other injury. 

Treatment. — Either hot or cold applications are good first aid measures, 
but they should be distinctly either hot or cold, and not tepid. Soaking 
the part for half an hour several times a day in water as hot as can be borne, 
and gently rubbing the skin, are excellent. If it is more convenient to 
apply a bag of ice, this can be used, but the heat and cold should not alter- 
nate. ^ Propping the part up on pillows assists. If there is much pain, great 
relief is obtained by surrounding the joint with a thick layer of cotton and 
applying a plaster bandage. The circulation of the lower part of the limb 
should be watched, and if found to be impaired the bandage should be cut 
from above downward and the sides spread apart to relieve any constric- 
tion that may be present. After the swelling has subsided somewhat, 
rubbing with any kind of liniment or with alcohol will help, but it is the 
rubbing more than the liniment that does the good. 

It is popular belief among laymen that a large quantity of liniment, 
perhaps applied on flannel cloth, is all that is necessary, and that the rub- 
bing is only of secondary importance. This is a decided mistake. Later 
on the part should be grasped and gently moved in various directions, 
making what is known as passive motion. In some cases this is inadvisable 
and the patient appears to do better with the part at rest, which can be 
obtained by strapping the joint with strips of sticking plaster or placing 
the limb in a splint. The black and blue condition of the skin that some- 
times appears will gradually subside as the part gets better. 

FOREIGN BODIES IN THE EYE, EAR, NOSE AND THROAT 
Foreign Bodies in the Eye. — When a piece of sted, a cinder, or any 
foreign body enters the eye, nature at once floods the eye with tears in an 
endeavor to wash the offending agent away, and frequently succeeds. 
Sometimes, however, the foreign body is embedded in the eyeball, the lid, 
or other part of the eye, or keeps moving about from one part to another 
without escaping; then assistance is necessary. 

Occasionally drawing the upper lid well down with the fingers, and allow- 
ing the lashes of the lower Hd to act as a brush, will remove the body if it 
is not tightly embedded. Usually, however, it is necessary to invert the 
upper lid; in other words, turn it inside out. This is not difficult with a 
little practice. The upper eyelid contains a piece of cartilage or gristle 
along its lower edge which makes it easy to turn. To invert the eyelid 
face the patient, or stand behind him as seems more convenient; have hiim 
look well down toward the floor; take hold of the lashes of the upper lid 
with the fingers and thumb of one hand; they lay entirely across the middle 
of the eyelid a wooden toothpick, match, knitting needle, lead pencil, or 
other thin object (Fig. 89); press it downward, and at the same time 
gently pull the lashes upward, when the lid will suddenly turn inside out 
(Fig. 90). Drawing down the lower lid by simply pressing upon it will 
expose its inside surface. If the foreign body is seen, it should be very 
gently removed with the corner of a handkerchief. If it is partly embedded 
in the eyelid, it may be possible to gently dislodge it with a wooden tooth- 
pick or other similar object. If the foreign body is on the eyeball, it some- 
times requires a good light, good eyesight, and even a magnifying glass to 
detect it. If found, it should be removed with a handkerchief or other soft 
material, but if embedded too tightly to be removed in this manner, it is 
best for the layman not to attempt anything further for fear of greater j 
injury to the eye. Under such circumstances one or both of the eyes ' 
should be snugly bandaged with soft light proof material, such as red flannel, 
and the doctor should be called as soon as possible. The patient should be 
cautioned not to wink his eyes, as all motion will increase the irritation. 



I 



ACCIDENTS 



463 



If you have succeeded in removing the body, and the eye appears very 
red, a little sweet oil, dropped in will be very soothing. It should be re- 
membered that the scratching of the eyeball makes it feel as if the body 
were still present after its removal. The old household remedy of drop- 
ping a flaxseed into the eye in the hope that in slipping about it may dis- 
lodge the body is said by specialists to do no good, and may do harm. 

Foreign Bo4ies in the Ear. — Children occasionally place buttons or similar 
objects in the ear. If near the outlet, they can sometimes be removed 
(in the absence of suitable instruments) by gently passing along one side a 
crochet needle or other similar implement. It should oe remembered, how- 
ever, that the dnjm of the ear, which is extremely delicate, and means 
so much to the child in the future, is only a short distance inside, and any 
effort of this kind made by the layman 
should be very gentle indeed. ^ A 
stream of water from a small syringe 
may wash the object out. _ If these 
measures do not succeed, wait for the 
doctor by all means. Sometimes an 
insect crawls into the ear. The actual 
physical danger is less than the mental 





Pig. 89. 



Pig. 90. 



horror, as the insect soon dies. A little sweet oil dropped into the ear may 
cause the insect to back out to free itself from the unpleasant predicament; 
if not the oil will kill it. 

Foreign Bodies in the Nose. — If near enough to the nostril to be seen the 
body may possibly be expelled by compressing the other nostril and having 
the patient blow his nose hard. ^ A fountain syringe placed i foot above the 
head, the nozzle of the syringe inserted in the clear nostril and the patient's 
face looking somewhat downward, will cause the water to gently flow in 
at one side of the nose and out at the other side, and may dislodge the 
object. ^ A crochet needle may be gently tried as described for the ear. AH 
these things failing, wait for the doctor. 

Foreign Bodies in the Throat. — If the body can be seen by holding the 
tongue down with a spoon or by drawing the tongue out with a towel, it 
can sometimes be hooked out by means of a finger passed well in. If the 
body is in the_ windpipe, this will be manifested by violent coughing, which 
may dislodge it. Inverting the patient and slappng his back may be tried. 
If these measures do not succeed, then use every effort to quiet the patient, 
and if practicable send for a physician. If the body is in the gullet on the 
way to the stomach, vomiting may bring it up, and this can be excited by 
tickling the throat, or using some- of the simple vomiting agents mentioned 
in the data on poisons (page 481) provided the patient can swallow. 
If it is not dislodged, and is known to be an object without sharp edges, as 
a coin, for instance, it is best to induce it to go on into the stomach by 
drinking water, eating bread, mashed potatoes, or other soft food. Once 
in the stomach the patient, usually a child, should be made to eat all the 
mashed potatoes he can possibly hold, and a large dose of castor oil should 
follow. The potatoes form a mass around the foreign body, and the oil 
usually pushes this mass through the bowels without any trouble what- 



464 



CAMP MEDICINE 



ever. The stools or passages should be carefully watched to determine 
that the object passes, and if it does not, the doctor should be consulted 
without delay. 

SERIOUS ACCIDENTS— FIRST AID 
BITES AND STINGS OF POISONOUS ANIMALS OR INSECTS 

Snake Bites. — (Do not give alcohol or ammonia.) Poisonous snake bites 
must receive instant treatment. Fasten a bandage or handkerchief above 
the wound and twist it tight to prevent the flow of blood toward the body 
and heart. Cut the wounded flesh out so that it bleeds freely. If ther^ is 
anyone with you get them to suck the wound immediately, thoroughly and 
repeatedly spitting out the blood and washing their mouth with water 
eliminates all danger to them. A concentrated solution of potassium 
permanganate should then be poured into the wound or better injected 
around and above the wound using the full charge held by an ordinary 
hypodermic syringe. (When working in a snake country a small pocket 
case containing a sharp clean lancet, hypodermic syringe and a bottle of 
potassium permanganate should always be carried). The tight bandage 
cutting off the flow of blood must be loosened within ten minutes of its 
application to permit some circulation as a long continued stoppage of blood 
causes gangrene even when the blood is allowed to circulate freely at inter- 
vals of ten to fifteen minutes the tight bandage should be removed entirely 
within a couple of hours. There is great danger in its prolonged use. Snake 
bites treated promptly in this way are rarely fatal although they may 
make the victim very sick. The patient's vitality should be prompted by 
hot blankets, water bottles, etc. 

Wilson's Topographic Surveying states that in addition to this treatment 
the only sure cure particularly for the more dangerous tropical snakes is 
the hypodermic injection of Antivenene serum. "The injection is made 
in the cellular tissue of the right or left side of the abdomen. Treatment 
should be immediate for best results although it may be successful after 
as much as three -or four hours. If there is time the skin should be carefully 
cleansed before using the syringe, the needle of which should be inserted 
deeply closely compressed with the fingers for a couple of minutes and then 
hastily withdrawn. 

"Antivenene serum can be obtained from Les Establissements Poulenc 1 
Freres, 92 Rue Vieille-du-Temple, Paris. The serum will keep for years. | 
Dose 10 cc.( contents of one flask), or for large snakes as the cobra 20 cc. or ^ 
two full doses, at once." 

Bite of Dog or Cat. — This is usually a punctured wound; that is the 
teeth enter without tearing the flesh, and the wound almost entirely closes, 
thereby preventing drainage and increasing the danger. Sucking the wound 
hard repeatedly and washing out the mouth with hot water may remove 
some of the poison. Squeezing is less effective.^ The wound should then 
be burned either with carbolic acid or a red-hot iron carried to the bottom, 
and the skin about the wound should be scrubbed with alcohol or other 
antiseptic. A drain of several strands of boiled sewing silk should be pushed 
into the bottom of the wound, and an antiseptic dressing or boiled cloth 
applied over the wound. The patient should then be taken to the nearest 
place where the Pasteur treatment to prevent hydrophobia or rabies can be 
secured. The hygienic laboratory of the United States Public Health 
Service in Washington, D. C, administers this treatment without cost. 

If the animal is known to be mad this treatment is imperative, and 
whether mad or not it is a very wise precaution and relieves the anxiety 
of the patient. 

BLEEDING (HEMORRHAGE) 
Kinds of Blood-vessels. — There are two kinds of blood-vessels. Those 
that carry the blood from the heart to all parts of the body are called arteries. 
The blood in them is bright red, and escapes in jets or spurts correspondmg 
to each beat of the heart. Bleeding from these is more dangerous and more 
difficult to control, as a rule, than bleeding from the vessels that return the 
blood to the heart. Fortunately, however, the larger arteries in the limbs 
lie near the bones, and are consequently well protected in most parts by 
the mass of muscles covering them. The vessels that return the blood to 
the heart are called veins. They contain a darker blood than the arteries, 
and when cut, the blood escapes in a steady stream, not in spurts. While 



ACCIDENTS 



465 



the largest veins in the limbs are also near the bones, there are some of con- 
siderable size just under the skin. 

If we should desire to stop a stream of water flowing past a given point, 
we would naturally go upstream from that point and not downstream to 
adopt the necessary measures. When there is bleeding from an artery, 
the blood coming from the heart, the artery must be compressed at a place 
between the heart and the bleeding point. On the other hand, if a vein is 
bleeding, the blood flowing toward the heart pressure must be made on the 
vein at a place farther from the heart than the bleeding point. 

Bleeding, General Treatment. — Before beginning the treatment of any 
wound or any bleeding point, if there is time, the operator must carefully 
cleanse his hands and arms, and also the wound and surroundmg parts. 
The instruments and silk ligature should be boiled, as described under the 
head of wounds. 

In the after treatment of severe bleeding the patient should be kept 
perfectly quiet in mind and body, his head should be lowered by raising 
the foot end of his bed or bunk. Give him plenty of fresh air, keep his body 



«<0.<^ 




Pig. 91. 



Pig. 92. 



warm and give him hot drinks. After reaction the temperature of the body 
may rise a degree or two above normal, but if this should continue longer 
than two or, at most, three days, the dressing should be removed and the 
wound thoroughly irrigated, first with hot water, then with a solution of 
bichloride of mercury (i to 5000) and dressed with aseptic gauze. 

Bleeding from Arteries. — There are certain places in the body where the 
arteries are not covered by much muscle, and can be easily compressed 
against bone. These places are shown in the illustrations. The bleeding 
should be controlled first by thumb pressure at the points indicated in the 
illustrations, and if the services of a doctor can be secured without delay, 
this will be all that is necessary until he arrives. If there is any^ doubt as 
to the exact place at which pressure should be made, a slight shifting of the 
thumb from one point to another should be made rapidly, and when the 
bleeding stops it indicates that the proper location has been reached and 
pressure should be continuous at this point. If a doctor is not within 
reach, the bleeding must of course be controlled by sortie other device. 
When the bleeding is from one of the limbs, and some distance from the 
body, a bandage or clean handkerchief should be wrapped around the limb 
at the point indicated by a cross in the illustrations (Pigs. 93 to 102) and 
drawn tight enough to stop the bleeding. The "Spanish windlass" (Figs. 
91 and 92) is made by knotting a handkerchief around the limb loosely, 
passing a stick through the slack part, and taking up the slack by twisting 



466 



CAMP MEDICINE 



the handkerchief. To prevent untwisting, the stick is then bound to the 
limb by one or two other bandages or handkerchiefs. A small round stone, 
a cork, or other similar object placed in the folds of the handkerchief and 
lymg directly over the vessel will assist. Only sufficient pressure should 
be made to barely stop the bleeding. The windlass must be loosened every 

20 minutes to give a chance for the 
blood to flow through the part, as 
there ^ is great danger of gangrene 
(mortification) if the blood is entirely 
shut off for longer than this time. 

The knot in the windlass should not 
be untied, and the stick should be left 
in position for immediate tightening if 
the blood again begins to flow freely. 
If the windlass is to be used for several 
hours, it is best to encircle the limb 
with a folded towel before applying it, 
as there is less danger of injuring the 
skin and soft parts. If the bleeding 
artery is in or near the body, where a 
■vyindlass can not be applied, thumb 
pressure must be kept up until the 
doctor arrives, one person relieving 
another. The second person's thumb 
should gradually push the first per- 
son's thumb aside, and thus prevent a 
spurt of blood. In exceptional cases it 
rnay be necessary to place the thumb 
directly in the wound to control the 
bleeding, but, no matter how clean the 
thumb may be, this should only be re- 
sorted to in desperate cases, as there is great danger of infecting the wound. 
Reference is made in this connection to the chapter of antiseptics. 

In places where the services of a physician can not be obtained, the wound 
should be stretched open, the blood-vessel located, seized, and drawn 
gently forward with a pair of artery forceps and the ends tied with heavy 




Fig. 93. 




I 



Pig. 94. 



thread that has been boiled for five minutes. If artery forceps can not be 
obtained, take a needle or a bent pin, pass it through a flame several times, 
hook onto the vessel, and draw it out; then tie it tightly with the thread 
described above. If a. little flesh is tied in the knot with the artery, this 



ACCIDENTS 



467 



will be of no consequence. After the artery has been securely tied the 
"Spanish windlass" should be removed, or, if thumb pressure has been 
employed, this should be discontinued. The wound should then be closed 
as described under the heading "Wounds." 

Bleeding from Veins. — The deep veins as a rule follow closely the course 
of the arteries. If thumb pressure on the far side (the side farthest from the 





Pig. 95. 



Fig. 96. 





Pig. 97. 



Pig. 98. 



heart) of the bleeding point fails to control the bleeding, a Spanish windlass 
should be applied on the far side. If the bleeding vein is near the surface, 
it may be possible in some cases to control it by a windlass with a stone or 
cork, the windlass not being drawn tight enough to shut off the deeper 
vessels. In some cases bleeding from veins is best controlled by pressure 
directly over the bleeding point, but the thumb should be covered by a clean 



468 



CAMP MEDICINE 



cloth, such as a handkerchief or towel. Elevation of the part and removal 
of all constricting bands, such as garters will assist. 

Where there is simply an oozing of blood and it does not appear that any 
vessel of size has been severed the case can frequently be controlled by 




5. Pobt of Pressure 
for Hugh 



Pig. 99. 

steady pressure of the bleeding surface. Sometimes cloths soaked in water 
as near the boiling point as can be borne and constantly changed will accom- 
plish the result. If peroxide of hydrogen is at hand, it is one of the best 
known agents to stop simple oozing. 



BLEEDING 



469 



Bleeding from Head and Face. — Reference to Fig. 93 will show a point 
in front of the ear, compression upon which will control bleeding about the 
temple. Another important point for pressure is shown where the artery- 
crosses the edge of the lower jawbone. This controls bleeding in the parts 




1. Point of Freuxire on Carotid Artery 
for cut above 




3. Tourniquet on Brachial Arterv 



5. Pad on Temporal 
Artery 




4. Checking Arterial Bleeding 
by Poation . 




\6. Pad in Space at 
Back of Knee to 
Prevent Bleed- 
ing below 



^B 



Pig. 100. 



supplied by this artery, as shown in the illustration. If the bleeding is 
severe and it is evident that a larger and deeper vessel is responsible, it is 
necessary to compress the large artery in the neck. If y9u will turn your 
own head well toward one shoulder, say the right, you will be able to feel 
on the left side a strong muscle standing out under the skin and extending 



470 



MEDICAL NOTES 



frpm a point just back of the ear to the point where the left collar bone 
joins the breastbone. This is your guide to the deep artery. Pressure 
should be made deeply between the lower end of this muscle and the wind- 
pipe, compressing the artery directly against the backbone (Figs. 94 and 95). 

Bleeding from Shoulder. — If the bleeding is in the neighborhood of the 
shoulder joint, the artery to be controlled is the 9ne lying directly under 
the collar-bone. ^ Pressure is made downward, behind the collar-bone, near 
the point where it joins the breastbone, the artery being compressed against 
the rib (Figs. 94 and 96). 

Bleeding from Arm, Forearm, and Hand. — If you place your left hand 
on your right arm between the shoulder and elbow and then bend the right 
elbow and straighten it out several times, you will feel a muscle swell up 
in the arm and subside again. Extending along the inner edge of this 
muscle and close to the bone a large artery can be felt beating (Figs. 97 
and 98). This is the one to compress when bleeding is from a point in 
the arm or forearm. If the forearm, the best place to compress this last 
mentioned artery is just above the elbow; and is also the best point if there 
is severe bleeding in the hand. 

Bleeding from Thigh or Leg. — In the groin, halfway between the hip bone 
and the middle line of the body, the main artery supplying the thigh and 





Pig. ioi. 



Pig. 102. 



leg can be pressed against the bone (Fig. 10 1). If the bleeding is from the 
back of the knee, the leg, or foot, the best place to apply pressure is just 
above the knee at the back of the thigh (Fig. 102). 

Bleeding from Lungs and Stomach. — If the blood is from the lungs, it 
is generally coughed up and has the bright red appearance of ordinary 
blood. If from the stomach, the acid of the stomach juice changes the 
blood until it has more the appearance of coffee grounds. If, however, 
the bleeding is severe, the vomited blood may be bright red, as the acid of 
the stomach may not have had time to act upon it. Sometimes blood 
brought into the throat from the lungs is swallowed by the patient and 
later vomited in its changed condition. 

In the treatment of either of these conditions, it is best to keep the patient 
very quiet in bed, let him suck small pieces of ice in limited quantity, and 
apply cracked ice in some waterproof covering over the chest or pit of the 
stomach, as the case may be. Cheerfulness and an encouraging attitude 
on the part of the attendants are necessary. 

Bleeding from the Nose. — If bleeding of the nose occurs in a full blooded 
person, especially if such person is subject to dizziness, we should not be 
in too much of a hurry to stop it. But if the bleeding is the result of injury 
oT if it occurs in a person suffering from disease of the heart or lungs or 



BURNS 471 

from the effects of malarial fever, scurvy, or any disease of the general 
system, effort should be made to stop it. Nosebleed from a blow, in a 
healthy individual, usually stops in a short time without any particular 
treatment. If it does not stop, place a piece of paper folded to the thickness 
of a quarter of an inch well up between the upper lip and gum, and com- 
press the lip tightly against it. The main blood vessels supplying the nose 
pass upward from the corners of the mouth to the sides of the nose, and this 
paper tends to compress the vessels and shut off the blood supply. The 
patient should lie on his back with his head on a pillow. ^ If ice is obtainable, 
it should be cracked into small pieces, wrapped in a thin cloth, and placed 
over the nose, a sufficient quantity being used to cover the whole surface. 
Cold applied to the back of the neck will also do good in some cases. If 
the bleeding is obstinate, a strip of gauze or soft cloth can be pushed gently 
into the nostrils, the ends being allowed to hang out. 

Bleeding from the Urinary Canal. — This is usually caused by falling 
astride of a hard object. The bleeding may be profuse, but is usually con- 
trolled by pressure with a folded towel. If the bleeding is severe, a stick 
with a cross-piece at one end should be placed at the foot of the bed, the 
cross-piece pressing against the towel in the crotch. After the bleeding 
ceases, the patient should be kept quiet and cold applications should be used. 

BURNS AND SCALDS 

Burns. — Burns or scalds are serious and dangerous to life in proportion 
to the extent and depth of the injury. A burn covering a large area and 
producing mere reddening and swelling of the skin is as serious as a burn 
one-half the size in which the skin is destroyed. The danger is from shock, 
from fever following reaction, from hemorrhage following sloughing, arid 
from congestion and inflammation of internal organs. Burns of slight 
extent or moderate degree are not so dangerous, and most of the cases 
commonly met with will recover. But all cases require careful treatment. 

_ Treatment. — The indications for treatment in these two conditions are 
virtually the same if the damage is superficial; and this is usually the case, 
the injuries being only skin deep. Blisters should be pricked with a needle 
that has been passed through a flame several times. This allows the water 
to escape from the blisters, but the skin raised by the blisters should not be 
removed. If the burning agent is pitch or tar, and adheres to_ the skin, it 
should not be removed; it will come away later with the blistered skin. 
Any bland oil, such as sweet oil, linseed oil, or vaseline, forms a soothing 
application. Ordinary baking soda.or a saturated solution of soda in water 
can be used. The old "Carron oil" made of linseed oil and lime water, 
half and half, is excellent, but has an unpleasant odor. ^ If lime water is 
not at hand, it may be obtained as follows: Quicklime is first slaked by 
adding to it gradually about 30 times its weight of water. ^ Agitate during 
one-half hour, allow the lime to settle, and reject the liquid. Add to the 
residue of Ume about 300 times its weight of water, agitate frequently during 
the next 24 hours, and allow the lime to settle. The clear water standing 
above the undissolved lime is lime water. 

The jjarts burned or the entire body, except the head, may be kept im- 
mersed in tepid or warm water for days. Cream or white of eggs may be 
used, but they are apt to become offensive after 24 hours. Kerosene is an 
old household remedy. One teaspoonful of table salt in a pint of water 
makes a solution that can be employed. Keep the patient quiet and his 
bowels active. Pain or restlessness may be relieved by laudanum 20 drops, 
repeated in two hours if necessary. 

If the eye is red from contact with the flames or hot fluid, sweet oil is 
perhaps the best household remedy to drop in. ^ A bandage lightly applied 
over the eyes to keep out the light will be soothing. 

If the skin or the eye is burned with acid, a solution of baking soda should 
be used first. If the burning agent is an alkali, such as hartshorn or lye, 
weak vinegar or lemon juice should be used. Sweet oil should be dropped 
in the eye after such treatment. 

If the patient has breathed the flame or steam the condition is apt to be a 
serious one, even though it does not appear so at once. Complete rest and 
quiet, an ice-bag to the chest, the giving of milk and cream, half and half, 
if swallowing is possible, should be employed. Artificial respiration, as 
described elsewhere, may be applicable in some cases. 
.Speaking generally of bums and scalds, a superficial bum covering a 



472 MEDICAL NOTES 

large part of the skin may be more dangerous than a deep burn confined to a 
small part, for reasons which it is unnecessary to discuss in a book of this 
kind. No burn or scald should therefore be treated as a trivial matter. 
Where solutions are used the bandages should be soaked in the same before 
applying and the solution should be poured over the bandaged part at 
frequent intervals. 

Paraffin mixtures have been recently used extensively for the treatment 
of burns. The mixture is melted and then sprayed upon the burned surface. 
It is then covered with a layer of gauze and more of the mixture is sprayed 
on. ^ Instead of spraying, the mixture may be painted on the surface with a 
sterile brush. The mixture becomes hard when it cools, forming a pro- 
tective coating for the burn. This paraffin should be removed once a day, 
the wound washed with a weak antiseptic solution, dried with pellets of 
gauze or cotton, after which another coat of the paraffin mixture is applied. 
Melted wax may be employed instead of paraffin. In either case a coating 
of liquid petroleum or kerosene should be applied to the wound before the 
wax or paraffin is used. 

The scars resulting from burns and scalds always contract, and in severe 
cases terrible deformities are produced. These may be prevented to some 
extent by active and passive motion and by splints. 

EFFECTS OF COLD -FROSTBITE 

Frostbite. — Severe cold depresses the action of the heart, suspends the 
circulation. These effects are first noticed in the ears, nose, fingers, and 
toes. Numbness and tingling are the first symptoms, then loss of sen- 
sation. If not too long exposed, the circulation may be restored by proper 
treatment. But if the exposure is long continued or if the cold is very in- 
tense the parts are hopelessly frozen and gangrene will be the result. The 
parts may look all right for a few days after reaction and then become 
discolored, bluish, and finally black. Another effect of extreme cold is an 
overpowering sense of drowsiness, but to lie down and go to sleep under such 
circumstances is almost certain death. 

Treatment of Frostbites. — i. Do not bring the patient to the fire until 
the circulation is restored in the frozen part. 

2. If snow be on the ground or accessible, take a woolen cloth in the 
hand, place a handful of snow upon it, and gently rub the frozen part until 
the natural color is restored. In case snow is not at hand bathe the part 
gently with a woolen cloth in the coldest fresh water obtainable, ice water 
if practicable. 

3. In case the frostbite is old and the skin has turned black or begun to 
scale off do not attempt to restore its vitality by friction, but use the treat- 
ment for burns described on page 471. 

4. In the case of a person apparently dead from exposure to cold friction 
should be applied to the body and the lower extremities and artificial respira- 
tion practised as in case of the apparently drowned. As soon as the circula- 
tion appears to be restored administer strychnine sulphate one-fortieth 
grain. Even if no signs of life appear friction should be kept up for a long 
period, as instances are on record of recovery after several hours of suspended 
animation. 

ANTISEPSIS, ANTISEPTICS, AND THE DRESSING OF WOUNDS 
(Health Bulletin, No. 17) 

We are surrounded at all times by very minute organisms capable of 
producing various diseases or complications. They are sometimes called 
germs, and more vulgarly called "bugs." The latter name is incorrect, as 
the germs belong to the vegetable and not the animal kingdom. In first- 
aid work the germs that particularly interest us are those that get into 
wounds and infect them, causing pus or "matter" and sometimes blood 
poison. 

Definitions. — When these complications arise the process is known as 
"sepsis." "Antisepsis," therefore, refers to the guestion of removing or 
killing the germs, and "antiseptics" are the medicines or other agents used 
in accomplishing these purposes. This explanation is made for the reason 
that it is necessary to use the terms "antisepsis" and "antiseptics" in this 
chapter, there being no common names quite so expressive. There^ is 
another term, "asepsis" used by doctors, which refers to the condition 



ANTISEPTICS 473 

where all germs have been removed or killed, but this is a condition that 
does not often obtain in first-aid work administered by a layman, and 
therefore will not be further discussed. We frequently hear a person say 
that he has good blood because when he cuts himself the wound heals 
quickly. This is apt to give him a false sense of security and cause him 
to neglect the precautions that should be taken. Some of the worst cases of 
"sepsis" and blo9d poison occur in strong healthy men who have had no 
previous trouble in the healing of wounds. Germs are always present on 
the skin and can be demonstrated by laboratory methods. They can 
only be seen by a microscope of high power. A patient may have taken a 
hot soap) bath before being injured, but his skin is not surgically clean, and 
antiseptics are therefore employed to destroy the germs that remain. 

The Dresser's Hands. — The one who- is to make the dressing should 
see that his own hands are surgically clean before he attempts to clean or 
"sterilize" the wound; otherwise he is apt to transfer germs from his hands 
to the wounds or to the dressings. The hands should be scrubbed with a 
-Jiail-brush, hot water, and S9ap. Then the finger nails should be cleansed 
and the hands scrubbed again. A good way to clean the finger nails is to 
rake them across a cake of soap, filling the space under each nail with the 
soap. As this is removed with a pocketknife the dirt comes away with it. 
Then after the second scrubbing the hands should be soaked and rubbed 
in some antiseptic solution and not dried. The skin about the wound should 
now be scrubbed with the nailbrush and soap; and if it is a hairy part, the 
hair should be shaved for some distance on all sides of the wound before 
the scrubbing. The wound and the parts about it should then be thor- 
oughly cleansed with the antiseptic solution; and a cloth, preferably one 
that has been boiled, soaked in the antiseptic solution, laid over the wound, 
and bound there with a bandage. 

Alcohol. — The antiseptic that is most apt to be at hand or most easily 
obtained is alcohol. It should be diluted with water, making a mixture of 
I part water and 3 parts alcohol. It creates a burning sensation when 
applied to a wound, but this is a small matter if it prevents infection in 
the wound. Where alcohol can not be obtained, whisky or brandy, which 
contains about 50 per cent, of alcohol, may be obtainable. Some experi- 
ments have recently been made in the San Francisco Federal Laboratory 
by officers of the United States Public Health Service showing that whisky 
and brandy are very good antiseptics. 

Iodine. — Tincture of iodine, usually known by the layman as simply 
"iodine," is one of the best antiseptics known at the present time. Its 
power is far greater if applied to a dpy surface than to a wet surface. The 
burning sensation produced in the wound does not last long. A dry sterile 
dressing over it is preferable to a wet dressing, as the wet dressing lessens 
its power and is apt to blister the skin. Too much iodine may also blister, 
and it should therefore be diluted with an equal part of alcohol. 

Bichloride of Mercury. — An antiseptic much used in hospitals is bichloride 
of mercury or corrosive sublimate. It is not apt to be on hand in the 
ordinary household or camp, but is mentioned as one of the agents to be 
kept in the first-aid chest. It can be purchased in tablet form, and each 
tablet added to a pint of water makes a solution of a certain strength 
(see page 449). This strength that is safest for the layman to use is i 
part of bichloride of mercury to 5000 parts of water.^ This is an excellent 
antiseptic. It is a deadly poison, however, if taken internally, and should 
therefore be handled with care. 

Peroxide of Hydrogen. — Peroxide of hydrogen has become a favorite 
and popular antiseptic. Its power in this regard is weak, but it is a cleansing 
agent and can be employed as a dressing in the absence of anything better. 
It tends also to stop oozing of blood in a wound where no large vessels 
are cut. 

Carbolic Acid. — The pure carbolic acid should be obtained if possible, 
and as a dressing for wounds should be made into a solution of i part of 
carbolic acid to 100 parts of hot water. 

Compound Cresol Solution. — This is a very serviceable antiseptic solu- 
tion, as it readily dissolves in cold water and is as powerful as carbolic acid 
solutions of the same strength. It may be employed in i per cent, solutions 
for any purposes for which an antiseptic solution is required. It is especially 
good for sterilizing instruments, as it does not injure them. 

Sterile Dressings. — There can be purchased for the first-aid chest various 
kinds of sterile dressings; that is, dressings that have had all germs killed 



474 



MEDICAL NOTES 



by exposure to heat. Sterile gauze comes packed in a box in the form of a 
roll, and it unrolls as pieces are drawn out and cut off. From a theoretical 
standpoint the gauze is no longer sterile after the package has once been 
opened; but for practical first-aid work it answers the purpose if each piece 
•cut off is carefully unfolded with clean hands and the inside of the piece 
applied next to the wound. It is advisable to buy small packages, so that a 
new one will be opened from time to time. 

How to Sterilize Dressings. — The one most efficient and always available 
method of sterilizing dressings is hv boiling for lo minutes in plain water, 
which, from a practical standpoint, kills all germs that can infect a wound. 
If a dry dressing is desirable, it can be placed in a pan in a hot oven for 15 
or 20 minutes and removed just as it is beginning to be scorched. If several 
layers of a sterile dressing are applied directly over a wound and lapped 
around it at all sides, it is not absolutely necessary that the additional 
dressing material placed over this be sterile, although it is desirable. 

Sterilizing Instruments, etc. — If scissors, knitting needles, ordinary 
needles, or other metal instruments or implements are necessary in dressing 
a wound, they should be boiled in water for 10 minutes, or can be passed 
through a flame several times, or some alcohol can be poured on the in- 
strument and then set on fire with a match. Actual fire is apt to remove 
the temper from the instrument much more easily than boiling, for which 
reason boiling is preferable. 

Treatment of Wounds. — Doctors divide wounds into several classes, 
namely, incised, lacerated, contused, punctured, poisoned, gunshot and 

infected. The nature of the first three 
is sufficiently clear from their names and 
from a first-aid standpoint may be 
considered together. The first thing 
to do is to control severe bleeding by 
pressure on the wound or upon a distant 
part of the blood vessel, as explained in 
the data on "Bleeding." Then, after 
the dresser has disinfected his own hands, 
the wound should be thoroughly cleansed 
and disinfected; these matters will be 
explained in "Antiseptics." Iodine, if 
at hand, is the best agent to use. If the 
wound is on a hairy part, as the scalp, 
the hair should be shaved for a distance 
oi several inches from the wound. An 
antiseptic dressing should then be ap- 
plied, or in the absence of any such agent 
one may use a clean cloth boiled for 10 
minutes in clear water or in water to 
which table salt has been added in the 
proportion of i teaspoonful to the pint. 
This dressing is retained by a bandage 
and should not be disturbed for any reason except bleeding if the doctor 
can be reached within 48 hours. 

If it is impossible to secure the services 9f a doctor for several days and 
the wound gapes to such an extent that it can not be readily closed by 
bandaging, or is in a part where a scar will mean disfigurement, the layman 
may attempt to close the wound by stitching, and this can be done by using 
an ordinary sewing needle with silk or linen thread, both boiled for 10 
minutes, the needle being pushed through the flesh by means of a thimble, 
also boiled. The stitches should pierce the skin about an eighth or quarter 
of an inch from the edge of the wound and come out of the fleshy part of 
the wound about the same distance from the skin. They should be placed 
about half an inch apart, and each one should be tied and cut off. The 
stitches should only be drawn tight enough to barely close the wound, 
tJecause the swelling may make them too tight. No wound should be closed 
by a layman without leaving drainage; that is, something that will lead off 
the bloody water that oozes from a wound. 

A piece of boiled sewing silk or linen folded back and forth and then 
twisted until it makes a skein one-eighth of an inch thick should be laid in 
the bottom of the wound and allowed to hang out at the lower end for a 
distance of an inch. This drains by capillary attraction, and there is far 




Pig. 103. 



WOUNDS 475 

less danger of blood poison than if the wound were closed tightly. This 
drain should be removed after 24 hours by simply drawing it out without 
disturbing the stitches. The stitches themselves should be left in place 
from three to six days, depending principally upon the depth of the wound 
and its tendency to gape. The stitching of a wound should only be at- 
tempted by a layman when a doctor can not be reached within 48 hours. 

The closure of a wound by sticking plaster is a questionable expedient, 
because it seals the wound, prevents drainage, and blood poison may follow. 
If the wound is not large, a strip of boiled cloth may be laid directly over 
it and the wound then drawn together by strips of sticking plaster applied 
outside the cloth. 

Whether the wound is closed by stitches or not, the layman should apply 
an antiseptic dressing, if such is available, and if not, a boiled cloth, as 
described above, can be used. 

A badly contused or bruised wound should not be stitched by a layman. 
In a lacerated wound it may be necessary to trim off with boiled scissors 
a few ragged edges of skin before stitching. 

If a wound has penetrated the belly and the bowel is protruding, it is 
best not to attempt to push it back if the doctor can be reached within a 
few hours. It should be gently washed with the salt solution, described 
elsewhere (page 474), and kept covered with towels frequently wet with the 
same solution. If a doctor can not be reached within a few hours, and 
the person in charge of the patient after a careful examination is sure that 
the bowel has not been opened or otherwise seriously injured, he should, 
after carefully washing the bowel with the salt solution mentioned above, 
return it to the belly. ^ If the bowel is allowed to remain for too great a time 
outside of the belly, its circulation may be cut off by the pressure of the 
belly walls and gangrene result. If the bowel has been opened or severely 
bruised, it should not be returned, as there is danger of forcing fecal matter 
out of the bowel into the belly cavity, which would cause a dangerous 
inflammation. ^ If the bowel is not protruding from the wound, simply 
treat as an ordinary wound. 

Punctured Wounds. — A punctured wound is one made by a piercing 
agent, such as a nail, tack, knife, or needle. Such a wound is dangerous, 
because it almost completely closes and does not drain. If germs are 
introduced at the time of the accident, they can not escape. A wound 
of this kind, except of the chest or belly, should be disinfected or burned, 
and the best agent is pure carbolic acid. In the absence of suitable in- 
struments a knitting needle or other thin blunt implement should be dipped 
into the carbolic acid and then inserted to the full depth of the wound. This 
should be repeated several times. The first application causes a burning 
sensation, but the acid itself soon deadens the part, and the subsequent 
applications are less painful. If the knitting needle is then dipped in 
alcohol or whisky and inserted once or twice and a little is applied to the 
skin about the wound, it will stop the burning action of the carbolic acid. 
In the absence of the carbolic acid the alcohol or whisky can be used alone, 
but are far less efficient. After this treatment an antiseptic dressing or a 
boiled cloth should be applied to the wound. The frequency with which 
lockjaw follows punctured wounds, particularly nail wounds, makes it 
imperative that the doctor be consulted promptly and that the wound be 
not regarded as trivial because it is small in size. An injection of serum 
(tetanus antitoxin) will prevent lockjaw. 

Poisoned Wounds. — The principal poisoned wounds met with are those 
due to bites of animals or bites and stings of insects, and these will be con- 
sidered under a separate heading (see page 464) .^ 

Gunshot Wounds. — A gunshot wound is similar to a punctured wound 
in that it is small and almost completely closed. If the ball has passed 
entirely through a part, as the leg, and has not struck an important vessel 
or broken a bone, the wound is apt to cause less trouble than one in which 
the ball remains in the flesh. If a portion of clothing is found in the mouth 
of the wound, it should be removed. The part should be well cleansed with 
soap and hot water and an antiseptic dressing or a boiled cloth applied. 
Further than this it is not best for the layman to attempt anything, par- 
ticularly probing for the bullets. If a bone has been broken by the ball, 
the case should be treated as described under "Compound Fracture." 

Infected Wounds. — A wound should never be permitted to become 
infected, but it is not always possible to prevent it, as germs may be intro- 
'duced at the time of the injury by the weapon causing the injury or on pieces 



47^ MEDICVL NOTES 

of cloth or in dirt carried in with it. Badly contused wounds are also liable 
to become infected as the devitalized tissue is unable to resist the attack of 
harmful bacteria. Continuous or frequent irrigation with an antiseptic 
solution has been found to be the best method of thoroughly cleansing 
wounds of this kind and to keep them free from bacteria. A very weak 
bichloride solution (i to 15,000) may be used for this purpose, or, even 
sterile water containing one teaspoonful of salt to the quart may be em- 
ployed if nothing else is available. The Dakin-Carrel solution, is however, 
the best for this purpose. Tablets for the preparation of this solution, 
known under the trade name of Chlorazene Tablets, can now be obtained in 
the drug stores. In order to be effective, the solution should be introduced 
to the bottom of the wound. A special apparatus is employed for this 
purpose. Gauze is packed around rubber tubes after they are placed in 
the wound. Only enough solution to keep the dressing damp should be 
allowed to flow into the tubes. ^ A modification of this solution has recently 
been made in which oil is used instead of water. This makes it unnecessary 
to be continually wetting the gauze as the oil keeps the wound moist for a 
longer period and the wound need therefore be dressed but once a day. 

RESUSCITATION FROM APPARENT DROWNING 

In the act of breathing, the oxygen from the air is absorbed from the 
lungs into the blood vessels and purifies the blood; at the same time the 
impure matters picked up by the blood in circulating through the body 
are filtered out by the lungs and pass off to the atmosphere with the breath. 
When a person is under water he can hold his breath for a short time, keep- 
ing out the water; then he swallows some water into the stomach, and 
as his strength fails water enters the lungs. ^ The water in the stomach does 
no particular harm; but that in the lungs is of vital importance because it 
stops breathing, causes poisoning of the system from lack of purification 
of the blood, and if allowed to remain for any length of time produces stop- 
page of the heart and death. 

The indications, therefore, in one apparently drowned are to remove 
the water from the lungs, to make the patient breathe, and to stimulate the 
weak heart. 

The old method of rolling a patient over a barrel to remove the water 
from the lungs is not considered efficient by those who have had most 
experience. Inverting the patient by grasping his feet and holding him 
head down for a few moments, at the same time making pressure on his 
belly inward and toward the chest, may remove part of the water. The 
chest is separated from the belly by a partition consisting of a thin flat 
muscle, and pressure inward and upward on the belly forces this partition 
up against the lungs and may mechanically squeeze some water out of the 
tubes in the lungs. Time should not be wasted in prolonged efforts to re- 
move the water, as it is important to proceed as quickly as possible with 
artificial breathing, which will not only squeeze the water out of the lungs 
but will renew respiration and revive the patient. 

There are several methods that have been suggested and used for inducing 
artificial breathing, but to save delay in selecting one the layman should 
have explained to him in a book of this kind one method only, and that 
one the method that has been accepted as the best, namely, the Schafer 
method (see Fig. 105). , 

Schafer's description of this method, as quoted by Crile, is as follows, 
'except that the technical words and expressions have been eliminated 
and ordinary ones that will be understood by a layman substituted: 

The subject, whether a drowned person or not, is allowed to lie prone, 
i.e., face downward, no preliminary manipulation of the tongue being 
required. The operator kneels or squats either across or on one side of the 
subject, facing the head, and places his hands close together flat upon the 
back of the subject over the loins, the fingers extending over the lowest 
ribs. By now leaning forward upon the hands, keeping the elbows ex- 
tended, the weight of the operator's body is brought to bear upon the sub- 
ject, and this not only compresses the lower part of the chest but also the 
belly upon the ground, the pressure being fairly equally distributed. The 
result of this is that not only is the chest diminished in extent from before 
back, but, owing to the pressure which is communicated to the belly, the 
belly contents 'are compressed and tend to force the muscle partition be- 
tween the chest and belly up, so that the chest is diminished in capacity 



DROWNING 



477 



from above down. This is no doubt the reason why the pressure method 
when applied with the subject lying on his belly is more effective than when 
applied, as by Howard, with the subject lying on his back. The pressure 
is applied not violently but gradually during about three seconds, and is 



RESCUE METHODS 

RcKiMT diouM aoC (O iBte tbc water «uleu NeccMftry but ihouM um » Line. Buoy or Boat 




6. lceRe«cue 



Pig. 104. 



then released by the operator swinging his body back, but without removing 
his hands. The elasticity of the chest and belly causes these to resume their 
original dimensions and air passes in through the windpipe. After two 
seconds the process is again commenced, and is continued in the same 



478 



MEDICAL NOTES 



way, the operator swinging his body forward and backward once every five 
seconds, or about twelve times a minute, without any violent effort and 
with the least possible exertion. This last condition, viz., the absence of 
muscular exertion, other than that involved in swinging forward and back- 




2. When Rescuer u Clinched around the Neck 
R£SIX>R]NC NEARLY DROWNED 




3. When Rescuer b Clutched around 
the Body or Arm» 



Z ArtincUl Respiration (B) 



Fig. 105. 



ward, renders it possible to continue the process without fatigue for an* 
indefinite time. It can further be carried out unaided by a woman alnaost/ 
as well as a man, by children upon children; it hardly requires to be taught,' 
a simple demonstration sufficiently teaches it to a large audience. Its 



ELECTRIC SHOCK 479 

advantages in drowning cases over any other method which involves the 
position on the back are sufficiently obvious, for with it there is no risk of 
obstruction by water or sUme or the contents of the stomach, which can 
not accumulate in the throat, but must come away by the mouth, and 
the tongue, in place of falling back, as in the position on the back, falls 
forward and is unable to produce obstruction. 

Crile says in regard to this method: /'Schafer's method should be used 
in all cases in the absence of medical assistance or outside of a hospital, and 
even in a hospital in the absence of immediate surgical aid." He further 
says: *' Simple artificial respiration is the only hope in drowning and other 
accidents occurring when professional help is not at hand." When the 
patient is able to swallow, a small cup of black coffee, or hot milk may be 
given, and repeated a few times at intervals of an hour. If he does not 
swallow well, and an ordinary syringe is available, the coffee may be in- 
jected into the bowel and left there, but the effect is slower. 

It is scarcely necessary to state that the patient should be removed to a 
warm place, the wet clothing removed, and the lower parts of the body 
covered and artificially warmed. Pending the arrival of the doctor the 
patient should be closely watched, and if signs of collapse appear, renewed 
efforts should be made. Prolonged and systematic rubbing of the skin 
and kneading of the muscles will assist in promoting the circulation of 
the blood. 

RESUSCITATION FROM ELECTRICAL SHOCK^ 

An accidental electric shock usually does not kill at once, but may only 
stun the victim and for a while stop his breathing. 

The shock is not likely to be immediately fatal because (a) The con- 
ductors may make only a brief and imperfect contact with the body, (b) 
The skin, unless it is wet,_ offers high resistance to the current. 

Hope of restoring the victim lies in prompt and continued use of artificial 
respiration. The reasons for this statement are: (a) The fact continuously 
depends on an exchange of air, as shown by the fact that we must breathe 
in and out about 18 times a minute, (b) If the body is not thus repeatedly 
supplied with air, suffocation occurs, (c) Persons whose breathing has 
been stopped by electric shock have been restored after artificial respiration 
has been continued for approximately two hours. _ 

Instructions. — Follow these instructions even if the victim appears dead. 

I. Break the circuit immediately. 

I. With a single quick motion separate the victim from the live conductor. 
In so doing avoid receiving a shock yourself. Many have, by their care- 
lessness, received injury in trying to disconnect victims of shock from live 
conductors. 

Observe the following precautions: (a) Use a dry coat, a dry rope, a dry 
stick or board, or any other dry nonconductor to move either the victim or 
the wire, so as to break the electrical contact. Beware of using metal or 
any moist material. The victim's loose clothing, if dry, may be used to 
pull him away; do not touch the soles or heels of his shoes while he remains 
in contact, the nails are dangerous. ^ (b) If the body must be touched by 
your hands, be sure to cover them with rubber gloves, mackintosh, rubber 
sheeting, or dry cloth; or stand on a dry board or some other dry insulating 
surface. If possible, use only one hand. If the victim is conducting the 
current to ground, and is convulsively clutching the live conductor, it 
may be easier to shut off the current by lifting him than by leaving him 
on the ground and trying to break his grasp. 

^ 2. Open the nearest switch, if that is the quickest way to break the 
circuit. 

3. If necessary to cut a live wire use an ax or a hatchet with a dry wooden 
handle, or properly insulated pliers. 

II. Attend instantly to the victim's breathing. Use the Schafer method 
of artificial respiration as described under treatment of the apparently 
drowned (page 477). Bums of the skin should be treated as described for 
ordinary bums. Warmth to the body, gentle rubbing, and later hot water, 
milk, or coffee if the subject can swallow, are indicated, but do not give any 
liquids whatever by mouth until the subject is fully conscious. 

1 Taken from "Rules for resuscitation from electric shock." Issued by 
the National Electric Light Association. 



48o 



MEDIC\L NOTES 



HOW TO RESCUE PERSON FROM CONTACT WTTH ELECIRIC CURRENT 
(WhoD posaMe the reaaterB sIumU Stand OB Dry Wood er Oolh) 




Fig. io6. 



POISONING 481 

DIRECTIONS TO BE FOLLOWED IN CASE OF POISONING 

(Health BuUetin No. 17) 

Send for the doctor immediately, if practicable, and if the nature of the 
poison is known, have the messenger inform the doctor so that he may come 
prepared. If the poison is unknown, but the bottle from which it was 
taken is found, save the bottle as it may help in case of legal investigation. 
If the poison has been taken with suicidal intent and the patient survives, 
the same caution is applicable that was mentioned under drowning, gas 
poisoning, etc. Warmth to the body, light stimulation, and encouragement 
are indicated. 

In treating cases of poisoning first give an antidote, if one is available; 
second, promote early and repeated vomiting to remove the bulk of the 
poison; third, give something that will help envelope the poison left in the 
I stomach and prevent its further absorption into the system; fourth, remedy 
I the damage that has been done, so far as this is possible. 
( The following "general antidote," which should be prepared as needed, 
• should be given when poisoning by any of the poisons mentioned in this 
book occurs or if the poison is unknown: Magnesia, 2 teaspoonfuls; char- 
coal, 2 teaspoonfuls; tannic acid, i teaspoonful. These dry powders should 
be kept thoroughly mixed in the above proportions in an air tight bottle 
and when needed one heaping tablespoonful should be mixed with a cupful 
' of water. This is one adult dose and should be repeated. 
i Should there be no tannic acid on hand, a cupful of very strong tea or 
> tea of oak bark will take the place of the tannic acid and water. 
' Vomiting or puking may be induced by tickling the throat with a feather 
or pushing the finger down the throat, or by the administration of one of the 
I following emetics by mouth: 

Mustard. — One tablespoonful stirred to a cream with a cupful of tepid 
water. 

Common Salt. — One tablespoonful to a cupful of tepid water. Not very 
certain as an emetic. 

Alum. — Two teaspoonfuls to a cupful of tepid water This is a rather 
feeble emetic. 

Ipecac. — Give i tablespoonful of the sirup in a cupful of tepid water. 
Repeat once if necessary. 

The doses recommended throughout this article are for adults; the amount 
should be proportionately small for children (see p. 452). 

Unknown Poison 

Give "general antidote" following by emetics or raw whites of several 
eggs; or, in their absence, milk, or flour and water. The white of egg, 
particularly, is incHned to pick up part of the poison left in the stomach 
and hold it until the patient can be made to vomit again. If the body is 
limp and respiration is feeble, tea or coffee can be given as a stimulant, and 
warmth applied to the body with massage or rubbing will tend to support 
the circulation. 

OPIUM, LAUDANUM, PAREGORIC, MORPHINE, CODEINE, HEROIN, 
INDIAN HEMP 

Give the "general antidote," or potassium permanganate (one-third 
teaspoonful dissolved in a pint of water, no undissolved crystals should 
remain in the fluid), or peroxide of hydrogen (2 teaspoonfuls in a pint of 
water) , or^borax, or baking soda (about i tablespoonful to the pint of water) 
followed by an emetic. Whites of eggs and considerable quantities of strong 
tea or strong black coffee should be given, or if unable to swallow, inject 
the coffee into the bowel with a syringe. 

^ Give sweet spirits of niter (i teaspoonful in water three times a day) to 
aid excretion by kidneys. 

Keep patient awake by shaking, striking with wet towel, applying cold 
water over face and chest, or forced walking. 

Wines and liquors must not be given. 

When respiration becomes slow and irregular, artificial respiration should 
be employed, the same as is used to restore the partially drowned. 

After the dangerous symptoms have subsided, the patient should be put 
in bed, warmth applied, and he should be carefully watched for some time. 



482 



MEDICAL NOTES 



ARSENIC, RATSBANE, PARIS GREEN, "ROUGH ON RATS." 
FOWLER'S SOLUTION 

The best antidote, if the ingredients can be obtained, is prepared by 
mixing a teaspoonful of magnesia with a cup of water, adding 2 tablespoon- 
fuls of tincture of iron, stirring well, and giving the whole in one dose; or 
the "general antidote" may be given, followed by emetics, raw whites of 
eggs mixed with water, or large drinks of hot greasy water, or salt and 
water (tablespoonful to pint), or strong tea. Magnesia may be given in 
tablespoonful doses mixed with water. Lime water in large quantities 
is of some value, and in its absence lime which may be scraped from the 
walls or ceiling and mixed with water may be administered. 

Protect stomach with 2 tablespoonfuls of sweet oil, gruel, starch, mucilage, 
flaxseed tea, or elm-bark tea. Castor oil (2 tablespoonfuls) should be given 
after vomiting occurs even though the bowel movements are frequent. 

Pain can possibly be lessened by hot bottles to the stomach and bowels. 

Keep patient warm with artificial heat or extra garments, and give strong 
coffee to avert collapse. 

STRYCHNINE, NUX VOMICA (DOG BUTTON), FISH BERRIES, 
IGNATIA BEAN 

Give "general antidote" or charcoal (i tablespoonful) or strong tea 
followed by an emetic, then 15-grain doses of bromide of soda or potash in 
water repeated every hour until three or four doses have been taken. Several 
whiffs of ether may be inhaled from a handkerchief at the beginning of a 
spasm. 

Give sweet spirits of niter (i teaspoonful in water three times a day). 

Follow by a purge of Epsom salt or any other saline cathartic that is at 
hand. 

Artificial respiration should be employed the same as is used to restore 
the partially drowned (page 476). Remove the patient to a darkened 
room and keep as quiet as possible; avoid any sudden noises. 

BICHLORIDE OF MERCURY (CORROSIVE SUBLIMATE) 

Promote vomiting, if not already present, by giving mustard in water. 
Do not use salt as an emetic. 

Give raw whites of eggs in water or milk or give milk or mucilage in 
abundance. In absence of eggs, choiD up raw, lean meat finely and diffuse 
through water or milk and give. It is necessary that vomiting be induced 
after the eggs, milk, or meat are given, as the mixture formed of these sub- 
stances will be absorbed if allowed to remain. 

The "general antidote," strong tea, and later flour and water, barley 
water, or flaxseed tea. or elm-bark tea may be given. 

Borax in water, about a tablespoonful to the pint of water, is recom- 
mended, but is of doubtful value. 

Stimulate with strong coffee if necessary. 

ACID POISON-ACETIC, MURIATIC, NITRIC, SULPHURIC, ETC. 

Give no emetic. 

Give "general antidote," large drinks of water (or milk) with chalk, 
whiting, borax, magnesia, or baking soda, or wood ashes, or strong soap- j 
suds; plaster from the wall may be given in emergency; olive oil, raw whites 
of eggs beaten up with water, and later flaxseed tea, elm-bark tea, gruel, 
starch, mucilage freely. 

Laudanum (20 drops) may be given if there is much' pain. 

CARBOLIC ACID AND CRESOL AND COAL-TAR DISINFECTANTS 
GENERALLY 

Give alcoholic liquors (whisky, brandy, etc.) or egual parts of alcohol 
and water freely to dissolve the poison. Produce vomiting to get rid of the ! 
alcoholic mixture. In the absence of alcoholic liquors, give vinegar, soap- 
suds, or raw whites of eggs in water. Give solution of Epsom or Glauber 
salt or sodium phosphate well diluted to hasten elimination of acid that 
may have entered the circulation. 



POISONS 483 

Do not give oils or glycerin. 

Milk, gruel, flaxseed tea, or elm-bark tea may then be given. Hot applica- 
tions to extremities. For collapse give strong coffee. Apply artificial respi- 
ration if breathing stops. 

ALKALI POISONS-LYE, HARTSHORN, PEARLASH, ETC. 

Assist vomiting with large drinks of tepid water. 

Give vinegar, lemon juice or orange juice, hard cider, whites of eggs 
beaten with water. 

Follow by sweet oil, milk, gruel, barley water, flaxseed tea, or elm-bark tea 

; PTOMAINE POISONING FROM FISH 

The symptoms of ptomaine poisoning are practically the same as those 
i of " Cholera Morbus. " 
• "General antidote," emetics, copious drinks of strong tea, repeat emetic, 

then castor oil (2 tablespoonfuls) should be given. Continue treatment as 

given for cholera morbus. 

CHOLERA MORBUS (SPORADIC CHOLERA) 

Cholera morbus is an affection of the stomach and intestines, attended 
by vomiting, purging, and cramps. It comes on suddenly, and may begin 
by vomiting or purging. It is usually met with during the hot months of 
summer. It is frequently caused by eating unripe and indigestible fruits 
and vegetables, decomposed or improperly cooked fish, shellfish, or salad 
mixtures. Drinking large quantities of iced water and sudden checking of 
the perspiration, or irritants of any kind, may set up the trouble. The dis- 
ease usually begins suddenly, often at night, with vomiting, after a feeling of 
uneasiness, nausea, or a severe cramp. The contents of the stomach are 
first thrown up, then a bilious matter. The stools are at first solid or semi- 
solid, but they soon become more watery, lose their color, and sometimes 
appear not unlike the rice-water stools of genuine Asiatic cholera. The 
patient soon has a wasted look. His thirst is unquenchable. His skin may 
become cold and clammy and the pulse very weak. Cramps may occur in 
the feet and in the calves of the legs. The disease runs a rapid course. 
The acute symptoms may subside irua few hours. The attack seldom lasts 
more than 12 hours. Recovery is the rule, but treatment should be promptly 
applied. 

Treatment. — Apply a large mustard plaster to the abdomen. Give 15 
drops of laudanum. If the dose is rejected (immediately vomited), try it 
again. ^ If it is still not retained, then try 2 tablets of Sun Cholera Mixture. 
If vomiting quickly occurs, then inject into the rect um by means of a glass 
or rubber syringe about 20 drops of laudanum mixed with a little thin starch 
or a little water. The rectal injection should be given immediately after 
an evacuation, and the patient should be instructed to hold it as long as 
possible. In whatever way the remedy is given, the dose should be repeated 
in about one hour if the vomiting and purging continue. 

If must not be forgotten, however, that all these remedies contain opium, 
and that if the patient is inclined to sleep or shows other constitutional 
effect of the drug the dose must not be repeated. 

The nausea and thirst may be controlled by cracked ice placed in the 
mouth. Small quantities of carbonated water may be allowed. If the 
thirst is very urgent a tablespoonful of iced water may be given at short 
intervals. 

BROKEN BONES (FRACTURES) 

There are many varieties of fracture. A fracture is said to be simple 
where there is no open wound directly over the bone injury; compound when 
there is an opening in the skin and soft parts extending down to the broken 
bone; comminuted when the bone is broken in several places; complicated 
when it is associated with other injuries, as dislocation of the joint or rupture 
of the main artery of the limb; impacted when one fragment is driven into 
another. 

SIMPLE FRACTURES 

In a typical, well-marked fracture of a bone in one of the limbs we will 
find the following: 



484 



MEDICAL NOTES 



1. History of an injury. 

2. Pain and tenderness, and later swelling; and sometimes discoloration 
of the part. 

3. Deformity in some cases. 

4. Shortening, due to the fact that in most cases the break is obliquely 
across the bone and the fragments override. 

5. Scraping noise, called crepitus, when the ends of the bones are rubbed 
together. 

6. Inability or disinclination to use the part. 

Any of these signs may be absent in a given case. Sometimes it is im- 
possible to tell without an x-tsly examination whether one has to deal with a 
fracture, a sprain, or a bruise, but in such cases it is always best to assume 
that there is a fracture. 

In transverse fracture, where the break is straight across the bone at a 
right angle with the long axis of the bone, or in a fracture near a joint, 
there may be no shortening and no deformity. In fractures of certain 
bones, as the skull or the spine, or in an impacted fracture, there may be no 
motion. In fracture of the kneepan or the elbow the fragments are pulled 
apart by the muscles, so that there is lengthening instead of shortening. 

Examination should always be made as soon as possible after the accident. 
Under the most favorable circumstances it is sometimes difficult to deter- 
mine whether a bone is broken or not, and the difficulty is greatly increased 
if the examination is delayed until inflammatory swelling has set in. In 
fractures of the extremities the sound limb should always be placed along- 
side the injured one for comparison.^ The shortening in fracture of the 
thigh may be from i to 3 inches, but it must not be forgotten that in some 
persons there is a natural difference of as much as half an inch in length 
of the pair of legs; and a limb may be otherwise naturally deformed and 
this deformity should not be mistaken for accidental deformity. In the 
leg below the knee there are two parallel bones (tibia and fibula). In 
simple fracture affecting only one of these bones the deformity and crepitus 
are less marked; and the same may be said of the forearm, if fracture exists 
in only one of the bones (radius or ulna). If both bones of the leg (tibia and 
fibula) or of the arm (radius and ulna) are affected, there may be con- 
siderable deformity, and it is a curious fact that fracture of these bones 
seldom occurs on the same level. The distance between the fractures may 
be from i to 3 inches, usually greater in the leg than in the forearm. 

Crepitus (the sound heard or feeling imparted to the hand when the 
broken ends of the bone are rubbed together) is a valuable symptom of 
fracture, but it can not always be detected, and when other marked signs 
or symptoms are present, need not and should not be looked for. In frac- 
tures of the leg below the knee or the forearm, involving only one of the bones, 
it is hard to make out because of the difficulty of rubbing the broken ends 
together, and when much swelling exists the difficulty is increased, or a 
false crepitus may be produced. In impacted fractures, which occur chiefly 
in the neck of the thigh bone, no effort should be made to obtain crepitus. 
The important thing in such cases is not to disturb the impacted fragments, 
for if pulled apart recovery is rendered more difficult. 

Treatment. — This can best be described by taking as an example a 
fracture of both bones in the middle of the leg. The object of the treat- 
ment is to 

1. Set the bone (known as reducing the fracture) ._ 

2. Apply some dressing that will hold the broken pieces of bone in position. 

3. Watch for swelling, and see that the bandages are not too tight. 

In handling a broken leg, or one in which a broken bone is suspected,' 
the leg should always be stretched by grasping it above and below the 
fracture point. This prevents deformity, injury to the blood-vessels, 
nerves, and soft parts of the sharp ends of the bones, and causes the patient 
less pain. If a patient with a broken leg is to be placed on a bed, one or 
two boards should be passed under the springs of the bed from side to side 
to prevent sagging, as this would cause displacement of the bones and pain 
to the patient. One person grasps the foot firmly, with both hands placed 
over the instep and heel, respectively, and pulls down, while another person 
grasps the thigh just above the knee with both hands and pulls in the oppo- 
site direction. While the leg is thus extended and the attention of the two 
assistants is directed solely to this injured leg, other persons pick up the 
patient carefully and transfer him to the bed. If a doctor can be reached 
in a comparatively short time, the leg can be held in portion by means of 



FRACTURES 



48s 



sandbags. The two legs of a pair of overhauls cut off, filled with sand or 
heavy earth, and tied at the ends, when placed along either side of the leg 
will answer the purpose. The broken leg is approximately in proper posi- 
tion when the ball of the great toe, the inner ankle, and the inside of the 
knee are in the same vertical plane; in other words, if a board were placed 
on edge along the inside of the leg, the three points mentioned would all 
touch the board. 

If the patient is to be transported to the doctor, or if some time will elapse 
before the doctor can arrive, the leg must be incased in some dressing that 





/sS£fit^ 




will hold it stiff and not allow the broken bones to move. Any dressing 
applied for this purpose should be well padded with cotton, soft under- 
clothing, moss, or anything that is available. Particular attention should . 
be paid to the ankle, the heel, and also the parts near the break to see that 
they are all well cushioned. A piece of heavy pasteboard moistened can be 
molded fairly well to the leg. Sometimes a pillow, particularly a hair pil- 
low, if supported by strips of wood on the outside to prevent it bending, 
can be used. The dressing is bound to the limb with bandages. These 
may be made by tearing up a sheet, pillowcase, shirt, or blanket. 



486 



MEDICAL NOTES 



The toes should not be Inclosed in the dressing, because If the doctor 
can not be reached in a short time, it is necessary to watch the toes to 
determine whether the swelling has made the dressing too tight. If the 
toes are bluish and cold, the bandages should be loosened to let the blood 
circulate. If plaster-of- Paris or cement is at hand, a Bavarian splint can 
be made by a layman. Take two pieces of blanket as long as the lower 
leg and i8 inches wide. Fold each piece in the center along its long di- 
mension and sew these folds together, as shown in the illustration. Place 
the leg on the seam, bring the upper fold up on either side, and let the two 
surround the leg, trimming off the blanket so that the edges simply come 
together but do not lap. Now smear the wet plaster-of- Paris or cement 
over this layer, and then bring up the other layer around the leg, trim it 
in the same manner, and tie the dressing on with several bandages un^l it 
"sets." This kind of a splint can be opened at any time for examma- 
tion of the leg, the seam at the back acting like the hinge of a clam shell. 
Possibly wet clay could be used in such a dressing if the limb could be 
placed before a fire to dry. 

The necessary thing in all first-aid work is to get the principles firmly 
fixed in the mind, and human ingenuity will find a way of carrying out 
these principles. A box can be constructed to incase the limb, it being 
properly padded. Whatever dressing is applied, if the patient is to be 
moved any distance, it is best to make the dressing long enough to cover 
the joints above and below the fracture and thus prevent the bones moving, 
as there will then be less danger of displacing them and the patient will be 
more comfortable. If the bandage is rolled loosely and stirred about in a 
vessel of thick starch it can then be applied hot, and when dry, forms an 
excellent stiff dressing; but such a bandage should not be stretched while 
being applied, because the starch contracts in drying and the dressing 
would in that case be too tight. A starch dressing after drying can be split 
up along the front leg to loosen it, and then held in position by several 
bandages. 

COMPOUND FRACTURES 

Compound fractures are serious accidents and require prompt attention 
The treatment, so far as the bone is concerned (place it in normal position 
and keep it there), is the same as for simple fracture. But to do this and at 
the same time give proper attention to the wound in the soft parts (the 
open wound extending down to the bone) frequently demands the highest 
surgical skill. 

Shock from loss of blood is the immediate danger. Inflammation, ery- 
sipelas, blood poisoning, or lockjaw may set in later, and still later the 
patient may become exhausted from long continued suppuration. 

Treatment. — If the wound is very small, it should be well cleaned with 
hot water (water that has been raised to the boiling point and allowed to 
cool down to about 120" F.) or by antiseptic solution (solution bichloride 
of mercury i to 5000) (see page 473) then covered with aseptic gauze, and 
the case treated as a simple fracture. (Clean hands as indicated on page 
473). The services of a physician should be obtained if possible as the 
patient should have an injection of serum (tetanus antitoxin) to prevent 
lockjaw. 

In nearly all cases, however, the safest and best plan is to leave the 
wound uncovered by splint or bandage, so that light dressings may be easily 
applied and frequently changed. The wound should be thoroughly cleansed 
with hot water and antiseptic solution before reducing the fracture, for if 
dirt on the end of the bone or skin is drawn into the wound when the bone is 
returned to its proper place, infection with organisms causing lockjaw or' 
other dangerous conditions may occur, by which the patient may lose his 
limb or his life. The splints or extending ai)paratus should be so arranged 
that the wound is freely accessible and easily drained. Strips of aseptic 
gauze should be placed in the wound and gently carried down to the bottom 
by nieans of a probe, and a larger piece of aseptic gauze, in loose folds should 
be laid over the wound. 

The aseptic gauze dressing should be renewed every day or every second 
day, or as often as necessary to keep the wound well drained until it heals 
from the bottom. 

In severe cases amputation may be necessary to save life, and in all cases 
the patient should be placed under the care of a surgeon as soon as possible. 



FRACTURES 487 

FRACTURE OF THE LOWER JAW 

Fracture of the lower jaw may be simple, compound, or comminuted. 
The mucous membrane of the mouth is nearly always lacerated, the bleed- 
ing is usually not severe (oozing only), but there may be hemorrhage from 
an artery (the inferior dental), saliva dribbles from the half open mouth, 
the teeth may be out of line, pain is apt to be severe, and there may be 
considerable deformity and a false point of motion. 

Treatment. — Restore the parts to the natural position and keep them 
at perfect rest, first washing out the mouth with hot water to cleanse it and 
check bleeding. If the bleeding is very severe, pressure should be made 
by the thumb or finger for a time on the bleeding point, if possible, or on the 
large artery (carotid) on the side of the neck, which may be easily located 
by the pulsation. Loose teeth or pieces of bone should not as a rule be 
removed. Mold them into place, bring the teeth and jaw into natural 
lines, and keep them so by a pasteboard or binder's boardsplint, held in place 
by a four-tailed bandage. 

If the parts can not be kept in place by the methods described, the teeth 
may be fastened together with wire passed between the teeth on each side 
of the break and twisting the ends together. Feed the patient on liquid 
food through a rubber tube introduced behind the last tooth or through any 
space left by the loss of a tooth, the object being to prevent movement of 
the jaw. Wash out the mouth frequently with hot water, and, if necessary, 
change the dressing every two or three days until the end of about the 
sixth or eighth week, when, if all goes well, union will be complete, and the 
splint and bandage may be discontinued. 

FRACTURE OF THE NOSE 

If the nose is broken and it is possible to reach a doctor within four or 
five days, it is best for the layman not to attempt to restore the bones to 
position. If, however, there is great depression of the nose, and a doctor's 
services can not be obtained for a long time, a gentle effort rnay be made 
to lift the bones into position by passing into the nostrils a thin stiff piece 
of metal well wrapped with some soft material. When the patient can 
breathe well through either nostril while the other nostril is held closed, it is 
an indication that the bones are in fairly good position. The operation 
described is a technical procedure and should not be attempted by a layman 
except in an extreme case where medical assistance can not be obtained. 

FRACTURE OF THE SKULL 

If the skull is fractured, there may be unconsciousness, paralysis, bleed- 
ing from the nose or ears, or other unusual manifestations. _ It is important 
to get the doctor as soon as possible. In the meantime, it is a very good 
general rule in this, as well as in all first-aid work, to keep the patient's 
head cool and the feet warm. If ice is at hand, an ice cap can be made 
by tying up the broken ice in a piece of mackintosh, oilcloth, rubber sheet- 
ing, or other waterproof material that will keep the patient from getting 
wet. Warmth to the feet and body can be applied by hot water in bottles 
or jugs, or by heating plates, stones, or bricks in water and wrapping them 
well. Remember .always that an- unconscious man or one seriously injured 
cannot tell his willing helpers when a thing is too hot, and due care should 
be exercised. Do not pour whisky down the patient's throat. If he is able 
to swallow, he probably does not need a stimulant; and if lie can not swallow, 
the whisky will choke him. In many cases, the first resort of the layman 
is the whisky bottle, and when the doctor arrives he can not tell how much 
of the stupor is due to the whisky and how much to the injury. 

If it is impossible to obtain the services of a physician for several days, 
care should be taken to see that the patient passes his urine. If no urine is 
voided for 24 hours after the injury a hot pack of towels, wrung out of 
hot water, should be placed over the bladder; the pack must not be too hot 
or the patient may be burnt. If this does not have the desired effect, a 
soft rubber catheter, if one is obtainable, after being boiled for five minutes, 
should be carefully introduced into the urinary canal and the urine drawn 
off. Before taking this step the person who has charge of the pjatient should 
thoroughly cleanse his own hands and carefully wash the genital organs of 
the patient with soap and water. 



488 



MEDICAI. NOTES 



FRACTURE OF RIBS 

Fractures of the ribs are sometimes difficult to determine, but if present 
there will usually be a stitchlike pain upon taking a deep breath: and if the 
chest is quickly compressed by one hand on the breastbone and tne other on 
the backbone the patient may complain of pain at the point where the bone 
is broken, usually somewhere under the armpit. As splints can not be 
applied to a part like this, and as the ribs are constantly moving in breathing, 
the best that can be done in the way of first aid is to strap the injured side 
with strips of sticking plaster 2 or 3 inches wide, long enough to reach from 
the middle line in front or a little beyond to the middle line behind or farther, 
the strips lapping over one another, drawn rather tightly ancj extending 
from the lowest ribs well up into the armpit. In the absence of sticking 
plaster a strip of muslin 12 inches wide, passed around the chest rather 
tightly several times and snugly pinned, will give some comfort until the 
doctor arrives. 

FRACTURE OF THE THUMB AND FINGERS 

Treatment. — Put the fragments in place by extension and pressure; then 
cut a piece of pasteboard, leather, cigar box, or thin board long enough to 
extend from above the wrist joint to a little below the ends of the fingers and 
a little wider than the hand. Cover the board with lint or any soft cloth, 
place the palm of the hand flat upon it, and apply a bandage around the 
whole hand and wrist. 

If pasteboard or leather be used, it may first be dipped into hot water 
and then molded to the shape of the thumb or finger and palm of the hand, 
then lined or covered with cloth and bandaged as above, care being taken 
not to make the bandage too tight. 

FRACTURE OF THE FOREARM 

The forearm extends from the wrist to the elbow. When both bones are 
broken there is apt to be marked displacement and crepitus (grating felt 
by rubbing the broken ends of the bone together). When only one bone 




m 



Pig. 107. 



is broken, the signs and symptoms are not so clear, but by careful examina- 
tion the nature of the injury may be determined. When fracture of one 
of the bones (the radius) occurs, near the wrist joint (Colles's fracture) 
there is generally marked deformity resembling a silver fork in shape. 

In fracture of the forearm take a thin board 3)4 inches wide and long 
enough to reach from the elbow to the tips of the fingers (Fig. 107). After 
stretching the forearm by grasping the hand and the arm above the elbow until 
it seems fairly straight, lay the palm side of the forearm and hand on the 
board, well padded, and place on the back of the forearm and hand another 
similar padded board extending from the elbow to the knuckles. Carefully 
and evenly bandage the splints, starting at the fingers and working up. 



FRACTURES 



489 



Leave the tips of the fingers uncovered to watch the circulation (Fig. 108). 
The bandaged arm can be carried in a sling. 

Another way to hold the splints in place is to apply strips of adhesive 
plaster around them, one at the upper and the other at the lower end. 




Fig. 108. 

If swelling occurs, the bandage must be loosened. The splints should be 
worn six weeks or two months, but must be removed temporarily every 
few days, and passive motion, that is, gently bending and straightening of 
the fingers with the other hand, made to prevent stiffening. 




Pig. 109. 

FRACTURE OF THE ARM (BETWEEN THE ELBOW AND 
SHOULDER) 

Treatment. — In a break of the upper arm it is well to make two gutters 
of moistened pasteboard, and apply them after padding to the outside and 
inside of the arm. The entire arm and forearm should then be supported 
by two angular splints (Figs. 107 and 109) made of this board, one applied 



490 



MEDICAL NOTES 



from the fingers to the armpit, the other from the fingers to the shoulder. 
The padding should be especially heavy and even about the elbow and any 
other place where the bones naturally come near the skin. 

If much swelling occurs, all bandages must be loosened. 
_ The splint should be worn about eight weeks. Under the most favorable 
circumstances, after fracture, this bone (the humerus) sometimes fails to 
unite. At least once a week the joints should be moved to prevent stiffness. 

Fractures of the arm (of the humerus) at or near the elbow joint or shoulder 
joint are frequently very difficult to determine, even by the most skillful 
surgeon, especially if some time has elapsed since the injury was received; 
and the treatment of necessity is equally difficult. 

If near or at the elbow joint, and if there is much pain, heat, and swelling, 
as is apt to be the case, cold applications should be used, and the arm laid 
upon a pillow until the swelling has gone down. A rectangular splint 
of binder's board or leather should then be dipped in hot water and applied 
to the inner side of the arm and forearm. The splint should be wide enough 
to extend nearly half-way around the arm. It must be well passed and 
held in place by a roller bandage, and the forearm supported by a sling. 






Pig. 1 10. 



Fig. III. 



Pig. 112. 



If the break is near the shoulder joint, the dressing can be supplemented 
by slitting a piece of pasteboard, at one end, moistening it, and molding it 
to form a shoulder cap (Figs, iio, iii and 112), which is bound in place by 
passing bandages from the injured shoulder around the body and opposite 
shoulder. 

After the application of any apparatus for fracture of the arm or forearm, 
the circulation should be carefully watched by feeling the pulse at the 
wrist. If it can not be felt, or if the fingers swell, the bandages should be re- 
moved and reapplied less tightly. 

FRACTURE OF COLLAR BONE 

The collar bone connects the breastbone to the shoulder. Children may 
have a greenstick fracture in which this bone is not completely broken 
across. In adults the fracture is nearly always a simple one, the bones 
overriding. The shoulder drops downward from its own weight and is 
drawn inward and forward by the muscles. The first aid indications are 
therefore to overcome these actions as far as possible, and_ to force the 
shoulder upward, outward, and backward. Placing the arm in a sling will 
draw the shoulder upward to a certain extent, and this can be assisted, if 
sticking plaster is available, by placing the hand of the injured side on the 
opposite shoulder and then binding it there by placing the middle of a long 
strip of 2 or 3 inch sticking plaster under the elbow, one end passing along 
the forearm to the hand on the shoulder and the other end passing diag- 
onally across the back to meet the first end on the shoulder. Other strips of 
sticking plaster or a bandage passed around the injured shoulder, then 
across the back, and fastened around the body, will force the shoulder 



FRACTURES 



491 



backward and to a slight extent outward and make the patient more com- 
fortable until the doctor arrives. In the absence of stickmg plaster a band- 
age applied in a "figure of eight" may hold the shoulders m fairly good 
position (Figs. 113 and 114). Stand at the patient's back, pass the bandage 
over one shoulder to the front, then under the armpit to the back, across the 
back to the front of the opposite shoulder, through this armpit to the start- 
ing point on the back. Go over the route several times with some tension 
on the bandage, and then make the end fast. 




Pig. 113. Pig. 114. 

FRACTURE OEL THE THIGH 

The thigh bone (femur) extends from the hip to the knee. Fracturet of 
this bone may occur in any portion of the shaft, but the most common seat 
of fracture is about the middle or the middle third. Fractures high up 
near the hip joint are frequently difficult to make 9ut, and the results of 
treatment in such cases, even under the care of skillful surgeons, are not 
always satisfactory. 




Pig. 115. 

In fracture of the middle or middle third of the bone the deformity is 
usually produced by the lower fragment (the broken end of the lower por- 
tion of the bone) being drawn up behind and to the inner side of the upper 
fragment; the weight of the limb then causes rotation and the foot and toes 
are turned outward. 

If the fracture is a little higher up, displacement is shown by the upper 
fragment, which, by the action of the muscles, is thrown strongly forward 
and outward. In either case there are complete loss of power, shortening 
to the extent of i to 2 or 3 inches, pain on the slightest movement, crepitus 
(grating) if the broken ends of the bone are rubbed together, and abnormal 
motion. 



492 



MEDIC.\L NOTES 



In impacted fractures, which are met chiefly at or near the hip joint, the 
shortening may be, and usually is, less marked. Loss of power is usually 
complete, but not always. Patients have been known to stand and even 
walk a few steps. Injuries of this kind require the greatest care; the limbs 
should be handled very carefully. If on slight traction or manipulation 
crepitus is not felt, no further attempt should be made to obtain this symp- 
tom, for in doing so the impacted bones may be pulled apart, which is 
to be avoided unless especially directed by a skillful surgeon. 




Pig. ii6. 



I 



Treatment. — In the absence of a physician, about all that can reasonably 
be done in impacted fracture is to apply a broad bandage around the hips 
and place the patient in a good bed on a firm mattress and make lateral 
support by means of boards (Fig. 115) or by sandbags, one on the outside 
long enough to reach. from the upper end of the hip bone to the foot, the 
other along the inner side of the leg from the crotch to the foot. Fill the 
bags three-quarters full of dry sand. Keep the leg straight, toes upward. 




Fig. 



117. 



• .^5®^*^?®'^* 2^ nommpacted fracture of the thigh bone at or near the hip 
JP^^.^-. Flaceboth legs on the double inclined plane, or make extension and 
nx this limb m the straight position by means of a long splint (a splint ex- 
tending from the armpit to the foot), or by the weight and pulley, or by the 
long splint and the weight and pulley combined in the manner now about 
to be explained m connection with the treatment of fractures of the shaft 
or the thigh bone, 



FRACTURES 493 

Treatment of fractures of the shaft of the thigh bone. In fractures of 
the shaft of this bone the signs and symptoms, as already stated, are usually 
well marked. If the fracture is at the upper end or in the upper third of the 
bone, especially if the upper fragment is tilted forward, the double-inclined 
plane (Fig. 116) well padded or covered with pillows, with weight and pulley 
attached by means of adhesive stuck to each side of the thigh as far as the 
knee, affords the easiest and probably the best means of treatment. ^ But 
in the majority of cases when the fracture is farther down, about the middle 
or in the middle third of the bone, the weight and pulley with leg and long 
splint combined (Fig. 118) are better adapted if properly applied. Sand- 
bags placed alongside may also be used in connection with any of the straight 
splints. In all cases the fracture should be reduced by gradually pulling 




Pig, 118. 

and carefully pressing the broken bones into their natural position. In 
addition to the splints already mentioned, short splints of narrow strips of 
thin board or binder's board should be applied directly over the seat of 
fracture. If a double-inclined plane is not at hand, two broad pieces of 
board may be nailed together at a suitable angle and used instead, always 
properly padded or covered with pillows. 

The Weight and Pulley (Figs. 116 and 118). — The weight and pulley are 
applied as follows: Measure the distance from i inch below the leg and thigh 
in a straight line (Fig. 117) or the weight and pul-crotch to a point 4 inches 
below the foot. Cut a strip of adhesive plaster exactly twice as long as 
the distance just measured and 3 inches wide, and stretch it on a table or 
on the floor, with the sticky side tip. Get a block of wood 4 inches long, 



SI 



c 



Fig. 119. 

about 3 inches wide, and about 3^^ inch thick, with a hole bored through the 
center large enough to admit a large cord. Place the block exactly in the 
center of the long strip of adhesive plaster. Cut another strip of plaster 
the width of the first and 18 inches long, and place it on the first strip, 
sticky surfaces together, so as to include the block between the center_ of 
each. Thus a stirrup is made, and the long strip of plaster on each side 
of it applied to the leg and thigh after they have been shaved, extending 
from a point just above the ankle bone to a point about i inch below the 
crotch on the inner side and to the same level on the outer side, the person 
applying the plaster being careful to keep the block square when the two 
ends of the plaster are stuck to the limb. A roller bandage is then applied 
over the plaster from the ankle up, and a strong cord passed through the 



494 



MEDICAL NOTES 



hole in the block and knotted so that it can not slip through. The other 
end is then passed over a pulley attached to the foot of the bed or elsewhere, 
as may be convenient, on a line with the extended limb, and a weight of 
from 5 to 30 pounds, as may be necessary or comfortable to the patient, 
attached, which may be increased if necessary to overcome muscular spasm. 
The same kind of apparatus may be used with the double-inclined plane, 
except that the plaster is applied only to the thigh, the stirrup coming 
just below the bent knee. 

Counterextension may be obtained by raising the foot end of the bed on 
blocks 4 to 6 inches high. The short splints should be well padded and 
extend well above and below the fracture, and be held in place by strips of 
plaster or bandage. 

The long splint gives additional support and prevents outward rotation 
of the leg. ^ It should be well padded, and have a crosspiece at the lower end 
to keep it in position.^ Treatment will be required for a period of 8 to 10 
weeks, but the extension may be lessened about the end of the sixth week 
and passive motion made at the knee joint each day, by grasping the leg and 
gently bending and extending it. 

FRACTURE OF THE KNEECAP 

Fracture of the kneecap may be transverse, vertical, or oblique. The 
bone may be broken into two or more irregularly shaped pieces. 

Symptoms and Signs. — Loss of power, inability to extend the joint or 
raise the limb from the bed. In the transverse variety the fragments are 
widely separated. If seen soon after the accident, the line of fracture, the 




Pig. 120. 



gap between the fragments, may be seen and felt. Swelling rapidly appears 
and the signs are obscured. 

Treatment. — Various foims of apparatus are employed, and in hospital 
practice the injury is frequently treated by surgical operation, with good 
result. The simplest form of treatment is to place the limb on a long splint 
with the foot raised so as to relax the thigh muscles, or if the patient is 
propped up in bed by pillows or a back rest, the limb may be allowed to 
lie on a level. 

This splint should be applied as follows: A padded straight board should 
be bound on the back of the limb, extending from the heel to the upper part 
of the thigh. A folded towel placed at the back of the knee, allowing the 
joint to bend slightly, will be comfortable. One handkerchief, or bandage 
should be applied below the knee. Another handkerchief should be passed 
above the kneecap, and be knotted at the back below the knee (Pig. 120). 
Nails driven into the edge of the board at convenient points assist in holding 
the bandage in position. 

Apply iced water or the ice bag for a few days. If swelling or numbness 
of the foot is complained of, the bandage is too tight and must be removed. 

If the bandages become loose, as they are apt to do every few days, they 
should be reapplied. 

The long splint should be worn about six weeks or two months, when it 
may be replaced by a shorter molded splint of leather, felt, or pasteboard, 
to prevent motion at the joint when the patient walks with a cane or crutches. 
The short splint should be worn for at least a month, and then suitably 
constructed kneecap should be worn for one year to support the joint. 
More or less stiffness of the joint is to be expected. 



FRACTURES 



49S 




Pig. 121. — Showing appearance of the right foot after Pott's 

fracture. 




. First Aid Dresang AppGed 
Armmd Body for Brdteo lUk 



2, First Aid Bandage Aroondlfipe 
lor Broken Pdvia. 



3. Blanket Sdint 
for Leg 




S. Improvised ^dint for Ann. 



JtmaaFSrermr 



Pig. 122. — Temporary splints. {American Red Cross.) 



496 



MEDICAL NOTES 



FRACTURE OF THE LEG (BETWEEN THE KNEE AND ANKLE) 

The leg extends from the knee to the ankle and has two bones, tibia 
and fibula. 

Fracture of the leg may be simple or compound. Both bones may be 
broken or only one; the line of fracture may be oblique or transverse. When 
both bones are broken at the middle or lower third the deformity is usually 
quite marked. The break is apt to be in an oblique direction and at a 
lower level in the tibia (the shin) than in the fibula. In simple fracture of 
the upper part of the leg the deformity may be less marked, but if the knee 
is involved there may be great swelling because of acute and serious in- 
flammation of the joint. 

When the shaft of only one bone (the tibia or fibula) is broken there is 
not much displacement, because in such cases the sound bone acts as a side 
splint. Fracture at the lower end of the tibia at the projection on inner side 
of ankle is sometimes mistaken for sprained ankle, and if the small fragment 
of bone is not accurately adjusted and kept in proper position the result 
may be a weak and stiff joint. 

The fibula may be fractured at any point, but the important fracture of 
this bone is known as "Pott's fracture" (Fig. 121). This fracture occurs 
about 3 inches above the ankle, on outer side of the leg, and is accompanied 
or complicated by outward dislocation of the foot, and not infrequently 
by the breaking or tearing off of the tip of the lower end of the tibia. 




Fig. 123. 

Treatment. — If the line of fracture is oblique the limb must be handled 
very carefully so as to prevent injury to the soft parts by the sharp ends of 
the bone and thus avoid the conversion of a simple fracture into a com- 
pound one. 

The treatment of fracture of the leg has been described under the headmg 
** Simple Fractures," page 484. 

A Pott's fracture should be treated as follows: Take a board splint long 
enough to extend from the knee to a few inches beyond the sole of the foot. 
Pad the splint well, have the lower end of the padding at least 2 inches thick, 
and do not let it extend quite to the ankle joint below. Apply the splint 
to the inner side of the leg so that the foot and ankle project below the 
padding. The foot and leg are then bandaged to the splint in such a way 
as to turn the foot inward and thus correct the outward displacement (Fig. 
123). 

FRACTURE IN FOOT 

If a bone in the foot is broken, have the patient place his sound foot on a 
thin board or heavy pasteboard. With a lead pencil draw an outline of the 
foot, allowing an eighth of an inch extra all the way around. Cut this out, 
turn it over, and it will fit the sole of the injured foot. Pad this and bind 
it to the foot, the starch bandage making an excellent dressing. Leave 
the toes exposed for observation of the circulation. 

DISLOCATIONS 

A bone is dislocated or "out of joint" when it is displaced or forcibly 
separated from another bone entering into the composition of a joint. 

Dislocations may be complete or incomplete. A dislocation is complete 
when the joint surfaces are entirely separated and the ligaments torn, as 
in dislocation of the hip joint; incomplete when the jokit surfaces are not 
entirely displaced. Dislocations may be simple, compound, or complicated. 



DISLOCATIONS 497 

A dislocation is simple when there is no wound of the skin and soft parts 
when the joint surfaces are not exposed to the outer air; compound when 
there is an open wound and the outer air is brought into contact with the 
joint surfaces of the joint; complicated when besides the dislocation there 
is a fracture and serious damage to the soft parts or to blood vessels or nerves. 

Dislocations are said to be most common in adult or middle life, when the 
bones are strong and the muscles powerful. In the young and old the 
bones are more apt to break. There are, however, striking exceptions to this 
rule when applied to the elbow joint and the shoulder J9int. The elbow 
joint in yqun^ subjects is frequently dislocated, and dislocation of the 
shoulder joint in old men is not uncommon. 

Symptoms and Signs of Dislocations.— Deformity is always present, and 
may be determined by comparing the injured side with the sound one. 
The head or end of the bone is in an abnormal position; the attitude of the 
limb is changed; the patient can not move the limb; and when effort is 
made to move the joint it is found to be very stiff. There may be shortening 
or lengthening. For example, in dislocation of the hip the head of the 
thigh bone may be thrown outward and upward, when there will be short- 
ening of the leg; or it may be forced downward and inward, when the length 
of the limb will be increased. 

Treatment. — The indications are to replace the bones in their natural 
position and to keep the parts at rest until the ligaments and damaged 
tissues about the joint are healed. A dislocation should be reduced imme- 
diately after the accident, while the patient is faint and the muscles are in a 
relaxed condition. 

Having thus briefly described a dislocation and the treatment indicated, 
the question now arises, How shall the treatment be applied; how shall the 
dislocation be reduced ? And when it is taken into consideration that the 
reduction of dislocations not infrequently taxes the skill of the most ex- 
perienced surgeon (even with the aid of general anesthetics), it is hardly 
to be expected that a non-professional man will be able to accomplish the 
desired results in many cases. It must also be borne in mind that there are 
certain dangers attending efforts at reduction, especially at the larger joints, 
if improperly or too forcibly applied, such as fracture of bone or rupture of 
blood vessel. 

DISLOCATION ^F THE FINGERS 

Dislocation of the bones of the fingers may be backward or forward. 

Treatment. — Extension and counter extension and manipulation. Pull 
the finger directly in line with the hand, and when fully extended make 
pressure on the head of the bone. Reduction is usually affected without 
much difficulty. Place the finger on a well-padded splint for one week, then 
make passive motion by gently bending it each day, and, if necessary, re- 
applying the splint after each daily exercise. 

DISLOCATION OF THE THUMB 

Dislocation of the thumb may be backward or forward. 

Treatment. — The treatment is not the same as for dislocation of the 
fingers, and reduction, especially of the backward dislocation, is usually 
very difficult. Try by pushing the end of the thumb upward and backward 
until it stands perpendicularly on the bone from which it is dislocated, then 
make strong pressure against the base of the dislocated bone from behind 
forward, sliding it on the bone beneath till it gets to the end, then flex or 
bend the thumb into place. 

DISLOCATION OF THE WRIST 

Dislocation of the wrist joint may be backward or forward. It is a rare 
injury. Fracture about the wrist is more common, and is sometimes mis- 
taken for dislocation. _ A stiff joint is apt to be the result. 

Treatment. — Extension, counterextension, and direct pressure. Grasp 
the hand of the patient, pull in a straight line, and have an assistant pull 
on the forearm in the opposite direction, and when the parts are fully ex^ 
tended make direct pressure upon the wrist bones. Apply a bandage, and 
place the hand and forearm on a well-padded splint for a week; then remove 
the splint and make passive motion at the joint each day by gently bending 
the wrist in all directions, reapplying the splint after each daily exercise; 



498 



MEDICAL NOTES 



reapply the splint and remove it after an interval of another week. If 
there is much pain or swelling after reduction of the dislocation, apply- 
cold water. 

DISLOCATION OF THE ELBOW 

Dislocations of the elbow are serious accidents. They present a variety 
of forms, backward, forward, outward, and inward, and these are divided 
into a number of subvarieties. One or both bones may be involved, and 
the dislocation may be associated with fracture. Reduction in some cases 
is comparatively easy; in others it is very difficult, even in the hands of 
experienced surgeons. 

Without a thorough knowledge of the anatomy of the normal joint it is 
very difficult to understand the different forms of dislocation, and of necessity 
equally difficult to apply the proper treatment. 

Immediately after the accident and before swelling sets in, the injured 
elbow should be carefully compared with the sound one. When the normal 
arm is extended (straight), the tip of the elbow and the bony points on 
either side should be in a transverse line across the joint. If these promi- 
nences are found out of line, dislocation or fracture is probably present. 

Treatment. — Fixation of the arm above the elbow, extension or flexion 
of the forearm, and direct pressure by means of the thumbs or fingers on 
the head of the dislocated bone, so as to push it back into the socket. After 
reduction an angular splint should be applied to inner side of arm, lightly 
bandaged, and the forearm carried in a sling. ^ Cold water may be applied 
to reduce inflammatory action. Passive motion should be employed at 
the end of a week, by gentle movements of the joint each day. 

DISLOCATION OF THE SHOULDER 

Dislocation of the shoulder joint is a very common accident. It occurs as 
frequently as all other dislocations put together. The frequency is explained 
by the great latitude of motion of the joint, the shallowness of the socket, 
and the size and rounded shape of the head of the bone, the laxity of the 
capsular ligament, and the leverage exerted on the joint by the long bone. 

There are three chief forms of dislocation of the shoulder :_ (i) forward and 
downward below the collar bone; (2) directly downward into the armpit; 
and (3) backward on the shoulder blade. 

The symptoms and signs are pain, swelling, rigidity (stiffness), loss of 
power, flattening and angular appearance of the shoulder as compared with 
the other shoulder, abnormal situation of the head of the bones, and change 
in the axis of the long bone (Fig. 124). In the first variety, the most common 
of all, the head of the bone may be left in front of the armpit and below the 
collar bone, and the elbow points outward and backward. In the second 
the head of the bone may be felt in the armpit, and the elbow points out- 
ward. In the third the head of the bone may be felt on the back of the 
shoulder blade, the elbow points forward, and the forearm is thrown across 
the chest. Another valuable sign is that when the elbow is placed on the 
chest the patient can not place the hand of the injured side upon the oppo- 
site shoulder, or, if the hand is placed on the shoulder the elbow can not be 
brought into contact with the chest. 

Treatment. — The treatment for the first variety (forward and downward) 
is as follows: Lay the patient down or let him sit on a chair; bend the 
forearm on the arm; press the elbow against the side of the chest and hold 
it there; rotate the arm outward by carrying the forearm outward; pull 
steadily on the arm and rotate inward by carrying the elbow upward and 
forward with forearm across the chest. While this is going on have an 
assistant place his hand in the armpit and press the head of the bone into 
place. 

For the second variety (directly downward into the armpit) place the 
patient on his back; remove your boot; place your heel in the armpit; 
grasp the wrist and pull steadily on the arm. If the dislocation is in the 
right shoulder, seat yourself on the right side of the patient and use your 
right foot ; and if the injury is in the left shoulder, seat yourself on the left 
side and use your left foot. The same principles may be carried out by 
seating the patient on a low chair and placing your knee in the armpit. 

Another method is to have an assistant stand upon a table and make 
counterextension with a towel, or a strong piece of soft cloth of any kind, 
passed under the armpit of the patient, while the operator pulls the arm 
downward. The same method may be employed by causing the patient 



DISLOCATIONS 



499 



to lie on his back, and an additional advantage may be obtained by placing 
a rolled bandage or a pad of any kind in the folds of a towel in the armpit. 

In dislocation backward on the shoulder blade, pull the arm forward and 
make direct pressure forward on the head of the bone, or stand behind the 
patient, draw the elbow backward, and with the thumb press upon the head 
of the bone and guide it into place. 

After reduction a soft pad should be placed in the armpit, the upper arm 
bandaged to the body, and the forearm placed in a sling across the chest. 
Passive motion at the joint should begin at the end of a week and be repeated 
daily by grasping the arm and gently moving the shoulder in all directions. 
The arm should be carried in the sling about three weeks. 




Fig. 124. — Dislocation of the right shoulder. 



DISLOCATION OF THE COLLAR BONE 

^ The collar bone extends from the upper border of the breast bone to the 
highest point of the shoulder blade. Dislocation may occur at either end. 
Reduction is comparatively easy, but it is difficult to retain the bone in 
position. 

Treatment. — Make extension by drawing back the shoulders, the knee, 
if necessary, being placed between the shoulder blades; push the end of the 
bone in place and try to keep it there by a firm pad fastened by adhesive 
plaster and bandage. The best result may be obtained by placing the 
patient at rest on his back for three weeks. 

DISLOCATIONS OF THE TOES 

Dislocations of the toes are very rare accidents. The treatment is the 
same as for dislocation of the fingers. Dislocation of the big toe may be 
treated the same as dislocation of the thumb. 



SCO MEDICAL NOTES 

DISLOCATION OF THE ANKLE 

The foot may be dislocated forward, backward, outward, inward, or 
upward. The dislocation may be complete or incomplete. 

The lower ends of the bones of the leg enter into the formation of the 
ankle joint, the end of the tibia on the inner side, and the end of the fibula 
on the outer side of the joint. Dislocations of the ankle are usually com- 
plicated by fracture of the tip of one or both of these bones. When, in 
addition, the fibula is broken above the ankle the injury is known as Pott's 
fracture, already referred to. 

Treatment. — Extension, counterextension, and pressure. Flex the leg 
on the thigh and the thigh at right angle to body; pull steadily on the foot, 
while an assistant makes counterextension at the thigh, and press the bones 
in place. Apply cold water and place the foot and leg in a fracture box or 
apply well-padded molded splints. Binder's board dipped in warm water 
and molded to the part and lined with thick layers of cotton will answer 
the purpose. If a Pott's fracture, use the splint shown in Fig. 123. Make 
passive motion at the joint at the end of two weeks. (See method .described 
under dislocation of the elbow.) 

DISLOCATION OF THE KNEE 

Dislocation of the knee may be complete, incomplete, compound, or 
complicated. The direction of the dislocation may be forward, backward, 
outward, or inward. The deformity is quite marked. Reduction is not very 
difficult, but the injury is a serious one and care must be taken in making 
reduction not to produce additional damage by too forcible extension. 
Fortunately the injury is exceedingly rare. 

Treatment. — Extension, counterextension, and pressure. Have one 
assistant pull steadily, not too hard, on the leg or ankle, while another fixes 
or pulls on the thigh and presses the bone into place. After reduction apply 
cold- water, and place the leg in a posterior straight splint, well padded* 
especially below the hollow of the knee, and make passive motion at the 
end of two weeks. When the patient begins to walk, a kneecap or flannel 
bandage should be applied. 

DISLOCATION OF THE HIP 

Dislocation of the hip joint is a serious injury. It occurs much less 
frequently than dislocation of the shoulder joint. The socket of the hip 
joint is very deep, and the ligaments and muscles surrounding the joint 
are very strong and powerful. Dislocation occurs only when the limb is 
in a certain position, when its axis is changed from that of the body, and 
when in consequence of any sudden or great force received on the lower end 
of the leg or knee the head of the bone is forced through the ligament (the 
capsule) which surrounds the joints. The head of the bone may then be 
thrown (i) backward and upward; (2) backward; (3) forward and down- 
ward; (4) forward. The different directions indicate the different forms of 
dislocation. The first is the most common. 

In the first form, examination from below up shows the big toe turned 
toward or resting on the instep of the opposite foot; the knee flexed and 
resting against thigh at upper margin of opposite kneecap; the thigh rotated* 
inward and drawn toward its fellow; bulging of the hip; and about 2 inches 
shortening of the entire limb. 

In the second form the signs are the same as m the first, but less marked. 
(Fig. 125). Fracture of the neck of the thigh bone is sometimes mistaken for 
this injury. But in fracture there is abnormal motion, and the foot is 
turned outward. . , , , 

In the third form (Fig. 126) the signs are almost exactly the reverse of 
the first form. The foot and knee are turned outward, the hip is flattened, 
and the entire limb is lengthened. 

The signs of the fourth form are nearly the same as those of the third 
except that the entire limb is shortened. 

Treatment. — The treatment is by manipulation or by extension and 
counterextension. ..., . , , , •i.jx^ 

For the first and second forms of dislocation, the above described treat- 
ment may be applied as follows: Place the patient on his back on a mattress 
on the floor. Seize the foot or ankle with one hand and place the other 



DISLOCATIONS 



501 



hand under the knee. Flex the leg upon the back of the thigh, and the 
thigh upon the body to about a right angle; then carry the knee inward and 
rotate on its own axis, then suddenly raise it (lift it toward the ceiling) so 
that the head of the bone may be thrown over the rim of the socket, and 
immediately extend the limb with outward rotation to its normal position 
so that the head of the bone may return to the socket through the hole in 
the capsule by which it escaped. 

The treatment of the third and fourth forms of injury corresponds to 
that for the first and second, except that the limb should be carried out- 
ward first, then inward, across the median line, and rotated inward on its 
own axis, and then suddenly lifted and brought down to its normal position 
by the side of its fellow. 





Fig. 125. 



Fig. 126. 



N9 great force should be used in making these movements. If any 
considerable resistance is "met with in rotating or lifting the bone, the move- 
ment should be modified in such a way that the head of the bone may follow 
the path of least resistance. _ . 

If extension and counterextension be applied, they should follow the line 
of the axis of the dislocated thigh. It must not be forgotten in the con- 
sideration of these methods that the application of too much force or of 
force improperly applied may produce fracture of the bone. 



CHAPTER XIII 

OFFICE PRACTICE 

The treatment of Office Practice will be handled in the same 
manner as the Survey; that is under the Main Divisions of 

(a) The Improvement of Existing Roads. 

(b) The Location of New Roads. 

It is impossible in a book of this character and size of page to 
illustrate exactly the detail methods of design which carry out the 
principles of economy discussed in Part I but we have made an 
effort to give an idea of the practical methods by restricted ex- 
amples and rather full instructions for drafting room procedure 
which the author has used in instructing men not familiar with the 
details of road work. 

We have in mind getting out in the next year or so data in treatise 
form containing large charts and plates to illustrate in detail the 
office methods of economical alignment and grade line design. 

The collection of tables in this chapter have been found from 
actual office use to be of value in saving time in the design and 
estimate of quantities. 

List of Tables in Chapter XIII 

No. Page 

36. Sight distance . 504 

37. Vertical curve radii 513 

38. Vertical curve sight distance 513 

39. Earthwork quantities 516 

40. Cx)nversion cu. ft. to cu. yd 518 

41. Earthwork quantities 526 

42. Conversion feet to miles 538 

43. Pounds of stone per 100' of road 540 

44. Cu. yd. of macadam 543 

45. Sq. yd. of surface per 100' . . 543 

46. Amount of oil 553 

47. Mesh reinforcement 555 

48. Bar reinforcement 556 

49. Cast iron pipe weight 558 

50. Corrugated metal pipe weights 559 

50A. Weight and Dimensions Vitrified Pipe 560 

51. Strength steel I beams 561 

52. Strength wooden beams 5^3 

53. Strength concrete slabs 564 

53A. Recommended depths of concrete slabs in road bridges 

under different depths of fill . * 565 

54. Strength concrete beams 566 

55. Safe Long column loads timber 567 

502 



SCALES 



503 



For stream runoff, capacity of culverts, bridge loading, safe 
loads on piles, safe loads on foundation soils for structures, etc., see 
Chapter III on Drainage. 

For Depths of Macadam roads on different soils, see Chapter V 
on Foundation Courses, page 152. 

(a) The Improvement of Existing Roads 

Under office practice we include 

1. Mapping the preliminary survey. 

2. Designing the improvement and estimating the quantities. 

3. Producing a finished set of plans from which the road can 
be constructed." 

I. MAPPING THE PRELIMINARY SURVEY 

The mapping of the preliminary survey serves as a base from 
which the design of the new work, and the quantities necessary 
thereto, can be built up. It consists of three views of the road: 
the plan, showing the topographic features; the profile, showing 
the longitudinal differences of elevation, and the cross-sections, 
showing the constantly changing transverse shape. 

The scales in general use are as follows: 



Plan 


Profile 


Cross-sections 


i" = 100' 


i" = 100' horizontal 
i" = 10' vertical 


1" = 10' 


i''= 50' 


i" = 50' horizontal 
i" = 10' vertical 


I" = 5' 
or 1' = 4' 


i" = 20' 


i" = 20' horizontal 
i" = 5' vertical 


or i" = 4' 


i" = 10' 


i" = 10' horizontal 
i" = 10' vertical 


i" = 2' 



The 100' scale is too small for convenience in design, and earth- 
work quantities figured from cross-sections plotted i" to 10' are 
not reliable. For work on ordinary country roads, the 50' scale 
is generally adopted, using cross-sections plotted i" to 5' or i" to 4'; 
this scale is satisfactory for laying the grade line and computing 
the earthwork. 

The larger scales of i" = 20' or i" = 10' are useful in village 
work where a large amount of detail must be shown. 



504 



OFFICE PRACTICE 



Plotting the Center Line. — The survey center line can be plotted 
by deflection angles at the transit points, using a table of natural 
tangents, a vernier protractor or an ordinary paper protractor gradu- 
ated to 15 minutes. 

Where the center line has been well located in the field and 
there seems to be no necessity for a paper re-location, no great 
care need be taken in plotting the deflection angles, as in such a 
case the map serves more as a picture of the topographic features 
than as a basis for alignment. 

Where a random line has been run in the field and some shifting 
of the center line is necessary, both angles and distances must be 
accurately plotted. If any extensive change of alignment is 
made, the new deflections and distances should be checked by 
figuring the difference of latitude and longitude for both the 
survey line and the office line between the points of equality. 

Where the consideration of sight distance (see page ss) governs, 
Table 36 will be of service. 

T/VBLE 36 



Table 36 gives the approximate distance that an automobile 


driver can see an approaching car, assuming that he is driving 


in the center of the macadam and that the approaching car 


is also in the center. Two distances are given for each curve, 


the first assuming that the line of sight is six feet from the ground, 


which is about right if the curve is on a straight grade, and makes 


the line of sight tangent to the cut slope of i on 1 3-^ 19 feet off 


center for the narrow section shown in Fig. 11, page 44, and. 


second, assuming that the line of sight is close to the ground, 


as occurs on rounding the top of a hill, in which case the line 


of sight will be tangent to the side slope at, approximately, 11' 
off center. 


Degree of 


Radius of Curve 


Sight Distance 


Sight Distance 


Curvature 


Feet 


Case One. Feet 


Case Two. Feet 


5 


1 146.0 


400 


310 


6 


955.0 


375 


290 


7 


818.6 


350 


270 


8 


716.3 


330 


250 


9 


636.6 


310 


23s 


10 


573.0 


295 


220 


12 


477-5 


270 


200 


14 


409.3 


245 


185 


16 


358.1 


230 


175 


18 


318.3 


220 


165 


20 


286.5 


210 


160 


30 


191.0 


170 


130 


40 


143.2 


145 


IIO 


SO 


1 14.6 


130 


100 



TOPOGRAPHY 



SOS 



For convenience in plotting the topography, the loo' survey 
stations are plainly marked. 

The most common mistakes in plotting the map are made by 

reversing the deflection, as right instead of left and vice versa, 

or in adding or omitting loo' in scaling long-tangent distances. 

The work should be checked for mistakes of this nature. 

All curve data is marked plainly on the map near the P.I. 

and shows 

The deflection angle A 
The degree of curve D 
The radius of curve R 
The tangent length T 
The length of curve L 
The station of the P. I. 
The station of the P.C, 
The station of the P. r. 

If the curves have been figured in the office and have not been 
run in the field it is good practice to scale 
the offsets from the tangent to the curve and 
mark them on the map. 

These offsets from the center line as run 
are then transferred to the cross-sections and 
the profile plotted from center line elevations 
on the cross-sections. 

Plotting the Topography. — If the topography 
has been recorded by a system of right-angle 
offsets, as suggested and illustrated on page 
328, it can be easily and quickly plotted by 
using the transparent scale shown here. 

This scale gives the plus distance along 
the survey base line, or center line, and the 
offset distance from the line in one operation. 

As a general rule the plotting of the topog- 
raphy need not be checked. 

Level Computations. — The survey compu- 
tations of the Bench Levels are checked and a 
list of bench elevations prepared; these eleva- 
tions are used in cross-section level notes and 
from them the notes are computed between 
benches. As each bench is reached these 
notes are corrected to agree with the elevation 
adopted for that bench and then carried for- 
ward on the corrected basis. The allowable 
error for cross-section levels, as mentioned in 
the chapter on surveys, is less than o.i foot. The correction of 
the levels at each bench prevents any cumulative error and makes 
the elevations of the cross-section shots agree with the adopted 
bench elevations with an error of less than o.i'. This is as close as 
the readings can be plotted and as close as they can be read in the 
field. 




Fig. 127. — Con- 
venient trans- 
parent scale for 
plotting topog- 
raphy. 



5o6 



OFFICE PRACTICE 



The computation of the bench levels and the adjustment of 
the cross-section notes should be checked by a competent ms-n. 
The most common mistake in figuring the cross-section read- 
ings is to use the wrong height of instrument for a section. Such 
a mistake can not be detected in plotting the sections, but is gener- 
ally discovered when the profile is plotted. 

In checking the notes particular care should be taken on this 
one point. 

Potting the Cross-sections. — The cross-sections must be Dcry 
carefully plotted, as the reliability of the earthwork computation 
depends largely on their accuracy. 

The cross-section paper used should be exact in the divisions 
and should be printed or engraved from plates. 

Ruled paper is inaccurate. 

The plotting is checked by reliable men. Reading the shots 
back from the plotted cross-section is preferable to reading them 
from the book. The elevations of the center line and of the ditch 
line are written over the section. The station number or plus 
of each section is written on the right margin. The fact that 




Fig. 12S 



the section has been graveled within the traveled way, that stone 
has been spread to a certain thickness, or any other fact that 
would influence the designer when laying a grade line, is noted on 
the section. See Fig. 128. 

It is common practice to allow the inexperienced men to plot 
and check the cross-sections. We believe this is a mistake. This 
part of mapping is the most important of the preliminary plans, 
and the work should be plotted and checked so that the points are 
correct to the nearest o.i feet in elevation. 

These points are then connected with a fine ink line. 

Plotting the Profile. — The profile is plotted from the center-line 
elevations given in the cross-section notes unless the proposed center 
line does not coincide with the survey center line, in which case 
the elevations of the proposed line are projected from the previously 
plotted cross-sections. 

It is not necessary to spend so much time for accuracy in plotting 
as on the sections, as the profile only serves as a guide in laying 
the grade line and no quantities depend upon its correctness. An 
error of 0.2 feet is allowable. 

The elevation of each plotted center-line point is recorded with 
its stationing (see Figure 131, page 510). 



DESIGN 507 

The Design. — The completion of the profile finishes the pre- 
liminary mapping. The first operations of the office design are 
as follows: 

A. The selection of section. 

B. The depth of metalling. 

C. The laying of the grade line. 

These three points are so dependent on each other that they can- 
not be separated. 

The most experienced man available should do this part of the 
work. He should be thoroughly familiar with the road from field 
inspection, and in designing he follows the general principles dis- 
cussed in the chapters on Grades, Sections, and Foundations. His 
selection depends on a report of the character given in the chapter 
on Preliminary Investigation (see page 274). 

Maximum gradients for the various types of pavement are as 
follows: 

Wooden block 2 % 

Asphalt block 4% 

Brick 5% 

Concrete 5% 

Bituminous macadam with flush or squeegee coat. 4% 

(In sandy country, six per cent, when coarse sand is sprinkled on 
surface.) 

Bituminous macadam without squeegee 8% 

Waterbound macadam 8% 

"Hillside" brick 12% 

Stone block with open joints 12% 

Shrinkage of Earthwork. — We have made no mention heretofore 
of the shrinkage of earth cut when placed in fill. This is an im- 
portant factor of an economical grading design. 

Trautwine states that for railroad work it takes 

1.08 cu. yd. gravel or sand excavation to make i cu. yd. em- 
bankment. 

1. 10 cu. yd. clay excavation to make i cu. yd. embankment. 

I.I 2 cu. yd. loam excavation to make i cu. yd. embankment. 

1. 1 5 cu. yd. vegetable surface soil excavation to make i cu. yd. 
embankment. 

The quantities 1.08 cu. yd. gravel, etc., refer to the volume 
occupied by the material before removal. 

Trautwine also states that in loosening earth and loading into 
wagons or cars i cu. yd. of earth swells about one-fifth and measures 
loose practically 1.2 cu. 3^d. 

These values, however, cannot be used in roadwork, as a certain 
percentage of the excavation is sod or vegetable matter that is not 
suitable for embankment and. must be wasted. 

This waste material raises the percentage of cut necessary to make 
the fill. 

The correct ratio for roadwork has been a source of contention 



So8 OFFICE PRACTICE 

among engineers, and we believe that the use of too high a value 
has resulted in a needless waste of thousands of dollars during 
the last five years in New York State alone. 

Under this head it may be stated that on several roads under 
the supervision of W. G. Harger, a careful study of this point 
was made, taking unusual care with the original and final cross- 
sections, the plotting and planimeter work, and it was found that 
for the cases investigated, the ratio of cut to fill varied from 1.15 
in heavy cuts to 1.27 in light skimming work. 

It is the general opinion among engineers of Division 5, N. Y. S. 
Dept. of Highways, that the percentage formerly used (namely 
1.35) is too high. In nearly all cases where the work was at all 
heavy, a large excess of dirt had to be wasted. There have been 
some roads designed on a basis of 1.35 where more dirt was needed, 
but in the author's opinions this was due to discrepancies in the 
field or office work or by allowing the contractor to use the roadbed 
excavation for filler or concrete material. If the soil encountered 
is suitable for such purposes, it is plainly up to the contractor 
to furnish other material for the places excavated. 

The authors believe that the following ratios will be satis- 
factory for ordinary cases : 

Table 32 

Light skimming work, large amount of heavy sod 1.35 

Light skimming work, considerable sod i . 30 

Light skimming work, not much sod i . 25 

Medium work i . 20 

Heavy work i . 15 

Trautwine's earth ratios are correct where earth borrow is 
obtained from a pit. 

Trautwine states that i.o cu. yd. of solid rock, when broken 
up, will make 1.66 to 1.75 cu. yd. of rock fill. 

In this statement he assumes that the fill is made of stone alone 
and that the voids are not filled. In most roadwork, the small 
quantities of rock encountered are dumped in with the earth as 
embankment, and as the voids are all filled with earth it is evident 
that I cu. yd. of rock will make only i cu. yd. of fill; however, 
if a large unmixed stone fill is made, his ratio holds. 

The discussion of these ratios has been carried out to some 
length because we believe it is one of the points that illustrate 
the advantage of careful engineering. Several of the New York 
State plans, the cost of which has ranged from $100 to $200 per 
mile, have been revised with this end in view; the revision costing 
an additional $15 to $30 per mile, with a resultant saving in con- 
struction cost of from $200 to $700 per mile. 

The use of a rolling grade was recommended in the chapter on 
Grades. The designer is -cautioned, however, not to carry this to 
extremes as there are many short, small hummocks which must be 
disregarded if a reasonably good profile is to be obtained. Figure on 
page 509 indicates a proper and improper use of an undulating profile. 



ECONOMICAL GRADE 



509 



Templets. — For the convenience of the designer in drawing the 
shape of the finished road on the cross-sections, a number of 
transparent composition templets are made, cut to proper scale, 
representing the different shaped sections to be used. See Figs. 
129 and 130. 

Economical Grade Line. — On page 26, the most economical 
grading conditions were mentioned. A convenient method of 






Fig. 129. — Transparent templet for use on cross-sections giving 
finished shape of road. 



\^ t TTL 



Fig. 130. — Transparent templet with stone trench cut; saves time 
in drawing in sections for figuring cut and fill. 






.'Undulatfng Orardef Proper Use Saves Etcavati'on and is 
/ at the Same Tirne an easy 

± f?/d/'n^ Profile. 



I'ght ^rade-, hnneces: aryAmc untofFxcavat/c n 



Sta.lO 



I& 



20 



. Hump cf this Kind must be 
f Disregarded 




Illustrating Proper Use of 
Straight and Undulating Grades 



aying a grade line that will approximate these conditions is as 
follows: take the case of determining an economical profile for a 
road from station 11 to station 16, where the grade can be placed 
at any desired elevation (see page 510). Place the adopted templet 
on each cross-section so that the cut will just make the fill (this 
position is estimated) and note the elevation of the center line of the 



Sio 



OFFICE PRACTICE 



Z'IZ£l 



proposed finished road for this position of the templet; mark this 
elevation on the profile for each section between stations ii and i6; 

to connect these points would 
give the most economical grade 
line, but this can rarely be done 
with a resulting smooth profile. 
The adopted grade is obtained 
by drawing in a smooth grade 
line, that averages the elevations 
of these points and varies in ele- 
vation above or below them as 
little as possible. 

The adopted grade elevation 
at each station is then figured, 
the shape of the finished road 
drawn on the cross-sections at 
these elevations, and the exca- 
vation and embankment com- 
puted. If the ratio of cut to fill 
is not correct, the grade is raised 
or lowered slightly to produce the 
desired ratio. This method is 
illustrated in Fig. 131. 

For each stretch of road where 
economy of grading governs the 
profile, this procedure is repeated, 
and for the sections of road where 
other considerations govern, the 
grade is placed at the required 
elevation and the borrow, waste, 
or overhaul figured. 

To obtain a smooth grade line 
vertical curves are used at the 
intersection of the different tan- 
gent rates of grade. Vertical 
curves are not usually used where 
the difference in rates of grade 
is less than J^ per cent. 

For the final plans these vertical 
curve elevations may be com- 
puted by the following formulae, 
but for the trial grade line they 
can be scaled from the profile, 
drawing in the curve by means of 
a regular curve templet, with 
which all modern offices are 
equipped, and in all ordinary 
cases this graphic method serves 
for the final grade line as with 
reasonable care the elevations 



srn£i 



efZ£i 




srzzzi' 



Sir'£Z£l 



9'£2£l 



i'i'Z£l 



are closer than can be constructed. 



VERTICAL CURVES 



SI I 



F. C. FormulcB: 
Formula A, Difference in elevation at Center of Curve. 

d expressed in feet = J^ (Algebraic difference of the tangent grades 
expressed in feet per loo) X (length of 
curve expressed in stations of loo^. 



InfersecHon of 

Tangent Orade^ 



Difference in Elevation — 
of V, C. and Tangent Intersection 




k Length of Curve 

Formula A 



— ->i 



.-'^, 






Formula B 



Formula B. Intermediate differences of Elevations between 
tangent grades and points on vertical curve. 

dt^ 



d' 




StalO 



10+50 



11+00 



11+50 



IZ+00 



Example of Vertical Curve Computation 

It is required to figure the vertical curve elevations for a vertical 
curve 2oo' long between tangent grades of + 2.0% and —3.0% 
meeting at station 11 + 00 at an elevation of 12 10.3. 

First, find the middle correction d: use formula ^. 

d = M (2.0 -(-3.0)) X (2) 
^ = M (5) X (2) = 1% = 1.25' 

Second, determine the corrections di and J2; use formula B, 



SI 2 OFFICE PRACTICE 

^1 = -^ = 1.25 —^ = 1.25 X M = 0.31 foot 
dt = 1.25 „ = 0.31 foot. 

Third, determine the elevation of the tangent grades at 10 + 
50 and 11 + 50. 

Fourth, subtract the V.C. corrections di, d, and d2 from these 
tangent grades at 10 + 50, 11 + 00 and 11 + 50. 

Vertical Curve Elevations 

Sta. 10 + 50 = Tangent Elev. 1209.3 — 0.31 = 1208.99 
" II + 00 = *' " 1210.3 — 1.25 = 1209.05 

" II + 50 = '' " 1208.8 - 0.31 = 1208.49 

The following table, No. 37, is useful for draftsmen in picking 
out the correct curve to use in inking in the vertical curves. This 
table is compiled for a horizontal scale of i'' = 50', and a vertical 
scale of i'' = 10'. For other scales a similar table can be 
constructed. 

Explanation of Table 37. — Suppose it is required to pick out the 
correct curve templet to draw in a vertical curve 300' long between 
two tangent grades having an algebraic difference of 5 per cent, (say 
a + 2.0 per cent, grade and a — 3.oper cent, grade). On the line 
opposite 5.0 in column i representing the algebraic difference of 
rate, pick out the value 24 in the column headed 300' curve; this 
means that a curve having a radius of 24 inches will fit the condi- 
tions. This curve can be found easily from the collection of curve 
templets which have been previously marked with their radii in 
inches. 

The limit of sight due to vertical curves is shown in Table sS. 

Table 38 gives the distance ahead that a driver can see on a 
straight road, assuming that his eye is 6 feet above the road, for 
vertical curves of 200 feet, 150 feet, and 100 feet long between grades 
having a large difference of rate. 

Example. Suppose a plus 5 per cent, grade meets a minus 7 
per cent, grade and that it is desired to put in the minimum length 
curve that will allow a sight ahead of 300 feet. The difference 
in gradient is 5 + 7 = 12 per cent. From Table 38, opposite 
12 per cent., we can readily pick the length required; it will be 
about 170 feet and 200 feet would probably be used. It is rare 
that the sight distance governs in the selection of length of curve. 

Placing the Templets and Planimetering the Areas.--- After 
the trial grade line has been placed the center line elevations of 
the proposed finished road are figured for each point on the profile 
where cross-sections have been taken and the section selected is 
drawn on the original cross-sections at these elevations, using the 
templets mentioned above. 

Because it is comparatively easy to make a mistake of one 
foot or ^ve feet in elevation, the elevation of new grade, as shown 



VERTICAL CURVES 



5^3 



Table 37. Table of Radii for Plotting Vertical Curves 
ON Profiles 



Algebraic 


100' Curve 


200' Curve 


300' Curve 


400' Curve 


Diff. 


Rad. 


Rad. 


Rad. 


Rad. 


I.O 


40 


80 


120 


160 


1.2 


33 


67 


100 


132 


1.4 


29 


57 


85 


116 


1.6 


25 


50 


75 


100 


1.8 


22 


44 


65 


88 


2.0 


20 


40 


60 


80 


2.2 


18 


36 


55 


72 


2.4 


i6i 


33 


50 


66 


2.6 


i5i 


30 


46 


62 


2.8 


14^ 


29 


43 


58 


3-0 


i3t 


27 


40 


54 


3.2 


I2i 


25 


37 


50 


3-4 


12 


23 


35 


48 


3.6 


II 


22 


33 


44 


3-8 


io| 


21 


32 


42 


4.0 


10 


20 


30 


40 


4-5 


9 


18 


27 


36 


5-0 


8 


16 


24 


32 


5-5 


7 


ui 


22 


28 


6.0 


6J 


131 


20 


26 


7.0 


6 


iii 


17 


24 


8.0 


5, 


10 


16 


20 


9.0 


4l 


9 


I3i 


18 


lO.O 


4 


8 


12 


16 


II.O 


3§ 


7 


II 


14^ 


12.0 


3i 


6i 


10 


i3f 


13.0 


3 


6 


9 


12I 


14.0 


3 


5l 


8i 


iij 



Table 38 



Difference in 
Rate of Grades 


Sight Distance for 
2ooft.V. C. 


Sight Distance for 
isoft. V. C. 


Sight Distance for 
100 ft. V. C. 


8% 
10% 
12% 
14% 
16% 


355 feet 
320 " 
290 " 
260 " 


315 feet 
290 " 
260 " 
230 '' 


370 feet 
290 " 
260 " 
230 " 
210 " 



514 OFFICE PRACTICE 

by the position of the templet, should be checked from the profile 
before computing the cuts and fills. 

Because of the small, irregular shape of these areas it is not 
possible to compute them arithmetically and the areas are deter- 
mined by planimeters. Great care must be exercised if the work 
is to be reliable; a double run is made and the second run should 
be twice the first area. A certain limit of error in the second area 
is adopted (see footnote).^ This method is sufficiently accurate for 
preliminary estimating. On final estimate work, where the payment 
for earth excavation depends on the planimeter work, a satisfactory 
method is to have two men, using separate planimeters, compute 
the areas independently without any knowledge of each other's 
result. If the amount of excavation as figured separately varies 
more than 2 per cent., a third run is made. 

The reason that it is difficult to get accurate planimeter re- 
sults is that the work is monotonous, confining, and hard on the 
eyes, and the tendency is toward carelessness unless the men 
know that their work is being checked. 

The temptation is strong to make the second reading equal 
twice the first, and unless some such method is used to check up, 
small errors will be passed over. 

As a matter of interest three miles of planimeter work, checked 
in this manner, was examined to see the average difference in areas, 
where two careful men using different planimeters computed 
their results separately. 

The sections used were plotted 1" = 5'; areas read to nearest 
0.1 sq. ft. 

The average percentage of difference for single areas was 

1. Small areas below 10 sq. ft per cent, of difference 5% 

2. " " ioto30 '' " " " " " 2% 

3. Areas above 30 " " " " " " i % 

However, these differences for single areas compensate, as some 
are above and some below the mean value, and computing the 
two separate results for the three miles gave the following result. 

Percentage differences for work of two men for three miles, 
showing the reduction of error due to compensation. 

1. Small areas below 10 sq. ft per cent, of difference i.o % 

2. '' " 10 to 30 " '' " '' " " 0.5 % 

3. Areas above 30 " ^' " " " " 0.05 % 

The average excavation per mile will run about 3000 cu. yd., 
which means the average area of cut is about 16 sq. ft. 

This comes under the second division and makes the probable 
error of final estimate planimeter work sufficiently close for all 
practical purposes. 

Areas by Measuring the Depth of Cut or Fill at Intervals of One 
Foot Across the Section. — It is often necessary for the field men to 
make a change in grade or alignment, and the following method of 

1 A satisfactory rule has been to allow a difference of 0.4 sq. ft. for areas up 
to 50 sq. ft., and i.o sq. ft. error above 50 sq. ft. 



EARTHWORK 



515 



estimating section areas is convenient when no planimeter is availa- 
ble. The method is illustrated in the figures shown below: 




Measure the depth of the cutting on vertical No. i. Call this 
depth i'. It can be readily seen that this depth is the average 
depth for the first foot of the cross section, and if multiplied by one 
foot equals the area of the first foot of the section. In like manner 
measure the depth of the section on vertical No. 2. This is the 
average depth of the second foot of the section, and multiplied by 
one foot equals the area of the second foot of the section. If the 
sum of the depths i', 2', 3', ^tc, is obtained for the entire width of 
the section it is evident that the sum must equal the area of the 
section. 

This summation can readily be made graphically as shown below 
by marking off on the edge of a piece of paper the successive depths. 



' I ' I ' I Vi — ' 



.35' 

:^ 

End 
Marh 



'eterer 



Reference 
Mark 



Strip of Paper 

Scale the distance from the reference mark to the end mark, using 
the same scale by which the cross section is plotted and the area of 
the section is obtained. This method is as reliable as planimeter 
work, but is necessarily slower. 

Computation of Earthwork. — Earthwork is usually computed 
from the planimeter results by the method of end areas; where 50 ft. 
sections are used the following table is convenient. 

Explanation of Table 39. — Suppose the area of excavation at, 
say, station 22 + 00 is 30.6 sq. ft.; suppose the excavation area at 
station 22 + 50 is 20.1 sq. ft. To get the number of cubic feet of 
excavation from station 22+00 to 22 + 50 add 30.6 + 20.1 = 
50.7. In Table 35 an area of 50.7 gives an excavation quantity 
of 1267.5 cu. ft. Where the normal cross-section interval is 50 ft. 
this table is a great time-saver. 

Table 40 is convenient in changing cubic feet to cubic yards. 

Table 41 is convenient for preliminary estimates, as it gives 
the cubic yards directly for the sum of the end areas in square 
feet. It, however, is not figured exactly and is not suitable for 
final estimate work. 



Si6 



OFFICE PRACTICE 



Table 39. Volume of 50-FT. Sections in Cubic Feet for 
Sum of End Areas 

COMPILED BY J. H. HTJBER, ASSISTANT ENGINEER, BUFFALO, N.Y. 



Sum of 






















End Areas 


0.0 


O.I 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


Sq. Ft. 




























2.5 


5.0 


7.5 


lo.o 


12.5 


15-0 


17.5 


20.0 


22.5 


I 


25.0 


27.5 


30.0 


32.5 


35.0 


37.5 


40.0 


42.5 


45.0 


47-5 


2 


50.0 


52.5 


55.0 


57.5 


60.0 


62.5 


65.0 


67.5 


70.0 


72.5 


3 


75.0 


77.5 


80.0 


82.5 


85.0 


87.5 


90.0 


92.5 


95.0 


97-5 


4 


lOO.O 


102.5 


105.0 


107.5 


IIO.O 


112. 5 


115.0 


117.5 


120.0 


122.S 


S 


125.0 


127.5 


130.0 


132.5 


135.0 


137.5 


140.0 


142.5 


145.0 


147.5 


6 


150.0 


152.5 


155.0 


157.5 


160.0 


162.5 


165.0 


167.5 


170.0 


172.S 


7 


175.0 


177.5 


180.0 


182.5 


185.0 


187.5 


190.0 


192.5 


195.0 


197.5 


8 


200.0 


202.5 


205.0 


207.5 


210.0 


212.5 


215.0 


217-5 


220.0 


222.5 


9 


225.0 


227.5 


230.0 


232.5 


235.0 


237.5 


240.0 


242.5 


245.0 


247.S 


10 


250.0 


252.5 


255.0 


257.5 


260.0 


262.5 


265.0 


267.5 


270.0 


272.5 


II 


275.0 


277.5 


280.0 


282.5 


285.0 


287.5 


290.0 


292.5 


295-0 


297.5 


12 


300.0 


302.5 


305.0 


307.5 


310.0 


312.5 


315-0 


317.5 


320.0 


322.5 


13 


325.0 


327.5 


330.0 


332.5 


335.0 


337-5 


340.0 


342.5 


345-0 


347.5 


14 


350.0 


352.5 


355.0 


357.5 


360.0 


362.5 


365.0 


367.5 


370.0 


372.5 


IS 


375-0 


377.5 


380.0 


382.5 


385.0 


387.5 


390.0 


392.5 


395.0 


397.5 


16 


400.0 


402.5 


405.0 


407.5 


410.0 


412.5 


415.0 


417.5 


420.0 


422.S 


H 


425.0 


427.5 


430.0 


432.5 


435-0 


437-5 


440.0 


442.5 


445-0 


447.5 


18 


450.0 


452.5 


455.0 


457.5 


460.0 


462.5 


465.0 


467-5 


470.0 


472.5 


19 


475.0 


477.5 


480.0 


482.5 


485.0 


487-5 


490.0 


492.5 


495-0 


497-5 


20 


500.0 


502.5 


505.0 


507.5 


510.0 


512.5 


515.0 


S17.5 


520.0 


522.5 


21 


525-0 


527.5 


530.0 


532.5 


535.0 


537.5 


540.0 


542.5 


S4S.O 


547.5 


22 


550.0 


552.5 


555.0 


557.5 


560.0 


562.5 


565.0 


567.5 


570.0 


572.5 


23 


575.0 


577.5 


580.0 


582.5 


585.0 


587.5 


590.0 


592.5 


595.0 


597.5 


24 


600.0 


602.5 


605.0 


607.5 


610.0 


612.5 


615.0 


617.5 


620.0 


622.5 


25 


625.0 


627.5 


630.0 


632.5 


635.0 


637.5 


640.0 


642.S 


645.0 


647.5 


26 


650.0 


652.S 


655.0 


657.5 


660.0 


662.5 


665.0 


(>(>7.S 


670.0 


672.5 


27 


675.0 


677.5 


680.0 


682.5 


685.0 


687.5 


690.0 


692.5 


695.0 


697.5 


28 


700.0 


702.5 


705.0 


707.5 


710.0 


712.5 


715.0 


717-5 


720.0 


722.5 


20 


725.0 


727.5 


730.0 


732.5 


735-0 


737.5 


740.0 


742.5 


745.0 


747.5 


30 


750.0 


752.5 


755.0 


757.5 


760.0 


762.5 


765.0 


767.5 


770.0 


772.5 


31 


775.0 


777.5 


780.0 


782.5 


785.0 


787.5 


790.0 


792.5 


795.0 


797-5 


32 


800.0 


802.5 


805.0 


807.5 


810.0 


812.5 


815.0 


817.5 


820.0 


822.5 


33 


825.0 


827.5 


830.0 


832.5 


835.0 


837-5 


840.0 


842.5 


845.0 


847-5 


34 


850.0 


852.5 


855.0 


857.5 


860.0 


862.5 


865.0 


867.5 


870.0 


872.5 


35 


875.0 


877.5 


880.0 


882.5 


885.0 


887.5 


890.0 


892.5 


895-0 


897.5 


36 


900.0 


902.5 


905.0 


907.5 


910.0 


912.5 


915.0 


917.S 


920.0 


922.5 


H 


925.0 


927.5 


930.0 


932.5 


935-0 


937.5 


940.0 


942.5 


945-0 


947.5 


38 


950.0 


952.5 


955.0 


957-5 


960.0 


962.5 


965.0 


967.5 


970.0 


972.5 


39 


975.0 


977.5 


980.0 


982.5 


985.0 


987.5 


990.0 


992.5 


995-0 


997.5 


40 


lOOO.O 


1002.5 


1005.0 


1007.5 


lOIO.O 


1012.5 


1015.0 


1017.5 


1020.0 


1022.S 


41 


1025.0 


1027.5 


1030.0 


1032.5 


1035.0 


1037.5 


1040.0 


1042.5 


1045.0 


1047-5 


42 


1050.0 


1052.5 


1055.0 


1057.5 


1060.0 


1062.5 


1065.0 


1067.5 


1070.0 


1072.5 


43 


1075.0 


1077.5 


1080.0 


1082.5 


1085.0 


1087.5 


1090.0 


1092.5 


1095.0 


1097-5 


44 


IIOO.O 


II02.5 


II05.0 


1 107.5 


IIIO.O 


1112.5 


iiiS.o 


1117.5 


1 1 20.0 


1122.5 


45 


II25.0 


II27.5 


1 130.0 


1132.5 


1135.0 


1137.5 


1 140.0 


1142.5 


1145.0 


1147.5 


46 


1 150.0 


1152.5 


II5S.O 


I157.S 


1 160.0 


1162.5 


1165.0 


1167.5 


1 1 70.0 


1172.5 


H 


II75.0 


II77.5 


1 180.0 


1182.5 


II85.0 


1187.5 


1 190.0 


1192.5 


1195-0 


1197.5 


48 


1200.0 


1202.5 


1205.0 


1207.5 


I2IO.O 


1212.5 


1215.0 


1217.5 


1220.0 


1222.S 


49 


1225.0 


1227.5 


1230.0 


1232.5 


1235.0 


1237.5 


1240.0 


1242.5 


1245.0 


1247.S 


50 


1250.0 


1252.5 


1255.0 


1257.5 


1260.0 


1262.5 


1265.0 


1267.5 


1270.0 


1272.5 



Note. — For volumes larger than those given, use figures in the table, moving 
decimal point one place to the right and add proportional part. 



EARTHWORK 



517 



Table 39. Volume of 50-FT. Sections in Cubic Feet for 
Sum of End Areas. — Continued 

COMPILED BY J. H. HUBER, ASSISTANT ENGINEER, BUFFALO, N.Y. 



Sum of 






















End Areas 


0.0 


0.1 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


Sq.Ft. 






















50 


1250.0 


1252.5 


1255.0 


1257.5 


1260.0 


1262.5 


1265.0 


1267.5 


1270.0 


1272.5 


51 


I27S-0 


1277.5 


1280.0 


1282.5 


1285.0 


1287.5 


1290.0 


1292.5 


1295.0 


1297.5 


52 


1300.0 


1302.5 


1305.0 


1307.5 


1310.0 


1312.5 


1315.0 


1317.5 


1320.0 


1322.5 


S^ 


1325.0 


1327.5 


1330.0 


1332.5 


1335.0 


1337.5 


1340.0 


1342.5 


1345.0 


1347.5 


54 


1350.0 


1352.5 


1355.0 


1357.5 


1360.0 


1362.5 


1365.0 


1367.5 


1370.0 


1372.5 


55 


1375.0 


1377.5 


1380.0 


1382.5 


1385.0 


1387.5 


1390.0 


1392.5 


1395.0 


1397.S 


56 


1400.0 


1402.5 


1405.0 


1407.5 


1410.0 


1412.5 


141 5.0 


1417.5 


1420.0 


1422.5 


57 


1425.0 


1427.5 


1430.0 


1432.5 


1435.0 


1437.5 


1440.0 


1442.5 


1445.0 


1447.5 


58 


1450.0 


1452.5 


1455.0 


1457.5 


1460.0 


1462.5 


1465.0 


1467.5 


1470.0 


1472.5 


59 


1475.0 


1477.5 


1480.0 


1482.5 


1485.0 


1487.5 


1490.0 


1492.5 


1495.0 


1497.5 


60 


1500.0 


1502.5 


1505.0 


1507.5 


1510.0 


1512.5 


1515.0 


1517.5 


1520.0 


1522.S 


61 


1525.0 


1527.5 


1530.0 


1532.5 


1535.0 


1537.5 


1540.0 


1542.5 


1545.0 


1547.5 


62 


1550.0 


1552.5 


1555.0 


1557.5 


1560.0 


1562.5 


1565.0 


1567.5 


1570.0 


1572.5 


63 


1575.0 


1577.5 


1580.0 


1582.5 


1585.0 


1587.5 


1590.0 


1592.5 


1595.0 


1597.5 


64 


1600.0 


1602.5 


1605.0 


1607.5 


1610.0 


1612.5 


1615.0 


1617.5 


1620.0 


1622.5 


65 


1625.0 


1627.5 


1630.0 


1632.5 


1635.0 


1637.5 


1640.0 


1642.5 


1645.0 


1647.5 


66 


1650.0 


1652.5 


1655.0 


1657.5 


1660.0 


1662.5 


1665.0 


1667.5 


1670.0 


1672.5 


67 


1675.0 


1677.5 


1680.0 


1682.5 


1685.0 


1687.5 


1690.0 


1692.5 


1695.0 


1697.5 


68 


1700.0 


1702.5 


1705.0 


1707.5 


1710.0 


1712.5 


1715.0 


1717.5 


1720.0 


1722.5 


69 


1725.0 


1727.5 


1730.0 


1732.5 


1735.0 


1737.5 


1740.0 


1742.5 


1745.0 


1747.5 


70 


1750.0 


1752.5 


1755.0 


1757.5 


1760.0 


1762.5 


1765.0 


1767.5 


1770.0 


1772.5 


71 


1775.0 


1777.5 


1780.0 


1782.5 


1785.0 


1787.5 


1790.0 


1792.5 


1795.0 


1797.5 


72 


1800.0 


1802.5 


1805.0 


1807.5 


1810.0 


1812.5 


1815.0 


1817.5 


1820.0 


1822.5 


73 


1825.0 


1827.5 


1830.0 


1832.5 


1835.0 


1837.5 


1840.0 


1842.5 


1845.0 


1847.5 


74 


1850.0 


1852.5 


1855.0 


1857.5 


1860.0 


1862.5 


1865.0 


1867.5 


1870.0 


1872.S 


75 


1875.0 


1877.5 


1880.0 


1882.5 


1885.0 


1887.5 


1890.0 


1892.5 


1895.0 


1897.5 


76 


1900.0 


1902.5 


1905.0 


1907.5 


1910.0 


1912.5 


1915.0 


1917.5 


1920.0 


1922.5 


77 


1925.0 


1927.5 


1930.0 


1932.5 


1935.0 


1937.5 


1940.0 


1942.5 


1945.0 


1947.5 


78 


1950.0 


1952.5 


1955.0 


1957.5 


1960.0 


1962.5 


1965.0 


1967.5 


1970.0 


1972.5 


79 


1975.0 


1977.5 


1980.0 


1982.5 


1985.0 


1987.5 


1990.0 


1992.5 


1995.0 


1997.5 


80 


2000.0 


2002.5 


2005.0 


2007.5 


2010.0 


2012.5 


2015.0 


2017.5 


2020.0 


2022.5 


81 


2025.0 


2027.5 


2030.0 


2032.5 


2035.0 


2037.5 


2040.0 


2042.5 


2045.0 


2047.5 


82 


2050.0 


2052.5 


2055.0 


2057.5 


2060.0 


2062.5 


2065.0 


2067.5 


2070.0 


2072.5 


83 


2075.0 


2077.5 


2080.0 


2082.5 


2085.0 


2087.5 


2090.0 


2092.5 


2095.0 


2097.5 


84 


2100.0 


2102.5 


2105.0 


2107.5 


2110.0 


2112.5 


2115.0 


2117.5 


2120.0 


2122.S 


85 


2125.0 


2127.5 


2130.0 


2132.5 


2135.0 


2137.5 


2140.0 


2142.5 


2145.0 


2147.5 


86 


2150.0 


2152.5 


2155.0 


2157.5 


2160.0 


2162.5 


2165.0 


2167.5 


2170.0 


2172.5 


87 


2175.0 


2177.5 


2180.0 


2182.5 


2185.0 


2187.5 


2190.0 


2192.5 


2195.0 


2197.5 


88 


2200.0 


2202.5 


2205.0 


2207.5 


2210.0 


2212.5 


2215.0 


2217.5 


2220.0 


2222.5 


89 


2225.0 


2227.5 


2230.0 


2232.5 


2235.0 


2237.5 


2240.0 


2242.5 


2245.0 


2247.S 


90 


2250.0 


2252.5 


2255.0 


2257.5 


2260.0 


2262.5 


2265.0 


2267.5 


2270.0 


2272.S 


91 


2275.0 


2277.5 


2280.0 


2282.5 


2285.0 


2287.5 


2290.0 


2292.5 


2295.0 


2297.5 


92 


2300.0 


2302.5 


2305.0 


2307.5 


2310.0 


2312.5 


2315.0 


2317.5 


2320.0 


2322.5 


93 


2325.0 


2327.5 


2330.0 


2332.5 


2335.0 


2337.5 


2340.0 


2342.5 


2345.0 


2347.5 


94 


2350.0 


2352.5 


2355.0 


2357.5 


2360.0 


2362.S 


2365.0 


2367.5 


2370.0 


2372.5 


95 


2375.0 


2377.5 


2380.0 


2382.5 


2385.0 


2387.5 


2390.0 


2392.5 


2395.0 


2397.5 


96 


2400.0 


2402.5 


2405.0 


2407.5 


2410.0 


2412.5 


2415.0 


2417.5 


2420.0 


2422.S 


97 


2425.0 


2427.5 


2430.0 


2432.5 


2435.0 


2437.5 


2440.0 


2442.5 


2445.0 


2447.5 


98 


2450.0 


2452.5 


2455.0 


2457.5 


2460.0 


2462.5 


2465.0 


2467.S 


2470.0 


2472.5 


99 


2475.0 


2477.5 


2480.0 


2482.5 


2485.0 


2487.5 


2490.0 


2492.5 


2495.0 


2497.5 


100 


2500.0 


2502.5 


2505.0 


2507.5 


2510.0 


2512.5 


2515.0 


2517.5 


2520.0 


2522.S 



PROPORTIONAL PARt|°* 



.0 O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 
2.5 5.0 7.5 lo.o 12.5 15.0 17.5 20.0 22.5 



SiS OFFICE PRACTICE 

Table 40. Cubic Feet and Cubic Yards 



0-1350 


1350-2700 


2700-4050 


4050- 


-5400 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 
151 


27 


I 


77 


SI 


2,727 


lOI 


77 


54 


2 


1,404 


2 


54 


2 


4,104 


2 


81 


3 


31 


3 


81 


3 


31 


3 


108 


4 


S8 


4 


2,808 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


1,512 


6 


62 


6 


4,212 


6 


89 


7 


39 


7 


89 


7 


39 


7 


216 


8 


66 


8 


2,916 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


10 


1,620 


60 


70 


IIO 


4,320 


160 


97 


I 


47 


I 


97 


I 


47 


I 


324 


2 


74 


2 


3,024 


2 


74 


2 


51 


3 


1,701 


3 


51 


3 


4,401 


3 


78 


4 


28 


4 


78 


4 


28 


4 


405 


5 


55 


5 


3,10s 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


1,809 


7 


59 


7 


4,509 


7 


86 


8 


. 36 


8 


86 


8 


36 


8 


513 


9 


63 


9 


3,213 


9 


63 


9 


40 


20 


90 


70 


40 


120 


90 


170 


67 


I 


1,917 


I 


67 


I 


4,617 


I 


94 


2 


44 


2 


94 


2 


44 


2 


621 


3 


71 


3 


3,321 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


2,025 


5 


75 


5 


4,725 


5 


702 


6 


52 


6 


3.402 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


2,106 


8 


56 


8 


4,806 


8 


83 


9 


33 


9 


83 


9 


33 


9 


810 


30 


60 


80 


3,510 


130 


60 


180 


37 


I 


87 


I 


37 


I 


87 


I 


64 


2 


2,214 


2 


64 


2 


4,914 


2 


91 


3 


41 


3 


91 


3 


41 


3 


918 


4 


68 


4 


3,618 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


2,322 


6 


72 


6 


5,022 


6 


99 


7 


49 


7 


99 


7 


49 


7 


1,026 


8 


76 


8 


3,726 


8 


76 


8 


53 


9 


2,403 


9 


P 


9 


5,103 


9 


80 


40 


30 


90 


80 


140 


30 


190 


1,107 


I 


57 


I 


3,807 


I 


57 


, I 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


2,511 


3 


61 


3 


5,211 


3 


88 


4 


38 


4 


8S 


4 


38 


4 


1,215 


5 


65 


5 


3,915 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


2,619 


7 


69 


7 


5,319 


7 


96 


8 


46 


. 8 


96 


8 


46 


8 


1,323 


9 


73 


9 


4,023 


9 


73 


9 


50 


50 


2,700 


100 


50 


150 


5,400 


200 



EARTHWORK 
Table 40 — Continued 



519 



5400-6750 


6750-8100 


8100-9450 


9450-10,800 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


5,427 


201 


77 


251 


8,127 


301 


77 


351 


54 


2 


6,804 


2 


54 


2 


9,504 


2 


81 


3 


31 


3 


81 


3 


31 


3 


5,508 


4 


58 


4 


8,208 


4 


S8 


4 


35 


5 


85 


5 


35 


5 


8S 


5 


62 


6 


6,912 


6 


62 


6 


9,612 


6 


89 


7 


39 


7 


89 


7 


39 


7 


5,616 


8 


66 


8 


8,316 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


210 


7,020 


260 


70 


310 


9,720 


360 


97 


I 


47 


I 


97 


I 


47 


I 


5,724 


2 


74 


2 


8,424 


2 


74 


2 


51 


3 


7,101 


3 


51 


3 


9,801 


3 


78 


4 


28 


4 


78 


4 


28 


4 


5,805 


5 


55 


5 


8,50s 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


7,209 


7 


59 


7 


9,909 


7 


86 


8 


36 


8 


86 


8 


36 


8 


5,913 


9 


63 


9 


8,613 


9 


63 


9 


40 


220 


90 


270 


40 


320 


90 


370 


67 


I 


7,317 


I 


67 


I 


10,017 


I 


94 


2 


44 


2 


94 


2 


44 


2 


6,021 


3 


71 


3 


8,721 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


7,425 


5_ 


75 


5 


10,125 


5 


6,102 


6 


52 


6 


8,802 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


7,506 


8 


56 


8 


10,206 


8 


83 


9 


33> 


9 


83 


9 


33 . 


9 


6,210 


230 


60 


280 


8,910 


330 


60 


380 


37 


I 


87 


I 


37 


I 


87 


I 


64 


2 


7,614 


2 


64 


2 


10,314 


2 


91 


3 


41 


3 


91 


3 


41 


3 


6,318 


4 


68 


4 


9,018 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


7,722 


6 


72 


6 


10,422 


6 


99 


7 


49 


7 


99 


7 


49 


7 


6,426 


8 


76 


8 


9,126 


8 


76 


8 


53 


9 


7,803 


9 


53 


9 


10,503 


9 


80 


240 


30 


290 


80 


340 


30 


390 


6,507 


I 


57 


I 


9,207 


I 


57 


I 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


7,911 


3 


61 


3 


10,611 


3 


88 


4 


38 


4 


88 


4 


38 


4 


6,615 


5 


65 


5 


9,31s 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


8.019 


7 


69 


7 


10,719 


7 


96 


8 


' 46 


8 


96 


8 


46 


8 


6,723 


9 


73 


9 


9,423 


9 


73 


9 


SO 


250 


8,100 


300 


50 


350 


10,800 


400 



S20 



OFFICE PRACTICE 

Table 40 — Continued 



10,800-12,150 


12,150-13,500 


13,500-14,850 


14,850-16,200 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


10,827 


401 


77 


4SI 


13,527 


501 


177 


551 


54 


2 


12,204 


2 


54 


2 


14,904 


2 


81 


3 


31 


3 


81 


3 


31 


3 


10,908 


4 


58 


4 


13,608 


4 


58 


4 


35 


5 


85 


' 


35 


5 


85 


5 


62 


6 


12,312 


6 


62 


6 


15,012 


6 


89 


7 


39 


7 


89 


7 


39 


7 


11,016 


8 


66 


8 


13,716 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


410 


12,420 


460 


70 


510 


15,120 


560 


97 


I 


47 


I 


97 


1 


47 


I 


11,124 


2 


74 


2 


13,824 


2 


74 


2 


SI 


3 


12,501 


3 


51 


3 


15,201 


3 


78 


4 


28 


4 


78 


4 


28 


4 


11,205 


5 


55 


5 


13,905 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


12,609 


7 


59 


7 


15,309 


7 


86 


8 


36 


8 


86 


8 


36 


8 


11,313 


9 


63 


9 


14,013 


9 


63 


9 


40 


420 


90 


470 


40 


520 


90 


570 


67 


I 


12,717 


I 


67 


I 


15,417 


I 


94 


2 


44 


2 


94 


2 


44 


2 


11,421 


3 


71 


3 


14,121 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


12,825 


5 


75 


5 


15,525 


5 


11,502 


6 


52 


6 


14,202 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


12,906 


8 


56 


8 


15,606 


8 


S3 


9 


33 


9 


S3 


9 


33 


9 


11,610 


430 


60 


480 


14,310 


530 


60 


580 


37 


I 


87 


I 


37 


1 


87 


I 


64 


2 


13,014 


2 


64 


2 


15,714 


2 


91 


3 


41 


3 


91 


3 


41 


3 


11,718 


4 


68 


4 


14,418 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


13,122 


6 


72 


6 


15,822 


6 


99 


7 


49 


7 


99 


7 


49 


7 


11,826 


8 


76 


8 


14,526 


8 


76 


8 


53 


9 


13,203 


9 


53 


9 


15,903 


9 


80 


440 


30 


490 


80 


540 


30 


590 


11,907 


1 


57 


1 


14,607 


1 


57 


I 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


13,311 


3 


61 


3 


16,011 


3 


88 


4 


38 


4 


88 


4 


38 


4 


12,015 


5 


65 


5 


14,715 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


13,419 


7 


69 


7 


16,119 


7 


96 


8 


46 


8 


0^6 


8 


46 


8 


12,123 


9 


73 


9 


14,823 


9 


, 73 


, 9 


50 


450 


13,500 


500 


50 


SSO 


16,200 


600 



EARTHWORK 
Table 40 — Continued 



521 



16,200-17,550 


i7,55<>-i8,900 


18,900-20,250 


20,250- 


21,600 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


16,227 


601 


77 


651 


18,927 


701 


77 


751 


54 


2 


17,604 


2 


?^ 


2 


20,304 


2 


81 


3 


31 


3 


81 


'3 


31 


3 


16,308 


4 


S8 


4 


19,008 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


17,712 


6 


62 


6 


20,412 


6 


89 


7 


39 


7 


89 


7 


§9 


7 


16,416 


8 


66 


8 


19,116 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


610 


17,820 


660 


70 


710 


20,520 


760 


97 


I 


47 


_ I 


97 


I 


47 


I 


16,524 


2 


74 


2 


19,224 


2 


74 


2 


51 


3 


17,901 


3 


51 


3 


20,601 


3 


78 


4 


28 


4 


78 


4 


28 


4 


16,605 


5 


55 


5 


19,305 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


18,009 


7 


59 


7 


20,709 


7 


86 


8 


36 


8 


86 


8 


36 


8 


16,713 


9 


^S 


9 


19,413 


9 


63 


9 


40 


620 


90 


670 


40 


720 


90 


770 


67 


I 


18,117 


I 


67 


I 


20,817 


I 


94 


2 


44 


2 


94 


2 


44 


2 


16,821 


3 


71 


3 


19,521 


3 


71 


3 


48 
75 


^ 


98 
18,225 


4 


48 


4 
5 


98 
20,925 


4 

5 


5 


75 


16,902 


. 6 


52 


6 


19,602 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


18,306 


8 


56 


8 ! 


21,006 


8 


83 


9 


3>3 


9 


^2> 


9 


^^ 


9 


17,010 


630 


60 


680 


19,710 


730 


60 


780 


37 


I 


87 


I 


. 37 


I 


87 


I 


64 


2 


18,414 


2 


64 


2 


21,114 


2 


91 


3 


41 


3 


91 


3 


41 


3 


17,118 


4 


68 


4 


19,818 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


18,522 


6 


72 


6 


21,222 


6 


99 


7 


49 


7 


99 


7 


49 


7 


17,226 


8 


76 


8 


19,926 


8 


76 


8 


53 


9 


18,603 


9 


53 


9 


21,303 


9 


80 


640 


30 


690 


80 


740 


30 


790 


17,307 


I 


57 


I 


20,007 


I 


57 


I 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


18,711 


3 


61 


3 


21,411 


3 


88 


4 


38 


4 


88 


4 


J^ 


4 


17,415 


5 


65 


5 


20,115 


5 


^5 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


18,819 


7 


69 


7 


21,519 


7 


96 


8 


46 


8 


96 


8 


46 


8 


17,523 


9 


73 


9 


20,223 


9 


73 


„ 9 


50 


650 


18,900 


700 


50 


750 


21,600 


800 



522 



OFFICE PRACTICE 

Table 40 — Continued 



2I,6CX>-22,9S0 


22,950-24,300 


24,300-25,650 


25,650-27,000 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


21,627 


801 


77 


851 


24,327 


901 


n 


951 


54 


2 


23,004 


2 


54 


2 


25,704 


2 


81 


3 


31 


3 


81 


3 


31 


3 


21,708 


4 


58 


4 


24,408 


4 


58 


■ 4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


23,112 


6 


62 


6 


25,812 


6 


89 


7 


39 


7 


89 


7 


39 


7 


21,816 


8 


66 


8 


24,516 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


810 


23,220 


860 


70 


910 


25,920 


960 


g7 


I 


47 


I 


97 


I 


47 


I 


21,924 


2 


74 


2 


24,624 


2 


74 


2 


51 


3 


23,301 


3 


51 


3 


26,001 


3 


78 


4 


28 


4 


78 


4 


28 


4 


22,005 


5 


55 


5 


24,705 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


so 


7 


23,409 


7 


59 


7 


26,109 


7 


86 


8 


36 


8 


86 


8 


36 


8 


22,113 


9 


63 


9 


24,813 


9 


63 


9 


40 


820 


90 


870 


40 


920 


90 


970 


67 


I 


23,517 


I 


67 


I 


26,217 


I 


94 


2 


44 


2 


94 


2 


44 


2 


22,221 


3 


71 


3 


24,921 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


23,625 


5 


75 


5 


26,325 


5 


22,302 


6 


52 


6 


25,002 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


23,706 


8 


56 


8 


26,406 


8 


83 


9 


2>Z 


9 


83 


9 


Zl 


9 


22,410 


830 


60 


880 


25,110 


930 


60 


980 


37 


I 


87 


I 


37 


I 


87 


I 


64 


2 


23,814 


2 


64 


2 


26,514 


2 


91 


3 


41 


3 


91 


3 


41 


3 


22,518 


4 


68 


4 


25,218 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


23,922 


6 


72 


6 


26,622 


6 


99 


7 


49 


7 


99 


7 


49 


7 


22,626 


8 


76 


8 


25,326 


8 


76 


8 


53 


9 


24,003 


9 


53 


9 


26,703 


9 


80 


840 


30 


890 


80 


940 


30 


990 


22,707 


I 


57 


I 


25,407 


I 


57 


I 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


24,111 


3 


61 


3 


26,811 


3 


88 


4 


38 


4 


88 


4 


38 


4 


22,815 


• 5 


65 


5 


25,515 


S 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


24,219 


7 


69 


7 


26,919 


7 


96 


8 


46 


8 


96 


8 


46 


8 


22,923 


„ 9 


73 


9 


25,623 


9 


73 


9 


SO 


850 


24,300 


900 


50 


9SO 


27,000 


1000 



EARTHWORK 

Table 40 — Continued 



523 



27,000-28,350 


28,350-29,700 


29,700-31,050 


31,050-32,400 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


27,027 


lOOI 


77 


1051 


29,727 


IIOI 


77 


1151 


54 


2 


28,404 


2 


54 


2 


31,104 


2 


81 


3 


31 


3 


81 


3 


31 


3 


27,108 


4 


58 


4 


29,808 


4 


S8 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


28,512 


6 


62 


6 


31,212 


6 


89 


7 


39 


7 


89 


7 


39 


7 


27,216 


8 


66 


8 


29,916 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


lOIO 


28,620 


1060 


70 


mo 


31,320 


1160 


97 


I 


47- 


I 


97 


I 


47 


I 


27,324 


2 


74 


2 


30,024 


2 


74 


2 


51 


3 


28,701 


3 


51 


3 


31,401 


3 


78 


4 


28 


4 


78 


4 


28 


4 


27,405 


5 


55 


5 


30,105 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


28,809 


7 


59 


7 


31,509 


7 


86 


8 


36 


8 


86 


8 


36 


8 


27,513 


9 


63 


9 


30,213 


9 


63 


9 


40 


1020 


90 


1070 


40 


1120 


90 


1170 


67 


I 


28,917 


I 


67 


I 


31,617 


X 


94 


2 


44 


4 


94 


2 


44 


2 


27,621 


3 


71 


3 


30,321 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 
27,702 


5 
6 


29,025 
52 


5 


75 


5 
6 


31,725 
52 


5 
6 


6 


30,402 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


29,106 


8 


56 


8 


31,806 


8 


83 


9 


33 


9 


83 


9 


33 


9 


27,810 


1030 


60 


1080 


30,510 


1130 


60 


1 180 


37 


I 


87 


I 


37 


I 


87 


I 


64 


2 


29,214 


2 


64 


2 


31,914 


2 


91 


3 


41 


3 


91 


3 


41 


3 


27,918 


4 


68 


4 


30,618 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


29,322 


6 


72 


6 


32,022 


6 


99 


7 


49 


.7 


99 


7 


49 


7 


28,026 


8 


76 


8 


30,726 


8 


76 


8 


53 


9 


29,403 


9 


53 


9 


32,103 


9 


80 


1040 


30 


1090 


80 


1 140 


30 


1 190 


28,107 


I 


57 


I 


30,807 


I 


57 


I 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


29,511 


3 


61 


3 


32,211 


3 


88 


4 


38 


4 


88 


4 


1^ 


4 


28,215 


5 


65 


5 


30,915 


5 


65 


5 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


29,619 


7 


69 


7 


32,319 


7 


96 


8 


46 


8 


96 


8 


46 


8 


28,323 


9 


73 


9 


31,023 


9 


73 


9 


50 


1050 


29,700 


IIOO 


50 


1150 


32,400 


1200 



524 



OFFICE PRACTICE 

Table 40 — Continued 



32,400-33,750 


33,750-35,100 


35,100-36,450 

1 


36,450-37.800 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


32,427 


1 201 


77 


1251 


35,127 


1301 


77 


1351 


54 


2 


33,804 


2 


54 


2 


36,504 


2 


81 


3 


31 


3 


81 


3 


31 


3 


32,508 


4 


58 


4 


35,208 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


S 


62 


6 


33,912 


6 


62 


6 


36,612 


6 


89 


7 


39 


7 


89 


7 


39 


7 


32,616 


8 


66 


8 


35,316 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


1210 


34,020 


1260 


70 


1310 


36,720 


1360 


97 


I 


47 


I 


97 


I 


47 


X 


32,724 


2 


74 


2 


35,424 


2 


74 


2 


51 


3 


34,101 


3 


51 


3 


36,801 


3 


78 


4 


28 


4 


78 


4 


28 


4 


32,805 


5 


55 


5 


35,505 


5 


55 


S 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


34,209 


7 


59 


7 


36,909 


7 


86 


8 


36 


8 


86 


8 


36 


8 


32,913 


9 


63 


9 


35,613 


9 


63 


9 


40 


1220 


90 


1270 


40 


1320 


90 


1370 


67 


I 


34,317 


I 


67 


I 


37,017 


I 


94 


2 


44 


2 


94 


2 


44 


2 


33,021 


3 


71 


3 


35,721 


3 


71 


3 


48 


4 


98 


4 


48 


4 


98 


4 


75 


5 


34,425 


5 


75 


5 


37,125 


5 


33,102 


6 


52 


6 


35,802 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


34,506 


8 


56 


8 


37,206 


8 


83 


9 


33 


9 


83 


9 


33 


9 


33,210 


1230 


60 


1280 


35,910 


1330 


60 


1380 


37 


1 


87 


I 


37 


I 


87 


I 


64 


2 


34,614 


2 


64 


2 


37,314 


2 


91 


3 


41 


3 


91 


3 


41 


3 


33,318 


4 


68 


4 


36,018 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


34,722 


6 


72 


6 


37,422 


6 


99 


7 


49 


7 


99 


7 


49 


7 


33,426 


8 


76 


8 


36,126 


8 


76 


8 


53 


9 


34,803 


9 


53 


9 


37,503 


9 


80 


1240 


30 


1290 


80 


1340 


30 


1390 


33,507 


I 


57 


I 


36,207 


I 


57 


I 


!•* 


2 


84 


2 


34 


2 


84 


2 


61 


3 


34,911 


3 


6i 


3 


37,611 


3 


88 


4 


38 


4 


88 


4 


38 


4 


33,615 


5 


65 


5 


36,31s 


5 


65 


S 


i^ 


6 


92 


6 


42 


6 


92 


6 


69 


7 


35,019 


7 


69 


7 


37,719 


7 


96 


8 


46 


8 


96 


8 


46 


8 


33,723 


9 


73 


9 


36,423 


9 


J^ 


9 


50 


1250 


35,100 


1300 


50 


1350 


37,800 


1400 



EARTHWORK 
Table 40 — Concluded 



525 



37,800-39,150 


39,150-40,500 


40,500-41,850 


41,850-43,200 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


Feet 


Yds. 


37,827 


1401 


1 77 


I4SI 


40,527 


1501 


rr 


ISSI 


54 


2 


39,204 


2 


54 


2 


41,904 


a 


81 


3 


31 


3 


8i 


3 


31 


3 


37,908 


4 


58 


4 


40,608 


4 


58 


4 


35 


5 


85 


5 


35 


5 


85 


5 


62 


6 


39,312 


6 


62 


6 


42,012 


6 


89 


7 


39 


7 


89 


7 


39 


7 


38,016 


8 


66 


8 


40,716 


8 


66 


8 


43 


9 


93 


9 


43 


9 


93 


9 


70 


1410 


39,420 


1460 


70 


1510 


42,120 


1560 '■ 


97 


I 


47 


I 


97 


I 


47 


I 


38,124 


2 


74 


2 


40,824 


2 


74 


2 


51 


3 


39,501 


3 


51 


3 


42,201 


3 


78 


4 


28 


4 


78 


4 


28 


4 


38,205 


5 


55 


5 


40,905 


5 


55 


5 


32 


6 


82 


6 


32 


6 


82 


6 


59 


7 


39,609 


7 


59 


7 


42,309 


7 


86 


8 


36 


8 


86 


8 


36 


8 


38,313 


9 


63 


9 


41,013 


9 


63 


9 


40 


1420 


90 


1470 


40 


1520 


90 


1570 


67 


I 


39,717 


I 


67 


1 


42,417 


I 


« 94 


2 


44 


2 


94 


2 


44 


2 


38,421 


3 


71 


3 


41,121 


3 


71 


3 


48 


4 


98 


4^ 


48 


4 


98 


4 


75 


5 


39,825 


5 


75 


5 


42,525 


5 


38,502 


6 


52 


6 


41,202 


6 


52 


6 


29 


7 


79 


7 


29 


7 


79 


7 


56 


8 


39.906 


8 


l^ 


8 


42,606 


8 


83 


9 


33 


9 


83 


9 


33 


9 


38,610 


1430 


60 


1480 


41,310 


1530 


60 


1580 


37 


I 


87 


I 


37 


I 


87 


I 


64 


2 


40,014 


2 


64 


2 


42,714 


2 


91 


3 


41 


3 


91 


3 


41 


3 


38,718 


4 


68 


4 


41,418 


4 


68 


4 


45 


5 


95 


5 


45 


5 


95 


5 


72 


6 


40,122 


6 


72 


6 


42,822 


6 


99 


7 


49 


7 


99 


7 


49 


7 


38,826 


8 


76 


8 


41,526 


8 


76 


8 


F 


9 


40,203 


9 


53 


9 


42,903 


9 


80 


1440 


30 


1490 


80 


1540 


30 


1590 


38,907 


I 


57 


I 


41,607 


I 


57 


1 


34 


2 


84 


2 


34 


2 


84 


2 


61 


3 


40,311 


3 


61 


3 


43,011 


3 


88 


4 


1^ 


4 


88 


4 


38 


4 


39,015 


5 


65 


5 


41,715 


5 


65 


S 


42 


6 


92 


6 


42 


6 


92 


6 


69 


7 


40,419 


7 


69 


7 


43,119 


7 


96 


8 


46 


8 


96 


8 


46 


8 


39,123 


9 


73 


9 


41,823 


9 


73 


9 


50 


1450 


40,500 


1500 


50 


1550 


43,200 


1600 



526 



OFFICE PRACTICE 



Table 41. New York State Department of Highways. 

Earthwork Computation Tables 

Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



2 


3 


4 


5 


6 


7 


8 


9 


10 


II 


12 


13 


14 


D'uble 
Areas 


0.0 


0.1 


0.1 


0.1 


0.1 


0.1 


0.1 


0.2 


0.2 


0.2 


0.2 


0.2 


0.3 I .0 


0.0 


0.1 


0.1 


0.1 


0.1 


0.2 


0.2 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 2 


O.I 


0.1 


0.1 


0.1 


0.2 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 


0.3 


0.4 4 


O.I 


0.1 


0.1 


0.1 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 


0.4 


0.4 


0.4 6 


O.I 


O.I 


0.1 


0.2 


0.2 


0.2 


0.3 


0.3 


0.3 


0.4 


0.4 


0.4 


0.5 


8 


O.l 


0.1 


0.1 


0.2 


0.2 


0.3 


0.3 


0.3 


0.4 


0.4 


0.4 


O.S 


o.S 


2.0 


O.l 


0.1 


0.2 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.4 


O.S 


o.S 


0.6 


2 


0.1 


0.1 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.4 


O.S 


O.S 


0.6 


0.6 


4 


0.1 


0.1 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


o.S 


O.S 


0.6 


0.6 


0.7 


6 


0.1 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


0.5 


o.S 


0.6 


0.6 


0.7 


0.7 


8 


0.1 


0.2 


0.2 


0.3 


0.3 


0.4 


0.4 


o.S 


0.6 


0.6 


0.7 


0.7 


0.8 


3.0 


O.I 


0.2 


0.2 


0.3 


0.4 


0.4 


o.S 


0.5 


0.6 


0.7 


0.7 


0.8 


0.8 


2 


0.1 


0.2 


0.3 


0.3 


0.4 


0.4 


o.S 


0.6 


0.6 


0.7 


0.8 


0.8 


0.9 


4 


0.1 


0.2 


0.3 


0.3 


0.4 


o.S 


o.S 


0.6 


0.7 


°-7 


0.8 


0.9 


0.9 


6 


O.I 


0.2 


0.3 


0.4 


0.4 


o.S 


0.6 


0.6 


0.7 


0.8 


0.8 


0.9 


I.O 


8 


O.I 


0.2 


0.3 


0.4 


0.4 


o.S 


0.6 


0.7 


^'l 


0.8 


0.9 


I.O 


I.O 


4.0 


0.2 


0.2 


0.3 


0.4 


o.S 


o.S 


0.6 


0.7 


0.8 


0.9 


0.9 


I.O 


l.I 


2 


0.2 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


°'l 


0.8 


0.9 


I.O 


I.I 


l.I 


4 


0.2 


0.3 


0.3 


0.4 


o.S 


0.6 


0.7 


0.8 


0.9 


0.9 


I.O 


l.I 


1.2 


6 


0.2 


0.3 


0.4 


0.4 


o.S 


0.6 


0.7 


0.8 


0.9 


I.O 


I.I 


1.2 


1.2 


8 


0.2 


0.3 


0.4 


o.S 


0.6 


0.6 


0.7 


0.8 


0.9 


I.O 


I.I 


1.2 


1.3 


S.o 


0.2 


0.3 


0.4 


o.S 


0.6 


0.7 


0.8 


0.9 


I.O 


1.1 


1.2 


1.3 


1-3 


2 


0.2 


0.3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


I.O 


I.I 


1.2 


1.3 


1.4 


4 


0.2 


0.3 


0.4 


o.S 


0.6 


0.7 


0.8 


0.9 


I.O 


I.I 


1.2 


1-3 


I.S 


6 


0.2 


0.3 


0.4 


o.S 


0.6 


0.8 


0.9 


I.O 


I.I 


1.2 


1.3 


1.4 


I.S 


8 


0.2 


0.3 


0.4 


0.6 


0.7 


0.8 


0.9 


I.O 


I.I 


1.2 


1.3 


1.4 


1.6 


6.0 


a2 


0.3 


o.S 


0.6 


0.7 


0.8 


0.9 


I.I 


I.I 


1.3 


1.4 


I.S 


1.6 


2 


0.2 


0.4 


o.S 


0.6 


0.7 


0.8 


0.9 


I.I 


1.2 


1.3 


1.4 


I.S 


1.7 


4 


0.2 


0.4 


0.5 


0.6 


0.7 


0.9 


I.O 


I.I 


1.2 


1.3 


I.S 


1.6 


1.7 


6 


0.3 


0.4 


o.S 


0.6 


0.7 


0.9 


I.O 


I.I 


1.3 


1.4 


I-S 


1.6 


1.8 


8 


0.3 


0.4 


o.S 


0.6 


0.8 


0.9 


I.O 


1.2 


1-3 


1.4 


1.6 


1-7 


1.8 


7.0 


0.3 


0.4 


0.5 


0.7 


0.8 


0.9 


I.I 


1.2 


1.3 


i-S 


1.6 


1.7 


1.9 


2 


0.3 


0.4 


O.S 


0.7 


0.8 


I.O 


I.I 


1.2 


1.4 


I.S 


1.6 


1.8 


1.9 


4 


0.3 


0.4 


0.6 


0.7 


0.8 


I.O 


l.I 


1-3 


1.4 


I.S 


1.7 


1.8 


2.0 


6 


0.3 


0.4 


0.6 


0.7 


0.9 


I.O 


1.2 


1-3 


1.4 


1.6 


1.7 


1.9 


2.0 


8 


0.3 


0.4 


0.6 


0.7 


0.9 


I.O 


1.2 


1.3 


I.S 


1.6 


1.8 


1.9 


2.1 


8.0 


0.3 


0.5 


0.6 


0.8 


0.9 


I.I 


1.2 


1.4 


I.S 


1.7 


1.8 


2.0 


2.1 


2 


0.3 


0.5 


0.6 


0.8 


0.9 


I.I 


1.2 


1.4 


1.6 


1.7 


1.9 


2.0 


2.2 


4 


0.3 


0.5 


0.6 


0.8 


I.O 


I.I 


1.3 


1.4 


1.6 


1.7 


1.9 


2.1 


2.2 


6 


0.3 


0.5 


0.7 


0.8 


I.O 


I.I 


1.3 


I.S 


1.6 


1.8 


2.0 


2.1 


2.3 


8 


0.3 


0.5 


0.7 


0.9 


I.O 


1.2 


1-3 


1.5 


1.7 


1.8 


2.0 


2.2 


2-3 


9.0 


0.3 


0.5 


0.7 


0.9 


I.O 


1.2 


1.4 


I.S 


1.7 


1.9 


2.0 


2.2 


2.4 


2 


0.3 


0.5 


0.7 


0.9 


1.0 


1.2 


1.4 


1.6 


1.7 


1.9 


2.1 


2.3 


2.4 


4 


0.4. 


0.5 


0.7 


0.9 


I.I 


1.2 


1.4 


1.6 


1.8 


2.0 


2.1 


2.3 


2.S 


6 


0.4 


0.5 


0.7 


0.9 


I.I 


1.3 


I.S 


1.6 


1.8 


2.0 


2.2 


2.4 


2.5 


8 


0.4 


0.6 


0.7 


0.9 


I.I 


1.3 


i-S 


1.7 


1.9 


2.0 


2.2 


2.4 


2.6 


lO.O 


0.4 


0.6 


0.8 


I.O 


1.2 


1.4 


1.6 


1.8 


1.9 


2.1 


2.3 


2.S 


2.7 


S 


0.4 


0.6 


0.8 


I.O 


1.2 


1.4 


1.6 


1.8 


2.0 


2.2 


2.4 


2.6 


2.9 


II.O 


0.4 


0.6 


0.9 


I.I 


1.3 


I.S 


1.7 


1.9 


2.1 


2-3 


2.S 


2.8 


3.0 


5 


0.4 


0.7 


0.9 


I.I 


1.3 


1.6 


1.8 


2.0 


2.2 


2.4 


2.7 


2.9 


3.1 


12.0 


O.S 


0.7 


0.9 


1.2 


1.4 


1.6 


1.9 


2.1 


2.3 


2.S 


2.8 


3.0 


3.2 


" S 


o.S 


0.7 


I.O 


1.2 


i.S 


1-7 


2-0 


2.2 


2.4 


2.6 


2.9 


3.1 


3.4 


13.0 


0.5 


0.7 


I.O 


1.3 


i.S 


1.8 


2.0 


2.3 


2.S 


2.7 


3.0 


3-3 


3-5 


3 


o.S 


0.8 


1.0 


1-3 


1.6 


1.8 


2.1 


2.3 


2.6 


2.8 


3.1 


3.4 


3.6, 


14.0 



EARTHWORK 



527 



Table 41 — Continued 
Distance Horizontal Sum or Areas Vertical Quantities in Cubic Yards 



15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


D'uble 
Areas 


0.3 


0.3 


0.3 


0.3 


0.4 


0.4 


0.4 


0.4 


0.4 


0.4 


0.5 


0.5 


0.5 


1.0 


0.3 


0.4 


0.4 


0.4 


0.4 


0.4 


0.5 


0.5 


0.5 


0.5 


0.6 


0.6 


0.6 


2 


0.4 


0.4 


0.4 


0.5 


0.5 


0.5 


0-5 


0.6 


0.6 


0.6 


0.6 


0.7 


0.7 


4 


0.4 


0.5 


0.5 


0.5 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.7 


0.8 


0.8 


6 


0.5 


0.5 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.8 


0.8 


0.8 


0.9 


0.9 


8 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.8 


0.8 


0.9 


0.9 


0.9 


1.0 


1.0 


2.0 


0.6 


0.7 


0.7 


0.7 


0.8 


0.8 


0.9 


0.9 


0.9 


1.0 


1.0 


I.I 


I.I 


2 


0.7 


0.7 


0.8 


0.8 


0.8 


0.9 


0.9 


1.0 


1.0 


I.I 


I.I 


1.2 


1.2 


4 


0.7 


0.8 


0.8 


0.9 


0.9 


1.0 


1.0 


I.I 


I.I 


1.2 


1.2 


1.3 


1-3 


6 


0.8 


0.8 


0.9 


1.0 


1.0 


1.0 


I.I 


I.I 


1.2 


1.2 


1-3 


1.4 


1.4 


8 


0.8 


0.9 


0.9 


l.Q 


I.I 


l.i 


1.2 


1.2 


1-3 


1.3 


1.4 


1.4 


1.5 


3.0 


0.9 


0.9 


1.0 


I.I 


I.I 


1.2 


1.2 


1-3 


1.4 


1.4 


1-5 


1.5 


1.6 


2 


0.9 


1.0 


l.i 


I.I 


1.2 


1.3 


1.3 


1.4 


1.4 


1.5 


1.6 


1.6 


1.7 


4 


I.O 


I.I 


I.I 


1.2 


1-3 


1.3 


1.4 


1-5 


1.5 


1.6 


1.7 


1.7 


1.8 


6 


I.I 


I.I 


. 1.2 


1.3 


1.3 


1.4 


1.5 


1.5 


1.6 


1.7 


1.8 


1.8 


1.9 


8 


I.I 


1.2 


1.3 


1.3 


1.4 


^•| 


1.6 


1.6 


1.7 


1.8 


1.9 


1.9 


2.0 


4.0 


1.2 


1.2 


1.3 


1.4 


1.5 


1.6 


1.6 


1.7 


1.8 


1.9 


1.9 


2.0 


2.1 


2 


1.2 


1.3 


1.4 


1-5 


1-5 


1.6 


1.7 


1.8 


1.9 


2.0 


2.0 


2.1 


2.2 


4 


1.3 


1.4 


1.4 


1-5 


1.6 


1.7 


1.8 


1.9 


2.0 


2.0 


2.1 


2.2 


2.3 


6 


1.3 


1.4 


i.S 


1.6 


1.7 


1.8 


1.8 


2.0 


2.0 


2.1 


2.2 


2.3 


2.4 


8 


1.4 


1.5 


1.6 


1-7 


1.8 


1.9 


1.9 


2.0 


2.1 


2.2 


2.3 


2.4 


2.5 


S.o 


1.4 


1.5 


1.6 


1.7 


1.8 


1.9 


2.0 


2.1 


2.2 


2.3 


2.4 


2.5 


2.6 


2 


1.5 


1.6 


^•7 


1.8 


1.9 


2.0 


2.1 


2.2 


2.3 


2.4 


2.5 


2.6 


2.7 


4 


1.6 


1-7 


1.8 


1.9 


2.0 


2.1 


2.2 


2.3 


2.4 


2.5 


2.6 


2.7 


2.8 


6 


1.6 


1.7 


1.8 


2.0 


2.0 


2.2 


2.3 


2.4 


2.5 


2.6 


2.7 


2.8 


2.9 


8 


1.7 


1.8 


1.9 


2.0 


2.1 


2.2 


2.3 


2.4 


2.6 


2.7 


2.8 


2.9 


3.0 


6.0 


1.7 


1.8 


1.9 


2.1 


2.2 


2.3 


T.4 


2.5 


2.6 


2.8 


2.9 


3-0 


3.1 


2 


1.8 


1.9 


2.0 


2.1 


2.2 


2.4 


2.5 


2.6 


2.7 


2.8 


3-0 


3-1 


3.2 


4 


1.8 


2.0 


2.1 


2.2 


2.3 


2.5 


2.6 


2.7 


2.8 


2.9 


3-1 


3.2 


3.3 


6 


1.9 


2.0 


2.1 


2.3 


2.4 


2.5 


2.6 


2.8 


2.9 


3.0 


3-2 


Z-2> 


3.4 


8 


1.9 


2.1 


2.2 


2.3 


2.5 


2.6 


2.7 


2.9 


3.0 


3.1 


3-2 


3-4 


3.5 


7.0 


2.0 


2.1 


2.3 


2.4 


2.5 


2.7 


2.8 


2.9 


3.1 


3.2 


3.3 


3-5 


3.6 


2 


2.1 


2.2 


2.3 


2.5 


2.6 


2.7 


2.9 


3.0 


3-1 


3.3 


3-4 


3.6 


3.7 


4 


2.1 


2.3 


2.4 


2.5 


2.7 


2.8 


3.0 


3.1 


3-2 


3-4 


3-5 


3.7 


3.8 


6 


2.2 


2.3 


2.5 


2.6 


2.7 


2.9 


3-0 


3.2 


Z'Z 


3.5 


3.6 


3.8 


3-9 


8 


2.2 


2.4 


^•| 


2.7 


2.8 


3.0 


3-1 


3.3 


3.4 


3-5 


3.7 


3.9 


4.0 


8.0 


2.3 


2.4 


2.6 


2.7 


2.9 


3.0 


3.2 


Z-Z 


3-5 


3-6 


3.8 


4.C 


4.1 


2 


2.3 


2.5 


2.6 


2.8 


2.9 


3-1 


3-3 


3.4 


3.6 


3-7 


3.9 


4.1 


4.2 


4 


2.4 


2.S 


2.7 


2.9 


3.0 


3^ 


3.3 


3-5 


H 


3.8 


4.0 


4.1 


4.3 


6 


2.4 


2.6 


2.8 


2.9 


3.1 


3.3 


3.4 


3.6 


3.8 


3.9 


4.1 


4.2 


4.4 


8 


2.5 


2.7 


2.8 


3.0 


3-2 


2>'Z 


3.5 


H 


3.8 


4.0 


4.2 


4.3 


4-5 


9.0 


2.6 


H 


2.9 


3.1 


3-2 


3.4 


3-6 


3.8 


3.9 


4.1 


4.3 


4.4 


4.6 


2 


2.6 


2.8 


3.0 


3-1 


3.3 


H 


3-7 


3.8 


4.0 


4.2 


4.4 


4.5 


4-7 


4 


2.7 


2.8 


3.0 


3.2 


3-4 


3.6 


H 


3-9 


4.1 


4-3 


4.5 


4.6 


4.8 


6 


2.7 


2.9 


3.1 


3-3 


3.4 


3.6 


3.8 


4.0 


4.2 


4.4 


4.5 


4.7 


4.9 


8 


2.8 


3.0 


3.1 


3.3 


3.5 


3.7 


3-9 


4.1 


4.2 


4.4 


4.6 


4.8 


5-0 


100 


2.9 


3.1 


3.3 


3-5 


3.7 


3.9 


4.1 


4.3 


4-5 


4.6 


4.9 


5-0 


5-3 


5 


3.1 


Z'Z 


3.5 


H 


3.9 


4.1 


4-3 


4.5 


4.7 


4.9 


5.1 


5.3 


5-5 


II.O 


3.2 


3-4 


H 


3.8 


4.0 


4.3 


4.5 


4.7 


4.9 


S-i 


5-3 


5-5 


5-7 


5 


3.3 


3.6 


3-8 


4.0 


4.2 


4.5 


4.7 


4.9 


5.1 


5.3 


5.5 


5.8 


6.0 


12.0 


3-5 


3.7 


3.9 


4.2 


4-4 


4.6 


4.9 


S.I 


5-3 


5.5 


5.8 


6.0 


6.2 


5 


3.6 


3.8 


4.1 


4.3 


4.6 


4.8 


5.0 


5.3 


5-5 


5.8 


6.0 


6.3 


6.5 


I3-0 


3.7 


4.0 


4.2 


4.5 


4.8 


5-0 


5.2 


5.5 


5.8 


6.0 


(>?, 


6.5 


6.7 


5 


3.0 


4.1 


4.4 


4.7 


4.9 


S'2 


5.4 


5.7 


6.0 


6.2 


6.5 


6.7 


7-°l 


14.0 



528 



OFFICE PRACTICE 



Table 41 — Continued 
Distance Horizontal Sum of Areas Vermcal Quantities in Cubic Yards 



28 


29 


30 


31 


32 


33 


34 


35 


36 


37 


38 


39 


40 


jD'uble 
Areas 


0.5 


0.5 


0.6 


0.6 


0.6 


0.6 


0.6 


0.7 


0.7 


0.7 


0.7 


0.7 


0.7 


1.0 


0.6 


0.6 


0.7 


0.7 


0.7 


0.7 


0.8 


0.8 


0.8 


* 0.8 


0.9 


0.9 


0.9 


2 


0.7 


0.8 


0.8 


0.8 


0.8 


0.9 


0.9 


0.9 


0.9 


1.0 


1.0 


1.0 


1.0 


4 


0.8 


0.9 


0.9 


0.9 


1.0 


1.0 


1.0 


1.0 


I.I 


I.I 


I.I 


1.2 


1.2 


6 


0.9 


1.0 


1.0 


1.0 


I.I 


I.I 


1.2 


1.2 


1.2 


1.2 


1.3 


1.3 


1.3 


8 


I.O 


i.i 


I.I 


1.2 


1.2 


1.2 


1.3 


1.3 


1.3 


1.4 


1.4 


1.5 


1.5 


2.0 


I.I 


1.2 


1.2 


1.3 


1.3 


1-3 


1.4 


1.4 


1.5 


1.5 


1.6 


1.6 


1.6 


2 


1.2 


1.3 


1.3 


1.4 


1.4 


1.5 


1.5 


1.6 


1.6 


1.7 


1.7 


1.7 


1.8 


4 


1.4 


1.4 


1.4 


1.5 


1.5 


1.6 


1.6 


1.7 


1.7 


1.8 


1.8 


1.9 


1.9 


6 


1.5 


1-5 


1.6 


1.6 


1.7 


1-7 


1.8 


1.8 


1.9 


1.9 


2.0 


2.0 


2.1 


8 


1.6 


1.6 


1.7 


1.7 


1.8 


1.8 


1.9 


1.9 


2.0 


2.1 


2.1 


2.2 


2.2 


3.0 


^'l 


1-7 


1.8 


1.8 


1.9 


2.0 


2.0 


2.1 


2.1 


2.2 


2.3 


2-i 


2.4 


2 


1.8 


1.8 


1.9 


2.0 


2.0 


2.1 


2.1 


2.2 


2.3 


2.3 


2.4 


2.5 


2.5 


4 


1.9 


1.9 


2.0 


2.1 


2.1 


2.2 


2.3 


2.3 


2.4 


2.5 


2.5 


2.6 


2.7 


6 


2.0 


2.0 


2.1 


2.2 


2.2> 


2.3 


2.4 


2.5 


2.5 


2.6 


2.7 


2.8 


2.8 


8 


2.1 


2.2 


2.2 


2.3 


2.4 


2.5 


2.5 


2.6 


H 


2.7 


2.8 


2.9 


3.0 


4.0 


2.2 


2.3 


2-Z 


2.4 


2.5 


2.6 


2.6 


2.7 


2.8 


2.9 


3.0 


3.0 


3.1 


2 


2.3 


2.4 


2.4 


2.5 


2.6 


H 


2.8 


2.9 


2.9 


3.0 


3.1 


3.2 


Z-2> 


.4 


2.4 


2.5 


2.6 


2.6 


2.7 


2.8 


2.9 


3.0 


3-1 


3.2 


3-'2. 


2,-3> 


3-4 


6 


2-5 


2.6 


2.7 


2.8 


2.8 


2.9 


3.0 


3-1 


3.2 


3.3 


3.4 


3.5 


3.6 


8 


2.6 


H 


2.8 


2.9 


3.0 


3.1 


3.1 


3-2 


S-Z 


3.4 


3.5 


3-5 


3.7 


5.0 


2.7 


2.8 


2.9 


3.0 


3-1 


3.2 


Z-i 


3.4 


3.5 


3.6 


3-7 


3.8 


3.9 


2 


2.8 


2.9 


3.0 


3.1 


3.2 


3.3 


3.4 


3.5 


Z-(> 


H 


3.8 


3.9 


4.0 


4 


2.9 


3.0 


3.1 


3.2 


2>-2, 


3.4 


3-5 


3-6 


3.7 


3.8 


3.9 


4.1 


4.2 


6 


3-0 


3-1 


3.2 


3.3 


3.4 


3.6 


3.7 


3.8 


3-9 


4.0 


4.1 


4.2 


4.3 


8 


3.1 


3.2 


3.3 


3.5 


3.6 


3.7 


3.8 


3.9 


4.0 


4.1 


4.2 


4.3 


4-5 


6.0 


3-2 


3-3 


3.5 


3.6 


3-7 


3.8 


3.9 


4.0 


4.1 


4.3 


4-4 


4.5 


4.6 


2 


3-3 


3-4 


3.6 


H 


3.8 


3.9 


4.0 


4.2 


4-3 


4.4 


4.5 


4.6 


4.7 


4 


3-4 


3-5 


H 


3.8 


3.9 


4.0 


4.2 


4.3 


4.4 


4.5 


4.7 


4.8 


4.9 


6 


3-5 


3.7 


3.8 


3.9 


4.0 


4.2 


4.3 


4.4 


4.5 


4.7 


4.8 


4.9 


5.0 


8 


3.6 


3.8 


3.9 


4.0 


4.2 


4-3 


4.4 


4.5 


4-7 


4.8 


4.9 


5.1 


5.2 


7.0 


H 


3.9 


4.0 


4.1 


4.3 


4.4 


4-5 


4.7 


4.8 


4.9 


5-1 


5.2 


5.3 


2 


3.8 


4.0 


4.1 


4.3 


4.4 


4.5 


4-7 


4.8 


4.9 


5.1 


5.2 


5.4 


5.5 


4 


3.9 


4.1 


4.2 


4.4 


4.5 


4-7 


4.8 


4.9 


5.1 


5.2 


5.4 


5-5 


5.6 


6 


4.0 


4.2 


4.3 


4-5 


4.6 


4.8 


4-9 


5.1 


5.2 


5.4 


5.5 


5.6 


5.8 


8 


4.2 


4.3 


4.4 


4.6 


4.7 


4.9 


5.0 


5.2 


5.3 


5-5 


s-(> 


5.8 


5.9 


8.0 


4.3 


4.4 


4.6 


H 


4.9 


5.0 


5.2 


5.3 


5.5 


5.6 


5.8 


5.9 


6.1 


2 


4.4 


4.5 


4.7 


4.8 


5.0 


5-1 


S'2, 


5.5 


5-6 


5.8 


5-9 


6.1 


6.2 


4 


4-5 


4.6 


4.8 


4.9 


5-1 


5-3 


5.4 


5.6 


5.7 


5.9 


6.1 


6.2 


6.4 


6 


4.6 


4.7 


4.9 


5.1 


5.2 


5.4 


5.5 


5.7 


5-9 


6.0 


6.2 


6.4 


6.5 


8 


4.7 


4.8 


5.0 


5.2 


5.3 


5.5 


5.7 


5.8 


6.0 


6.2 


6.3 


6.5 


6.7 


9.0 


4.8 


4.9 


5.1 


5.3 


5-5 


5.6 


5.8 


6.0 


6.1 


6.3 


6.5 


6.7 


6.8 
7.0 


2 


4.9 


5-1 


5.2 


5-4 


5.6 


5.8 


5.9 


6.1 


(>-2> 


6.5 


6.6 


6.8 


4 


5.0 


S.2 


5.3 


5.5 


5.7 


5.9 


6.1 


6.2 


6.4 


6.6 


6.8 


6.9 


7.1 


6 


S-i 


5-3 


5-5 


5-6 


5.8 


6.0 


6.2 


6.3 


^•5 


6.7 


6.9 


7.1 


7.3 


8 


5.2 


5.4 


H 


i^ 


5-9 


6.1 


e.s 


6.5 


6.7 


6.9 


7.0 


7.2 


\i 


lO.O 


5-4 


5.6 


5.8 


6.0 


6.2 


6.4 


6.6 


6.8 


7.0 


7.2 


7.4 


7.6 


5 


5.7 


5.9 


6.1 


6.3 


6.5 


6.7 


6.9 


7.1 


7.3 


7.5 


7.8 


7.9 


8.2 


II.O 


6.0 


6.2 


6.4 


6.6 


6.8 


7.0 


7.2 


7.5 


.7.7 


7.9 


8.1 


8.3 


8.5 


5 


6.2 


6.4 


6.7 


7.0 


7.1 


7-3 


7.6 


7.8 


8.0 


8.2 


8.5 


8.7 


8.9 


12.0 


i'^ 


6.7 


7.0 


7.2 


7-4 


7.7 


7.^ 


8.1 


8.3 


8.6 


8.8 


9.0 


9.3I 


5 


6.7 


7.0 


7.2 


7.5 


7-7 


8.0 


8.2 


8.4 


8.7 


8.9 


9.2 


9.4 


9.6 


13.0 


7.0 


7.3 


7-5 


7.8 


8.0 


5-1 


8.5 


8.8 


9.0 


9.5 


9-5 


9.8 


lO.O 


5 


7.2 


7.5 


7.8 


8.0 


8.3 


8.6 


8.8 


9.1 


9.3 


9.6 


9.8 


lO.I 


10.4' 


14.0 



EARTHWORK 



529 



Table 41 — Continued 

Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



41 


42 


43 


44 


45 


46 


47 


48 


49 


SO 


75 


100 




ip'uble 
Areas 


'0.8 


0.8 


0.8 


0.8 


0.8 


0.9 


0.9 


0.9 


0.9 


0.9 


1.4 


1-9 




1.0 


0.9 


0.9 


I.O 


1.0 


1.0 


1.0 


1.0 


I.I 


I.I 


I.I 


1.6 


2.2 




2 


I.I 


I.I 


I.I 


I.I 


1.2 


1.2 


1.2 


1.2 


1.3 


1.3 


1.9 


2.6 




4 


1.2 


1.2 


1-3 


1.3 


1.3 


1.4 


1.4 


1.4 


1.5 


1.5 


2.2 


3.0 




6 


1.4 


1.4 


1.4 


1.5 


1.5 


1.5 


1.6 


1.6 


1.6 


1.7 


2.5 


3.3 




8 


i.S 


1.6 


1.6 


1.6 


1.7 


1.7 


1.7 


1.8 


1.8 


1.8 


2.8 


3.7 




2.0 


1.7 


1.7 


1.8 


1.8 


1.8 


1.9 


1.9 


2.0 


2.0 


2.0 


3.1 


4.1 




2 


1.8 


1.9 


1.9 


'2.0 


2.0 


2.0 


2.1 


2.1 


2.2 


2.2 


3.3 


4.4 




4 


2.0 


2.0 


2.1 


2.1 


2.2 


2.2 


2.3 


2.3 


2.4 


2.4 


3.6 


4.8 




6 


2.1 


2.2 


2.2 


2.3 


2.3 


2.4 


2.4 


2.5 


2.5 


2.6 


3.9 


5.2 




8 


2.3 


2.3 


2.4 


2.4 


2.5 


2.6 


2.6 


2.7 


2.7 


2.8 


4.2 


5.6 




3.0 


2.4 


2.5 


2.6 


2.6 


2.7 


2.7 


2.8 


2.9 


2.9 


3.0 


4.4 


5.9 




2 


'2.6 


2.6 


2.7 


2.8 


2.S 


2.9 


3.0 


3-0 


3-1 


3.2 


4-7 


6.3 




4 


2.7 


2.8 


2.9 


2.9 


3.0 


3.1 


3.1 


3.2 


3.3 


3-3 


5-0 


6.7 




6 


2.9 


3.0 


3.0 


3.1 


3.2 


3.2 


3-3 


3.4 


3.5 


3.5 


5.3 


7.0 




8 


3.0 


3.1 


3.2 


3-3 


3-3 


3.4 


3-5 


3-6 


3.6 


3.7 


5.6 


7.4 




4.0 


3.2 


3-3 


3.4 


3-4 


3-5 


3.6 


H 


3-7 


3.8 


3-9 


5.9 


2-9 




2 


3.3 


3.4 


3-5 


3-5 


H 


3.8 


3.8 


3.9 


4.0 


4.1 


6.1 


8.2 




4 


3-5 


3.6 


3.7 


3.8 


3.8 


3-9 


4.0 


4.1 


4.2 


4-3 


6.4 


?-5 




6 


3.6 


3.7 


3.8 


3.9 


4.0 


4.1 


4.2 


4-3 


4.4 


4.5 


6.7 


8.9 




8 


3.8 


3-9 


4.0 


4-1 


4.2 


4.3 


4.4 


4.5 


4-5 


4.6 


7.0 


9.3 




5.0 


4.0 


4.1 


4.1 


4.2 


4-3 


4.4 


4.5 


4.6 


4.7 


4.8 


7.2 


9.7 




2 


4.1 


4.2 


4.3 


4.4 


4.5 


4.6 


4-7 


4.8 


4.9 


5.0 


7.5 


10.0 




4 


4-3 


4.4 


4-5 


4.6 


4.7 


4.8 


4.9 


5-0 


5.1 


5-2 


7.8 


0.4 




6 


4.4 


4.5 


4.6 


4-7 


4.8 


4.9 


5-0 


5.1 


5.2 


5.4 


8.1 


0.8 




8 


4.6 


H 


4.8 


4.9 


5-0 


5-1 


5^ 


5-3 


5.4 


5-6 


H 


I.I 




6.0 


4-7 


4.8 


4.9 


5-0 


5.2 


5-3 


5.4 


5-5 


5-^ 


5.7 


8.6 


1.5 




2 


: 4-Q 


5.0 


5.1 


5-2 


5.3 


5.5 


5-6 


5-7 


5.8 


5-9 


8.9 


1.8 




4 


5-0 


5.1 


5-2 


5-4 


5.5 


5-^ 


5.7 


5.9 


6.0 


6.1 


9.2 


2.2 




6 


5.2 


5-3 


5.4 


5-5 


5.7 


5.8 


5.9 


6.0 


6.2 


6.3 


9-5 


2.6 




8 


5-3 


5-4 


5.6 


5-7 


5.8 


5.9 


6.1 


6.2 


6.3 


6.5 


9.7 


3.0 




7.0 


5--5 


5.6 


5-7 


5.8 


6.0 


6.1 


6.3 


6.4 


6.5 


6.7 


lO.O 


3-4 




2 


5-6 


5-7 


5.9 


6.0 


6.2 


6.3 


6.4 


6.6 


6.7 


6.8 


0.3 


3.7 




4 


5.8 


5-9 


6.0 


6.2 


6.3 


6.5 


6.6 


6.7 


6.9 


7.0 


0.6 


4.1 




6 


5.9 


6.1 


6.2 


6.3 


6.5 


6.6 


6.8 


6.9 


7-1 


7.2 


0.8 


4.4 




8 


6.1 


6.2 


0.4 


6.5 


6.7 


6.8 


7.0 


7.1 


7.2 


7.4 


II.I 


4.8 




8.0 


6.2 


6.3 


6.5 


6.6 


6.8 


7.0 


7.1 


7-3 


7.4 


7.6 


1.4 


5.2 




2 


6.4 


6.5 


6.7 


6.8 


7.0 


7.2 


7.3 


7.5 


7.6 


7.8 


1.7 


5.6 




4 


6.5 


6.7 


6.8 


7.0 


7.2 


7.3 


7.5 


7.7 


7.8 


8.0 


2.0 


6.0 




6 


6.7 


6.9 


,7.0 


7.2 


7.3 


7.5 


7-7 


7.8 


8.0 


8.2 


2.2 


6.3 




8 


6.8 


7.0 


7.2 


7-3 


7.5 


7.7 


7.8 


8.0 


8.2 


8.3 


12. 5 


6.6 




9.0 


7.0 


7.2 


,7.3 


7.5 


7.7 


7.8 


8.0 


8.2 


S'3 


8.5 


2.8 


7.0 




2 


7.1 


7.3 


7.5 


7.7 


7.8 


8.0 


8.2 


8.4 


8.5 


8.7 


3.1 


7.4 




4 


7.3 


7.5 


7.6 


7.8 


8.0 


8.2 


8.3 


8.5 


8.7 


8.9 


3-3 


7.8 




6 


7.4 


7-6 


.7.8 


8.0 


8.2 


Sa 


8.5 


8.7 


8.9 


9.1 


3.6 


8.2 




8 


7.6 


l-^ 


8.0 


8.1 


8.3 


8-5 


8.7 


8.9 


9.1 


9-3 


13.9 


8.5 




lO.O 


8.0 


8.2 


8.4 


8.6 


8.8 


8.9 


9.1 


9-3 


9.5 


9-7 


4.6 


9.5 




5 


?-^ 


§•5 


8.7 


8.9 


9.2 


9.4 


9.6 


9.8 


lO.O 


10.2 


5-3 


20.3 




II.O 


,8.7 


8.9 


9.1 


9.4 


9.6 


9.8 


lO.O 


10.2 


0.4 


0.7 


6.0 


1.3 




5 


91 


9.3 


9.5 


9.8 


lO.O 


10.2 


0.4 


0.7 


0.9 


I.I 


6.7 


2.2 




12.0 


9.5 


.9.7 


lO.O 


10.2 


10.4 


10.6 


10.8 


ii.i 


11.4 


11.6 


17.4 


23.2 




5 


9.9 


lO.I 


0.4 


0.6 


0.8 


I.I 


1-3 


1.6 


1.8 


2.1 


8.0 


4.1 




13.0 


' T0.3 


0.5 


0.8 


1.0 


1.3 


1.5 


1.8 


2.0 


2.3 


2.5 


8.8 


5.0 




S 


0.6 


0.9 


1.2 


1.4 


1.7 


1.9 


2.2 


2.4 


2.7 


3.0 


9.4 


6.0 




14.0 



S30 



OFFICE PRACTICE 



Table 41 — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 











6 




8 














D'uble 


2 


3 


4 


5 


7 


9 


10 


II 


12 


13 


14 


Areas 


o.S 


0.8 


I.I 


1-3 


1.6 


1.9 


2.1 


2.4 


2.7 


3.0 


3.2 


3.5 


3.8 


14.S 


0.6 


0.8 


I.I 


1.4 


1-7 


2.0 


2.2 


2.5 


2.8 


3-1 


3-3 


3.6 


3.9 


15.0 


0.6 


0.9 


1.2 


1.5 


1.7 


2.0 


2.3 


2.6 


2.9 


3.2 


3.4 


3-7 


4.0 


5 


0.6 


0.9 


1.2 


1.5 


1.8 


2.1 


2.4 


2.7 


3.0 


3.3 


3.6 


3.8 


4.1 


16.0 


0.6 


0.9 


1.2 


1.5 


1.8 


2. 1 


2.4 


2.7 


3.1 


3-4 


3.7 


4.0 


4.3 


5 


0.6 


0.9 


1-3 


1.6 


1.9 


2.2 


2.5 


2.8 


3-1 


3.5 


3.8 


4.1 


4.4 


17.0 


0.6 


I.O 


1.3 


1.6 


2.0 


2.3 


2.6 


2.9 


3.2 


3.6 


3.9 


4.2 


4.5 


5 


0.7 


I.O 


1.3 


1.7 


2.0 


2.3 


2.7 


3.0 


S-Z 


H 


4.0 


4-3 


4.7 


18.0 


0.7 


I.O 


1.4 


1.7 


2.1 


2.4 


2.7 


3.1 


3.4 


3-8 


4.1 


4.4 


4.8 


5 


0.7 


I.I 


1.4 


1.8 


2.1 


2.5 


2.8 


3.2 


3-5 


3.9 


4.2 


4.6 


4.9 


19.0 


0.7 


I.I 


1.4 


1.8 


2.2 


2.5 


2.9 


3.2 


3.6 


4.0 


4-3 


4-2 


5.0 


5 


0.7 


I.I 


1.5 


1.9 


2.2 


2.6 


3.0 


3-3 


3.7 


4.1 


4.4 


4.8 


5.2 


20.0 


0.8 


1.2 


1.6 


2.0 


2.3 


2.7 


3.1 


3.5 


3-9 


4.3 


4.7 


5.1 


5.4 


I 


0.8 


1.2 


1.6 


2.0 


2.4 


2.8 


2,-2> 


H 


4.1 


4.5 


4.9 


5-3 


V 


2 


o.g 


1-3 


1-7 


2.1 


2.6 


3.0 


3.4 


3.8 


4.3 


4.7 


S-i 


5-5 


6.0 


3 


0.9 


1-3 


1.8 


2.2 


2.7 


3.1 


3.6 


4.0 


4.4 


4.9 


5.3 


5.8 


6.2 


4 


0.9 


1.4 


1.9 


2.3 


2.8 


3-2 


3.7 


4.2 


4.6 


5.1 


5.6 


6.0 


6.5 


25.0 


I.O 


1.4 


1.9 


2.4 


2.9 


3.4 


3.9 


4-3 


4.8 


5.3 


5.8 


6.3 


6.7 
7.0 


6 


I.O 


i.S 


2.0 


2.5 


30 


3-5 


4.0 


4.5 


5.0 


5.5 


6.0 


6.5 


7 


1.0 


1.6 


2.1 


2.6 


3.1 


3.6 


4.2 


4.7 


5-2 


5.7 


6.2 


6.7 


7.3 


8 


I.I 


1.6 


2.1 


2.7 


3.2 


3.8 


4.3 


4.8 


5-4 


5-9 


6.4 


7.0 


7.5 


9 


1. 1 


1-7 


2.2 


2.8 


3-3 


3-9 


4.4 


5.0 


5.5 


6.1 


6.7 


7.2 


7.8 


30.0 


1.2 


H 


2.3 


2.9 


3-4 


4.0 


4.6 


5-2 


V 


6.3 


6.9 


7.5 


8.0 
8.3 


I 


1.2 


1.8 


2.4 


3.0 


3.6 


4.2 


4-7 


5.3 


6.0 


6.5 


7-1 


7.7 


2 


1.2 


1.8 


2.4 


3.0 


3-7 


4.3 


4.9 


5.5 


6.1 


6.7 


7.3 


8.0 


8.6 


3 


1-3 


1.9 


2.5 


3-1 


I3.8 


4.4 


5.0 


5.7 


6., 


6.9 


7.5 


8.2 


8.8 


4 


1.3 


1-9 


2.6 


3-2 


3-9 


4.5 


5-2 


5-8 


6.5 


7.1 


V^ 


8.4 


9.1 


35-0 


1.3 


2.0 


2.7 


3.3 


4.0 


4-7 


5-3 


6.0 


6.7 


7.3 


8.0 


8.7 


9.3 


6 


1.4 


2.1 


2.7 


3.4 


4.1 


4.8 


5-5 


6.2 


6.9 


7.5 


8.2 


8.9 


9.6 


7 


1.4 


2.1 


2.8 


3-5 


4.2 


4.9 


5.6 


6.3 


7.0 


7.7 


8.4 


9.2 


9.8 


8 


1.4 


2.2 


2.9 


3.6 


4.3 


5.0 


5.8 


6.5 


7.2 


^9 


8.7 


9.4 


16. 1 


9 


1.5 


2.2 


3-0 


3.7 


4.4 


5.2 


5-9 


^A 


7.4 


8.1 


8.9 


9.7 


0.4 


40.0 


H 


2.3 


3.0 


3.8 


4.5 


5.3 


6.1 


6.8 


7.6 


8.3 


9.1 


9.0 


0.6 


I 


1.6 


2.3 


31 


3-9 


4-7 


5-4 


6.2 


7.0 


7.8 


8.'; 


9-3 


10. 1 


0.9 


2 


1.6 


2.4 


3.2 


4.0 


4.8 


5.6 


6.4 


7.2 


8.0 


8.8 


9.6 


10.4 


1.2 


3 


1.6 


2.4 


3-3 


4.1 


4.9 


H 


6.5 


7.3 


8.2 


9.0 


9.8 


10.6 


11.4 


4 


1.7 


2.5 


3-3 


4.2 


5-0 


5-8 


6.7 


7.5 


l'^ 


9.2 


lO.O 


0.9 


1.7 


45.0 


1.7 


2.6 


3.4 


4.3 


5-1 


6.0 


6.8 


7-7 


8.5 


9.4 


0.2 


I.I 


1.9! 


6 


1.7 


2.6 


3.5 


4.3 


5-2 


6.1 


7.0 


7.8 


8.7 


9.6 


0.5 


^•^ 


2.2' 


7 


1.8 


2.7 


3.6 


4.4 


5-3 


6.2 


7.1 


8.0 


8.9 


9.8 


0.7 


1.6 


2.4 


8 


1.8 


2.7 


3.6 


4-5 


5.4 


6.4 


7.3 


8.2 


9.1 


lO.O 


10.9 


11.8 


12.7, 


9 


1.8 


2.8 


3-7 


4.6 


^•t 


6.5 


7-4 


l-^ 


9-3 


0.2 


I.I 


2.1 


2.9 


50.0 


1.9 


2.9 


3-9 


4.8 


5.8 


6.7 


7-7 


8.7 


9.6 


0.6 


1.6 


2.5 


3.5 


2 


2.0 


3-0 


4.0 


S-o 


6.0 


7.0 


8.0 


9.0 


lO.O 


I.O 


2.0 


3.0 


4.0 


4 


2.1 


3-1 


4.1 


5.2 


6.2 


7-3 


8.3 


9.3 


0.4 


1.4 


2.5 


3-5 


'•'1 


6 


2.2 


3-2 


4-3 


5.4 


6.4 


7-5 


8.6 


9.7 


10.7 


II.8 


12.9 


13.9 


1 
15.0 


8 


2.2 


3-2> 


4.J 


5-5 


6.7 


7.8 


8.9 


lO.O 


I.I 


2.2 


3.3 


4.4 


5.5 


60.0 


2.3 


3.4 


4.6 


5.7 


6.9 


8.0 


9.2 


0.3 


1-5 


2.6 


3.8 


4.9 


6.1 


2 


2.4 


3.6 


4.7 


5.9 


7.1 


8.3 


9-5 


0.7 


1.9 


3.0 


4.2 


5-4 


6.6 


4 


2.4 


3-7 


4.9 


6.1 


7.3 


8.6 


9.8 


I.O 


2.2 


3-4 


4.7 


5.9 


7.1 


6 


2-5 


38 


5-0 


(>-3 


7.5 


8.8 


lO.I 


II.4 


12.6 


13.8 


15.1 


16.4 


17.6, 


8 


2.6 


3.9 


5.2 


6.5 


l-^ 


9.1 


10.4 


1.7 


3.0 


4-3 


5-5 


6.8 


8.2 


70.0 


2.7 


4.0 


5.3 


6.7 


8.0 


9.3 


10.7 


2.0 


3.4 


4.7 


6.0 


7.3 


8.6; 


2 


2.7 


4.1 


5.5 


6.9 


8.2 


9.6 


10.9 


2.3 


3-7 


5.1 


6.5 


7.8 


9.2; 


4 



EARTHWORK 



53T- 



Table 41 — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


D'uble 
Areas 


4.0 


4.3 


4.6 


4.8 


S-i 


5.4 


^i 


5.9 


6.2 


^•5 


6.7 


6.9 


7.3 


14.5 


4.2 


4.4 


4-7 


5-0 


5.3 


5.6 


5-8 


6.1 


6.4 


6.7 


6.9 


7.2 


7.5 


15.0 


4.3 


4.6 


4.9 


5-2 


5-5 


5.7 


6.0 


6.3 


6.6 


6.9 


7.2 


7.5 


7.8 


5 


4.5 


4.7 


5-0 


5-3 


H 


5.9 


6.2 


6.5 


6.8 


7.1 


7.4 


7.7 


8.0 


16.0 


4.6 


4.9 


5.2 


5-5 


5.8 


6.1 


6.4 


6.7 


7.0 


7.3 


7-7 


8.0 


8.3 


5 


4-7 


5-1 


5.3 


5.7 


6.0 


6.3 


6.6 


6.9 


7.2 


7.6 


7.9 


8.2 


8.5 


17.0 


4.9 


5.2 


5-5 


5.8 


6.2 


6.5 


6.8 


7.1 


7.5 


l-^ 


8.1 


8.4 


8.8 


5 


5-0 


5-3 


5-7 


6.0 


6.3 


6.7 


7.0 


7-4 


7-7 


8.0 


8.4 


8.7 


9.0 


18.0 


51 


5-5 


5.8 


6.2 


5-5 


6.8 


7.2 


7-5 


l-^ 


8.2 


8.6 


8.9 


9-3 


5 


5-3 


5.6 


6.0 


6.3 


6.7 


7.0 


7.4 


7-7 


8.1 


8.5 


8.8 


9.2 


9.5 


19.0 


5-4 


5-8 


6.1 


6.5 


6.8 


7.2 


7.6 


r^ 


?-^ 


8.7 


9.0 


9.4 


9.8 


5 


5.6 


5-9 


6.3 


6.7 


7.0 


7-4 


7.8 


8.2 


8.5 


8.9 


9.3 


9.7 


lO.O 


20.0 


5.8 


6.2 


6.6 


7.0 


7.4 


7.8 


8.2 


8.6 


9.0 


9-3 


9-7 


lO.I 


0.5 


I 


6.1 


6.5 


6.9 


7.3 


7.7 


8.1 


8.6 


9.0 


9.4 


9.8 


10.2 


0.6 


1.0 


2 


6.4 


6.8 


7.2 


7.7 


8.1 


8.5 


8.9 


9.4 


9.8 


10.2 


0.6 


I.I 


1-5 


3 


6.7 


7.1 


7.5 


8.0 


8.4 


8.9 


9-3 


9.8 


10.2 


10.7 


II. I 


11.6 


12.0 


4 


7.0 


7.4 


7.9 


8.3 


8.8 


9.3 


9-7 


10.2 


0.7 


I.I 


1.6 


2.1 


2.5 


25.0 


7.2 


7.7 


8.2 


8.7 


9.1 


9.6 


lO.I 


0.6 


I.I 


1.6 


2.0 


2.5 


3-0 


6 


7-5 


8.0 


8.5 


9.0 


9-5 


lO.O 


0.5 


1.0 


1-5 


2.0 


2.5 


3.0 


3.5 


7 


7.8 


8.3 


8.8 


9-3 


9.8 


0.4 


0.9 


1.4 


1.9 


2.4 


3.0 


3-5 


4.0 


8 


8.1 


8.6 


9.1 


9.7 


10.2 


10.7 


11.3 


11.8 


12.4 


12.9 


13.4 


13.9 


14-5 


9 


8.3 


8.9 


9.5 


lO.O 


0.5 


I.I 


1-7 


2.2 


2.8 


3-3 


3.9 


4.5 


5.0 


30.0 


8.6 


9.2 


9.8 


0.3 


0.9 


i.S 


2.1 


2.6 


3.2 


3.8 


4-3 


4.9 


5-5 


I 


8.9 


9-5 


lO.I 


0.7 


1.3 


1.9 


2.5 


30 


3.6 


4.2 


4.8 


5.4 


6.0 


2 


9.2 


9.8 


0.4 


1.0 


1.6 


2.2 


2.9 


3-5 


4.1 


4.7 


5-3 


5.9 


6.5 


3 


9-5 


lO.I 


10.7 


11.3 


12.0 


12.6 


^3-3 


13-9 


14-5 


15.1 


15.7 


16.4 


17.0 


4 


9-7 


0.3 


I.O 


1-7 


2.3 


2.9 


3.6 


4-3 


4.9 


5-5 


6.2 


6.9 


7-5 


35.0 


lo.o 


0.7 


1.3 


2.0 


2.7 


3-3 


4.0 


4.7 


5-3 


6.0 


6.7 


7.3 


8.0 


6 


0.3 


0.9 


1.7 


2.3 


3.0 


3.7 


4.4 


5-1 


5.8 


5-5 


'^■l 


7.8 


8.5 


7 


0.6 


1.3 


2.0 


2.7 


3.4 


4.1 


4.8 


5.5 


6.2 


6.9 


7.6 


8.3 


9.0 


8 


10.8 


11.6 


12.3 


13.0 


13.7 


14.5 


15.2 


159 


16.6 


17.3 


18.1 


18.8 


19.5 


9 


1.2 


1.8 


2.6 


3-3 


4.1 


4.8 


5.6 


6.3 


7-1 


l-^ 


8.5 


9.3 


20.0 


40.0 


1.4 


2.1 


2.9 


3-7 


4.4 


5-2 


6.0 


6.7 


7-5 


8.1 


9.0 


9.7 


0.5 


I 


1.7 


2.4 


3-2 


4.0 


4.8 


5-5 


6.3 


7.1 


7-9 


8.7 


9.4 


20.2 


1.0 


2 


2.0 


2.7 


3-5 


4-3 


5.1 


5-9 


6.7 


7.5 


8.3 


9.1 


9.9 


0.7 


1.5 


3 


12.2 


13.1 


13.9 


14-7 


15.5 


16.3 


17.1 


17.9 


18.7 


19.6 


20.4 


21.2 


22.0 


4 


2.5 


3.3 


4.2 


S-o 


5.9 


6.7 


7.5 


8.3 


9.2 


20.0 


0.8 


1-7 


2.5 


4S.O 


2.9 


3.6 


4-5 


5-3 


6.2 


7.1 


^9 


8.7 


9.6 


0.4 


1.3 


2.2 


3-0 


6 


3.1 


3-9 


4.9 


5.7 


5-5 


^1 


8.3 


9.1 


20.1 


0.9 


1.7 


2.6 


3-5 


7 


3.4 


4.2 


5.1 


6.0 


6.9 


7.8 


8.7 


9.6 


0.4 


1.3 


2.2 


3.2 


4.0 


8 


13.6 


14-5 


15-4 


16.3 


17.2 


18.1 


19.1 


20.0 


20.8 


21.8 


22.7 


23.6 


24.5 


9 


3.9 


4.8 


5-7 


6.7 


7.6 


8.5 


9-5 


0.4 


1.3 


2.3 


3.2 


4.1 


5.0 


50.0 


4.4 


5-4 


6.4 


7.4 


8.3 


9-3 


20.2 


1.2 


2.2 


3.2 


4.1 


§-^ 


6.0 


2 


5-0 


6.0 


7.0 


8.0 


9.0 


20.0 


1.0 


2.0 


3.0 


4.0 


5.0 


6.0 


y.d 


4 


5.6 


6.6 


7.6 


8.7 


9-7 


0.8 


1.8 


2.8 


3.8 


4.8 


5.9 


6.9 


8.0 


6 


16.1 


17.2 


18.3 


19.4 


20.4 


21.5 


22.5 


23.6 


24.7 


25.7 


26.8 


27.8 


29.0 


8 


6.7 


7.8 


8.9 


20.0 


i.i 


2.2 


3-4 


4.4 


5.6 


6.6 


7.7 


8.8 


30.0 


60.0 


7.2 


8.4 


9-5 


0.7 


1.8 


2.9 


4.2 


5.2 


6.4 


l^ 


8.7 


9.8 


1.0 


2 


7.8 


8.9 


20.2 


1.4 


2.5 


3.7 


4.9 


6.0 


7-3 


8.4 


9.6 


30.8 


2.0' 


4 


8.4 


9.5 


0.8 


2.0 


3.2 


4.4 


5-7 


6.8 


8.1 


9.3 


30.6 


1.7 


3.0 


6 


18.9 


20.1 


21.4 


22.6 


23.9 


25.2 


26.4 


27.7 


29.0 


30.2 


31.5 


32.7 


34.0 


8 


9.4 


0.7 


2.0 


3.4 


4.6 


^•9 


7.2 


8.5 


9.8 


I.I 


2.4 


3-7 


54 
6.d 


70.0 


20.0 


1.4 


2.6 


4.0 


5-4 


6.7 


8.0 


9.4 


30-7 


2.0 


3-4 4.6' 


2 


06 


1.8 


3.3 


4.7 


6.0 


7.4 


8.8 


30*2 


1.5 


2.9 


4.3! 5.7I 


7.o| 


4 



532 



OFFICE PRACTICE 



Table 41 — Contimced 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



28 


29 


30 


31 


32 


33 


34 


35 


36 


37 


38 


39 


40 


D'uble 
Areas 


7-S 


7.8 


8.1 


8.3 


8.6 


8.8 


9.1 


9.4 


9.7 


9.9I 10.2 


lO.e 


10.7 14.5 


7.8 


8.0 


8.3 


8.6 


8.g 


9.2 


9-5 


9-7 


lO.C 


10.5 


o.e 


O.9I I.] 


15.0 


8.0 


8.3 


8.6 


8.9 


9.2 


9-5 


9.8 


lO.C 


0.3 


o.e 


o.s 


1.2 


i-i 


5 


S.3 


8.6 


8.9 


9.2 


9-5 


9.8 


10. 1 


0.3 


0.7 


I.C 


1.3 


l.t 


i.dl 16.0 1 


8.5 


8.9 


9.2 


9.5 


9.8 


10. 1 


0.4 


0.7 


1.0 


1.3 


i.e 


l.9| 2.2 


' 


8.8 


9.1 


9.4 


9.8 


lO.I 


10.4 


10.7 


II.O 


11.3 


I.I.7 


11.5 


12.3 


12.6 17.0 


9.1 


9.4 


9.7 


10. 1 


0.4 


0.7 


1.0 


1-3 


1.7 


2.0 


2.3 


2.6 


3.c^ 5 1 


9-3 


9.7 


lO.O 


0.3 


0.7 


1.0 


1.3 


1-7 


2.0 


2.3 


2.7 


3.C 


3.3 


18.0 


9.6 


9.9 


0.3 


0.6 


I.O 


1.3 


1-7 


2.0 


2.3 


2.7 


3.0 


3-3 


3.7 


5 


9.8 


10.2 


o.s 


0.9 


1.3 


1.6 


1.9 


2.3 


2.7 


3.0 


S'3 


3.7 


4.1 


19.0 


lO.I 


10.5 


10.8 


II. 2 


II.6 


11.9 


12.3 


12.6 


13.0 


13.3 


13.7 


14.1 


14.4 


5 


0.4 


0.7 


I.I 


1.5 


1.9 


2.2 


2.6 


2.9 


3-3 


3-7 


4.1 


4.5 


4.8 


20.0 


0.9 


1.3 


1.7 


2.1 


2.5 


2.8 


3.2 


3.6 


4.0 


4.4 


4.8 


5.2 


5.5 


I 


1.4 


1.8 


2.2 


2.6 


3.1 


3-4 


3-9 


4.2 


4.7 


5.1 


5.5 


5.9 


6.3 


2 


1.9 


2.4 


2.8 


3.2 


3.6 


4.1 


4.5 


4.9 


5.3 


5.7 


6.2 


6.6 


.7.1 


3 


12.S 


12.9 


13.3 


13.8 


14.2 


14.7 


15.1 


15.5 


16.0 


16.4 


16.9 


17.3 


17.8 


4 


2.9 


3-4 


3-9 


4.4 


4.8 


5.3 


5.7 


6.2 


6.7 


7.1 


7.6 


8.1 


8.5 


25.0 


3-5 


3.9 


4.4 


4.9 


5-4 


5.9 


6.4 


6.8 


7.3 


7.9 


8.3 


8.8 


9-3 


6 


4.0 


4-5 


5.0 


5.5 


6.0 


6.5 


7.0 


^5 


8.0 


8.5 


9.0 


9.5 


20.C 


7 


4-5 


5.1 


5.5 


6.1 


6.6 


7-1 


7.6 


8.1 


8.7 


9-2 


9.7 


20.2 


0.7 


8 


iS.i 


IS-S 


16.1 


16.6 


17.2 


17.7 


18.3 


18.8 


19.3 


19.9 


20.4 


20.9 


21.S 


9 


5.5 


6.1 


6.7 


7.2 


7.8 


8.3 


8.9 


9.4 


9.9 


20.6 


1.2 


1.7 


2.2 


30.0 


6.1 


6.6 


7.2 


7.8 


8.4 


8.9 


9-5 


20.1 


20.7 


1.2 


1.8 


2.4 


2.9 


I 


6.6 


7.2 


7.7 


§•3 


8.9 


9.6 


20.2 


0.6 


1-3 


1.9 


2.5 


3.2 


3.7 


2 


7-1 


7-7 


S.3 


8.9 


9-5 


20.2 


0.7 


1.4 


1.9 


2.6 


3.2 


3-S 


4.4 


3 


17.6 


18.3 


18.9 


19.S 


20.2 


20.8 


21.4 


22.0 


22.7 


23-3 


23.8 


24.6 


25.2 


4 


8.1 


8.7 


95 


20.1 


0.7 


1.3 


2.1 


2.7 


3-3 


3-9 


4.7 


5-3 


5-9 


35.0 


8.7 


9.3 


20.0 


0.7 


1.3 


1.9 


2.7 


3.3 


3 9 


4.6 


5.3 


6.0 


6.7 


6 


9.2 


9.9 


0.6 


1.2 


1.9 


2.6 


3-2 


3.9 


4.6 


5-3 


6.0 


6.7 


^4 


7 


9.7 


20.4 


I.I 


1.8 


2.5 


3.2 


3.9 


4.6 


5.3 


6.0 


6.7 


7.4 


8.1 


8 


20.2 


20.9 


21.7 


22.3 


23.2 


23.8 


24.6 


25.3 


25.9 


26.7 


27.4 


28.2 


28.9 


9 


0.7 


1.4 


2.2 


2.9 


3-7 


4.4 


5-2 


5.9 


6.6 


7.4 


8.1 


8.8 


9.6 


40.0 


1.3 


1.9 


2.8 


3.6 


4-3 


5-1 


5.7 


6.5 


7.3 


8.1 


8.8 


9.6 


30.4 


I 


1.8 


2.6 


3-3 


4.2 


4.8 


5.6 


6.4 


'^■i 


1'2 


8.7 


9.6 


30.3 


1.0 


2 


2.3 


3.1 


3.8 


4.7 


5.4 


6.2 


7.1 


7.8 


8.6 


9.4 


30.2 


I.I 


1.8 


3 


22.8 


23.6 


24.4 


25.2 


26.1 


26.8 


27.7 


28.4 


29-3 


30.2 


30.9 


31.7 


32.6 


4 


3.3 


4.2 


5.0 


5.8 


6.6 


7-5 


8.4 


9.2 


9.9 


0.8 


1.7 


2.5 


3.4 


45.0 


3.8 


4.7 


1'^ 


6.4 


7.2 


8.1 


8.9 


9.8 


50.6 


1.5 


2.4 


3.2 


4.1 


6 


4-3 


5.2 


6.1 


6.9 


7.8 


8.7 


9.6 


30.4 


1.3 


2.2 


3.0 


3.9 


4.8 


7 


4.8 


5.7 


6.7 


7.6 


8.4 


9.3 


30.2 


I.I 


2.0 


2.8 


3-7 


4.7 


5.5 


8 


25-4 


26.3 


27.2 


28.2 


29.0 


29.9 


30.8 


31-7 


32.6 


33.6 


34.5 


35.4 


36.3 


9 


5-9 


6.8 


7.8 


8.7 


9.6 


30.5 


1.4 


2.4 


3.4 


4.2 


5.2 


6.2 


7.1 


50.0 


6.9 


7.8 


8.8 


9.8 


30.8 


1.7 


2.7 


3.7 


4.6 


5.6 


6.6 


7.5 


8.5 


2 


7.9 


8.9 


9.9 


30.9 


2.0 


3.0 


.4.0 


l'° 


5-9 


6.9 


8.0 


9.0 


40.0 


4 


9.0 


30.1 


3I-I 


2.1 


3-2 


4.2 


5-2 


6.2 


7.3 


S^3 


9.4 


40.4 


1.5 


6 


30.1 


31.1 


32.2 


33.2 


34-4 


35-4 


36.5 


37-5 


38.6 


39-6 


40.8 


41.8 


42.9 


8 


I.I 


2.2 


3-3 


4.4 


^J 


6.6 


7.7 


8.9 


40.0 


41.1 


2.2 


H 


4.4 


60.0 


2.1 


3-2 


4.4 


5.6 


6.7 


7.8 


9.0 


40.1 


1.3 


2.4 


3.6 


4.8 


5.9 


2 


3.2 


4.4 


S-S 


6.6 


7.8 


9.1 


40.2 


1.4 


2.6 


3.8 


5.0 


6.2 


7-4 


4 


4.2 


5'.4 


6.6 


7.8 


9.1 


40.2 


1-5 


2.7 


3.9 


5.2 


6.4 


7.6 


8.8 


6 


35-2 


36.4 


37.7 


39.0 


40.2 


41.S 


42.8 


44.0 


45.2 


46.S 


47.8 


49.0 


50.4 


8 


6.3 


7.6 


8.8 


40.1 


1.4 


2.8 


4.0 


5.4 


6.6 


8.0 


9.2 


S0.5 


1.8 


70.0 


7.3 


8.7 


9.9 


1.3 


2.6 


4.0 


5-3 


6.6 


8.0 


9.2 


50.6 


2.0 


3.3 


2 


8.4 


9.7 


41.1 


2.5 


3.8 


5.2 


6.6 


7.9 


9.4 


50.7 


2.1 


3.4 


4.8 


4 



EARTHWORK 



533 



Table 41 — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cfbic Yards 



41 


42 


43 


44 


45 


46 


47 


48 


49 


SO 


75 


100 




D'uble 
Areas 


II.O 


11.3 


11.5 


11.8 


12. 1 


12.3 


12.6 


12.9 


13.1 


13.4 


20.2 


26.8 





14.5 


1.4 


1.7 


1.9 


2.2 


2'.5 


2.8 


3.0 


3.3 


3.6 


3.9 


0.8 


7.8 


— 


15.0 


1.8 


2.1 


2.3 


2.6 


2.9 


3.2 


3-5 


3.8 


4.1 


4.4 


1.5 


8.7 


— 


5 


2.1 


2.4 


2.7 


3.0 


3-3 


3.6 


3.9 


4.2 


4.5 


4.8 


2.2 


9.6 


— 


16.0 


2.5 


2.8 


3.1 


3.4 


3.7 


4.1 


4.3 


4-7 


4.9 


5-3 


2.8 


30.5 


— 


S 


12.9 


13.2 


13.5 


13.8 


14.2 


14-5 


14.8 


15.1 


15.4 


1S.7 


23.6 


31.4 


— 


17.0 


3.3 


3.6 


3-9 


4.3 


4.6 


4.9 


5.2 


5.5 


5.9 


6.2 


4-3 


2.4 


— 


5 


3.7 


4.0 


4-3 


4.7 


5-0 


5.3 


5.7 


6.0 


6.3 


6.7 


4.9 


3-3 


— 


18.0 


4.1 


4.4 


4-7 


5.1 


5.4 


5.7 


6.1 


6.4 


6.7 


7-1 


5.7 


4.2 


— 


5 


4.4 


4.7 


S-i 


5.5 


5.8 


6.1 


6.5 


6.9 


7.2 


7.6 


6.4 


5.2 


— 


19.0 


14.8 


15.1 


15-5 


15.9 


16.3 


16.6 


16.9 


17.3 


17.7 


18.1 


27.1 


36.1 





5 


S.2 


5.5 


5.9 


6.3 


6.7 


7.1 


7-4 


7.7 


8.1 


8.5 


7.8 


7.0 


— 


20.0 


5.9 


6.3 


6.7 


7.1 


7-5 


^9 


8.3 


8.7 


9.0 


9-5 


9.2 


8.8 


— 


I 


6.7 


7.1 


7.5 


l'^ 


8.3 


8.7 


9.1 


9.5 


9.9 


20.4 


30.6 


40.7 


— 


2 


7-5 


7.9 


^■3 


8.7 


9-1 


9.6 


20.0 


20.4 


20.8 


1-3 


1.9 


2.6 


— 


3 


18.2 


18.6 


19.1 


19.5 


20.0 


20.4 


20.8 


21.3 


21.8 


22.2 


33.2 


44.4 


— 


4 


9.0 


9-5 


9.9 


20.3 


0.8 


1-3 


1-7 


2.2 


2.7 


3-2 


4-7 


6.2 


— 


25.0 


9.7 


20.2 


20.7 


1.2 


1.7 


2.2 


2.6 


3-1 


3-6 


4.1 


6.1 


8.2 


— 


6 


20.S 


I.O 


1.5 


2.0 


2.5 


^•? 


3.5 


4.0 


4.5 


5.0 


7-5 


50.0 


— 


7 


1.3 


1.8 


2.3 


2.8 


3-3 


3.8 


4.4 


4.8 


5.4 


5.9 


8.8 


1.8 


. — 


8 


22.0 


22.6 


23.1 


23.7 


24.2 


24.7 


25.2 


25.8 


26.3 


26.8 


40*3 


53-7 


— 


9 


2.8 


3.3 


3.8 


4.4 


5-S 


5-5 


6.1 


6.7 


7.2 


l'^ 


1.6 


5.5 


— 


30-0 


3-5 


4.1 


4.7 


5-2 


5.8 


6.4 


6.9 


7.6 


8.1 


.8.7 


3.2 


7.3 


— 


I 


4.3 


4.8 


5.4 


6.1 


6.6 


^^ 


7.8 


8.4 


9.1 


9.6 


4.4 


9.2 


— 


2 


5.0 


5.7 


6.3 


6.8 


7.5 


8.1 


8.7 


9.3 


9.9 


30.6 


5.8 


61.0 


— 


3 


25-7 


26.4 


27.0 


27.7 


28.3 


28.9 


29.6 


30.2 


30.8 


31.4 


47.2 


62.9 


— 


4 


6.6 
7.3 


7.2 
8.0 


7.8 
8.6 


8.5 
9-3 


9.2 

30.0 


9.8 
30.6 


3_p.4 
1.3 


I.I 


1.7 
2.6 


2.4 
3-3 


8.6 
9.9 


4.8 
6.7 


— ; 


35.0 
6 


2.0 


8.1 


8.8 


9.4 


30.1 


0.8 


i.S 


2.2 


2.8 


3.6 


4.3 


51.4 


8.5 


— 


7 


8.8 


9.6 


30.2 


1.0 


1.6 


2.4 


3.1 


3.7 


4.5 


5.2 


2.8 


70.4 


— 


8 


29.6 


30.4 


31.0 


31.7 


32.5 


33.2 


33.8 


34.6 


35.4 


36.1 


54.1 


72.1 


— 


9 


30.4 


1.2 


1.8 


2.6 


3-3 


4.0 


4.8 


5.6 


6.3 


7.0 


5-5 


4.0 


— 


\ 400 


1.2 


1.8 


2.6 


3.4 


4.2 


4.8 


5-6 


6.4 


7.2 


8.0 


6.9 


5.8 


— 


I 


1,8 


2.7 


3.4 


4.2 


5.0 


5.8 


6.6 


7.3 


8.2 


8.9 


8.3 


7.8 


— 


2 


2.6 


3.4 


4.2 


5.0 


5-8 


6.6 


7.4 


8.2 


9.0 


9.8 


9.6 


9.6 





3 


33.4 


34.2 


35.0 


35-8 


36.7 


37.4 


38.3 


39.2 


39.9 


40.8 


61.1 


81.5 


— 


4 


4.2 


4.9 


5-8 


6.7 


^4 


8.3 


9.2 


9.9 


40.7 


1.6 


2.4 


3.4 


— 


45-0 


4.8 


5.7 


6.6 


7-4 


8.3 


9.1 


40.0 


40.9 


1.7 


2.6 


3.8 


5.1 


— 


6 


5.7 


6.6 


•7.4 


8.3 


9.2 


40.0 


0.9 


1.8 


2.7 


3.5 


5-3 


7.0 


— 


7 


6.4 


7.3 


8.2 


9.2 


40.0 


0.8 


1.7 


2.6 


3.5 


4.4 


6.7 


8.9 


— 


8 


37.2 


38.1 


39.0 


39.9 


40.8 


41.7 


42.6 


43.5 


44.4 


45.3 


68.1 


90.6 


— 


9 


7.9 


8.8 


9.8 


40.7 


1.6 


2.6 


3.5 


4.4 


5.3 


6.4 


9-3 


2.6 


— 


So.o 


9-5 


40.4 


41.3 


2.3 


3.3 


4.2 


5.2 


6.2 


7.2 


8.2 


72.2 


6.3 


— 


2 


41.0 


2.0 


3-0 


4.0 


5.0 


6.0 


7.0 


8.0 


9.0 


50.0 


5.0 


lOO.O 


— 


4 


2.5 


3.5 


4.6 


5.6 


6.6 


7.7 


8.7 


9.8 


50.8 


1.8 


7.8 


03.6 


— 


6 


44.1 


45-2 


46.2 


47-3 


48.4 


49.4 


50.5 


51.5 


52.6 


53.7 


80.5 


107.3 


— 


8 


5.6 


6.7 


i 7.8 


8.9 


50.0 


^^'l 


2.2 


3-3 


4.4 


5-5 


3.4 


ii.o; — 


60.0 


7.1 


8.2 


9.4 


50.5 


1.6 


2.8 


4.0 


5.1 


6.2 


7.4 


6.1 


14.8 — 


2 


8.6 


9-7 


50.9 


2.1 


3.3 


4.5 


5.7 


6.9 


8.1 


9.3 


8.9 


i8.6i — 


4 


50.2 


51-3 


2.5 


3.7 


5.0 


6.1 


7.4 


8.6 


9.9 


61. 1 


91.7 


22.1; — 

1 


6 


51.6 


52.8 


54.1 


55.4 


56,7 


58.0 


59.2 


60.4 


61.7 


63.0 


94.5 


125.9 — 


8 


3-1 


4.4 


5.7 


7.0 


8.3 


9.6 


60.9 


2.2 


3.5 


4.8 


7.2 


29.5 — 


70.0 


4.7 


6.0 


7.3 


8.6 


60.0 


61.3 


2.6 


4.0 


5.4 


6.6 


lOO.O 


33.2| — 


2 


6.2 


7.6 


8.9 


60.3 


1.7 


3.1 


4.4 


5.8 


7.2 


8.6 


02.0 


37.i| - 


4 



534 



OFFICE PRACTICE 



Table 41 — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



2 


3 


4 


5 


6 


7 


8 


9 


10 


II 


12 


13 


14 


D'uble 
Areas 


2.8 


4.2 


5.6 


7.0 


?-5 


9.9 


11.3 


12.7 


14.1 


15.5 


16.9 


18.3 


19.7 


76.0 


2.9 


4.3 


5.8 


7.2 


8.7 


lO.I 


1.6 


3.0 


4.5 


5.9 


7.4 


8.8 


20.2 


8 


3-0 


4.4 


5.9 


7.4 


8.9 


0.4 


1.9 


3>-2> 


4.9 


6.3 


7.8 


9-3 


0.8 


80.0 


3-0 


4.6 


6.1 


7-J 


9.1 


0.7 


2.2 


3.7 


H 


6.7 


8.2 


9.8 


1.3 


2 


3-1 


4.7 


6.2 


7.8 


9.3 


0.9 


2.5 


4.0 


5.6 


7.1 


8.7 


20.2 


1.7 


4 


3-2 


4.8 


6.4 


8.0 


9.6 


II. 2 


12.7 


14.3 


15-9 


17.5 


19.1 


20.7 


22.3 


6 


3-3 


4.9 


6.5 


8.1 


9.8 


1.4 


3.1 


4-7 


5-^ 


2-9 


9.5 


1.2 


2.8 


8 


3,-i 


5.0 


6.7 


?-^ 


lO.O 


1.7 


Z-i 


5.0 


6.7 


l'^ 


20.0 


1.7 


3-4 


90.0 


3.4 


5.1 


6.8 


8.5 


0.2 


1.9 


3.6 


5-4 


7.1 


8.7 


0.4 


2.1 


3.8 


2 


3.5 


5.2 


7.0 


8.7 


0.5 


2.2 


3.9 


5.7 


7.4 


9.2 


0.8 


2.6 


4.4 


4 


3.5 


5-3 


7.1 


8.9 


10.7 


12.5 


14.2 


16.0 


17.8 


19.5 


21.3 


23.1 


24.9 


6 


3.6 


5-4 


7.3 


9.1 


0.9 


2.7 


4.5 


6.4 


8.2 


9.9 


1.8 


3.6 


5.4 


8 


3-7 


5.6 


7-4 


9.3 


1. 1 


3.0 


4.8 


6.7 


8.5 


20.4 


2.2 


4.1 


6.0 


lOO.O 


3.9 


5.8 


7.8 


9-7 


1.7 


3.6 


5.5 


^5 


9.5 


1.4 


3.3 


5-3 


7.2 


05 


4.1 


6.1 


8.1 


10.2 


2.2 


4.3 


6.3 


8.4 


20.4 


2.4 


4.4 


6.5 


8.6 


10 


4-3 


6.4 


8.5 


10.7 


12.8 


14.9 


17.0 


19.1 


21.3 


23-4 


25-5 


27.7 


29.8 


15 


4.4 


6.7 


8.9 


I.I 


Z-Z 


5.5 


7.8 


20.0 


2.3 


4.4 


6.6 


8.8 


31-2 


20 


4.6 


6.9 


9.2 


1.6 


3.9 


6.2 


8.5 


0.8 


3-2 


5.4 


7.7 


30.2 


2.4 


125.0 


4.8 


7.2 


9.6 


2.1 


4.5 


6.9 


9-3 


1.7 


4.1 


6.5 


8.8 


1.4 


3.7 
5.0 


30 


5.0 


7.5 


lO.O 


2.5 


5.0 


7.5 


20.0 


2.5 


5.0 


7.5 


9.9 


2.5 


35 


5-2 


7.8 


10.4 


12.9 


15.5 


18.2 


20.8 


23.4 


25.9 


28.5 


31.1 


33.7 


36.4 


40 


5-4 


^•° 


0.7 


3-4 


6.1 


8.8 


1-5 


4.2 


6.8 


9.5 


2.2 


4.8 


7.6, 


45 


5.6 


8.3 


1. 1 


3.9 


6.7 


9-5 


2.^ 


^•o 


7.8 


30.6 


3.4 


6.2 


8.8, 


150.0 


5.7 


8.6 


1.5 


4.3 


7.2 


20.1 


2.9 


5-8 


8.7 


1.6 


4.5 


7.3 


40.2 


55 


5.9 


8.9 


1.9 


4.8 


7.8 


0.7 


3.7 


6.7 


9-6 


2.6 


5-6 


8.5 


"1 


60 


6.1 


9.2 


12.3 


15.3 


18.3 


21.4 


24.4 


H-^ 


30.6 


33.6 


36.6 


39.7 


42.8, 


65 


6.3 


9.5 


2.6 


5.8 


8.9 


2.1 


5.2 


8.3 


1.5 


4.6 


7.7 


40.9 


4.1 


70 


6.5 


9.7 


3.0 


6.2 


9.4 


2.7 


5.9 


9.2 


2.4 


5.6 


8.9 


2.1 


5.5 


175.0 


6.7 


lO.O 


3.3 


6.7 


20.0 


S'Z 


6.7 


30.0 


3-3 


6.7 


40.0 


3.3 


6.6 


80 


6.9 


0.3 


3.7 


7.1 


0.6 


4.0 


7.4 


0.9 


4.2 


7.7 


1.2 


4.5 


8.0 


85 


7.0 


lo.s 


14.1 


17.6 


21.2 


24.6 


28.2 


31.7 


35.2 


38.7 


42.2 


45.7 


49.3 


90 


7.2 


0.8 


4.5 


8.1 


1.6 


5.2 


8.8 


2.5 


6.2 


9.7 


3'2> 


7.0 


50.5 


95 


7.4 


1. 1 


4.9 


8.5 


2.2 


5.9 


9.6 


3.4 


l''^ 


40.8 


4.4 


8.2 


1.9 


200.0 


7.8 


1.7 


5.6 


9-5 


3-4 


7.2 


31.1 


5.0 


8.9 


2.8 


6.7 


50.5 


4.4 


10 


8.1 


2.2 


6.3 


20.4 


4.4 


8.5 


2.6 


6.7 


40.8 


4.8 


8.8 


3.0 


7.1 


20 


8.5 


12.7 


17.1 


21.3 


25.6 


29.8 


34.1 


38.4 


42.6 


4^-? 


51.1 


55.4 


59.6 


30 


8.9 


3.3 


2-7 


2.2 


6.6 


31.1 


5.6 


40.0 


4.4 


8.8 


3.3 


7.8 


62.1 


40 


9.2 


3.9 


8.5 


3.1 


l'^ 


2.4 


7.0 


1.7 


6.4 


50.9 


H 


60.2 


4.8 


250.0 


9.6 


4.5 


9-3 


4.1 


8.9 


3.7 


8.5 


3.4 


8.2 


2.9 


7.8 


2.7 


7.4 


60 


lO.O 


5.0 


20.0 


5.0 


30-0 


5.0 


9.9 


5.0 


50.0 


5.0 


60.0 


4.9 


70.0 


70 


10.4 


15.6 


20.7 


25.9 


31. 1 


36.3 


41.4 


46.7 


51.9 


57.0 


62.2 


67.4 


72.5 


80 


0.8 


6.1 


1.4 


6.8 


2.2 


2-g 


3.0 


8.3 


3-8 


9.1 


^i 


9.8 


5.2 


90 


I.I 


6.7 


2.2 


7.8 


3.3 


8.8 


4.4 


50.0 


5.6 


61.1 


6.8 


72.2 


7.9 


300.0 


1.5 


7-2 


2.9 


8.6 


4.4 


40.2 


5.9 


1.8 


7.4 


3.1 


8.8 


4-5 


80.4 


10 


1.9 


7.8 


3.6 


9.6 


5.5 


1.4 


7-4 


3.3 


9.3 


5.2 


71.1 


7.0 


3.0 


20 


12.2 


18.3 


24.4 


30.6 


36.6 


42.8 


48.8 


55.0 


61.2 


67.2 


73.3 


P"^ 


85.6 


30 


2.6 


8.9 


5.2 


1.4 


7-7 


4.1 


50.5 


6.7 


2.9 


9.2 


5.5 


81.8 


8.2 


40 


3.0 


9.5 


5-9 


2.4 


8.S 


5.3 


1.8 


8.3 


4.8 


71-3 


7.8 


4.2 


90.8 


350.0 


3.3 


20.0 


6.6 


3-3 


9.9 


6.6 


3.4 


60.0 


6.8 


3'Z 


80.0 


6.8 


3.3 


60 


3.7 


0.6 


7.4 


4.3 


41. 1 


7.9 


4.8 


1.6 


8.5 


5.3 


2.1 


9.0 


6.0 


70 


14.1 


21.2 


28.2 


35.2 


42.2 


49.2 


56.3 


63.3 


70.3 


77.4 


84.3 


91.5 


98.5 


80 


4.4 


1.6 


8.8 


6.1 


Z-2> 


50.6 


7.8 


5-0 


2.3 


9.4 


6.6 


3.9 


lOI.I 


90 


4.8 


2.2 


9.6 


7.1 


4.4 


1.8 


9.2 


6.7 


4.1 


81.S 


8.9 


(>.z 


3.6 


400.0 



EARTHWORK 



535 



Table 41 — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


.7 


D'uble 
Areas 


21.2 


22.5 


23.9 


25.3 


26.7 


28.2 


29.6 


31.0 


32.4 


33.8 


35.2 


36.6 


38.0 


76.0 


1.7 


3.1 


4.6 


6.0 


2-4 


8.9 


30.3 


1.8 


3.2 


4.7 


6.0 


l-^ 


9.0 


8 


2.2 


3.7 


5.2 


6.7 


8.2 


9.6 


I.I 


2.6 


4.1 


5.6 


7.0 


8.5 


40.0 


80.0 


2.8 


4.3 


5.8 


1.Z 


8.9 


30.4 


1.8 


3.4 


4.9 


6.4 


7.9 


9.4 


1.0 


2 


3.3 


4.8 


6.4 


8.0 


9.6 


1.2 


2.7 


4.2 


5.8 


7.3 


8.8 


40.4 


2.0 


4 


23.8 


25.5 


27.1 


28.6 


30-2 


31.8 


33.4 


35-0 


36.6 


38.2 


39.8 


41.4 


43.0 


6 


4.4 


6.1 


7.7 


9.3 


0.9 


2.6 


4.2 


!•? 


^5 


9.1 


40.7 


2.3 


4.0 


8 


5.0 


6.7 


8.3 


30-0 


1.7 


3.4 


5.0 


6.6 


8.4 


40.0 


1.6 


3.3 


5.0 


90.0 


5.6 


7.2 


8.9 


0.6 


2.3 


4.1 


5.8 


7.5 


9.2 


0.9 


2.6 


4.3 


6.0 


2 


6.1 


7.8 


9.6 


1-3 


3.1 


4.8 


6.5 


8.2 


40.0 


1.8 


3.5 


5.2 


7.0 


4 


26.7 


28.4 


30.2 


32.0 


33.7 


35.5 


37.3 


39.0 


40.8 


42.7 


44.4 


46.2 


48.0 


6 


7.2 


9.0 


0.8 


2.6 


4.4 


6.3 


8.0 


9.8 


1.7 


3.6 


5.4 


7.1 


9.0 


8 


7.8 


9.6 


1.5 


S'2> 


5.2 


7.0 


8.9 


40.8 


2.6 


4.4 


6.3 


8.1 


50.0 


lOO.O 


9.2 


31-2 


3-0 


5-0 


7.0 


8.9 


40.8 


2.7 


4.7 


6.6 


8.5 


50.5 


2.5 


05 


30.6 


2.6 


4.6 


6.6 


8.7 


40.7 


2.7 


4.7 


6.8 


8.8 


50.9 


2.9 


5.0 


10 


32.0 


34.1 


36.2 


38.4 


40.5 


42.6 


44.7 


45-? 


48.9 


51.0 


53.2 


55.4 


57.5 


15 


3-3 


5.5 


7.7 


9.9 


2.2 


4.4 


6.6 


8.8 


Si.o 


3-3 


5.5 


7.8 


60.0 


20 


4.6 


7-° 


9.3 


41.6 


3.9 


i^ 


8.6 


50.9 


3.2 


5.5 


7.8 


60.1 


2.5 


125.0 


6.1 


8.5 


40.9 


3.3 


5-7 


8.2 


50.5 


2.9 


5-3 


7.8 


60.2 


2.6 


5.0 


30 


7.5 


40.0 


2.5 


5.0 


7.5 


50.0 


2.5 


5-0 


7.5 


60.0 


2.5 


5.0 


7.5 


35 


38.8 


41.4 


44.0 


46.6 


49-2 


51.8 


54-4 


57.0 


59.6 


62.2 


64.8 


67.4 


70.0 


40 


40.2 


2.9 


5.6 


8.3 


51.0 


3.7 


5-2 


9.0 


61.7 


4.4 


7,0 


9.8 


2.5 


45 


1.6 


4.4 


7.2 


9.9 


2.8 


5.7 


8.2 


61.1 


3.9 


6.6 


9.3 


72.2 


5.0 


150.0 


3-0 


5-9 


8.7 


51.6 


4-5 


7.6 


60.3 


3-1 


6.0 


8.8 


71.8 


4.6 


o7-5 


55 


4.4 


7.3 


50.4 


3-3 


6.2 


9.3 


2.1 


5.1 


.8.1 


71.1 


4.0 


7.0 


80.0 


60 


45.8 


48.8 


52. 


55.0 


58.0 


61.0 


64.2 


67.1 


70.3 


73.4 


76.2 


79.3 


82.5 


65 


7.2 


50.S 


3-5 


6.6 


9.8 


3.0 


6.0 


9.2 


2.3 


5-5 


8.7 


81.8 


S.o 


70 


8.6 


1.8 


5.0 


8.3 


61.5 


4.8 


"8.0 


71.2 


. 4-6 


7.7 


81.0 


4.3 


7.5 


175.0 


So.o 


3.3 


6.6 


60.0 


3.3 


6.8 


9.9 


3.2 


i'l 


80.0 


3.2 


6.7 


90.0 


80 


1.4 


4.8 


8.1 


1.6 


5.0 


8.5 


71.9 


5.3 


8.8 


2.2 


5.6 


9.0 


2.5 


85 


52.8 


56.2 


59.8 


63.3 


66.8 


70.4 


73.8 


77.3 


80.9 


84.3 


87.9 


91.7 


95.0 


90 


4.0 


7.8 


61.3 


5-0 


8.7 


2.1 


5-7 


9.4 


3-0 


6.7 


90.2 


3.9 


7.5 


95 


5-5 


9.2 


2.9 


6.7 


70.3 


4.0 


o^-^ 


81.4 


5-1 


8.9 


2.8 


6.4 


lOO.O 


200.0 


8.3 


62.1 


6.0 


70.0 


3-8 


7.8 


81.7 


5.5 


9.4 


93-4 


7.2 


101.2 


05.0 


10 


61.0 


5-1 


9.3 


3.2 


7.4 


81.S 


5.5 


9-5 


93.7 


7.8 


101.9 


06.0 


lO.O 


20 


63.9 


68.0 


72.4 


76.6 


80.9 


85.2 


89.4 


93.7 


98.0 


102.2 


106.5 


110.8 


II5.0 


30 


6.5 


71.0 


5-5 


9.9 


4-3 


8.9 


93.2 


7.8 


102.2 


106.8 


II. I 


15-5 


20.0 


40 


9.4 


4.0 


8.6 


83.2 


7-9 


92-5 


7.1 


101.9 


06.5 


II. I 


15.9 


20.5 


25.0 


250.0 


72.1 


7.0 


81.8 


6.5 


91.4 


6.5 


101.2 


06.0 


10.7 


15.5 


20.4 


25.3 


30.0 


60 


5.0 


80.0 


5.9 


90.0 


4.9 


lOO.O 


05.0 


lO.O 


iS.i 


20.0 


25.0 


30.0 


35.C 


70 


77.8 


82.9 


88.1 


93.2 


98.4 


103.8 


108.9 


114.1 


119.2 


124.5 


129.5 


134.8 


140.0 


80 


80.6 


5-9 


91.2 


6.5 


102. 1 


07.4 


12.9 


18.1 


23.5 


28.9 


34.3 


39.8 


45.0 


90 


3-2 


8.9 


4.4 


lOO.O 


05.7 


II. I 


16.8 


22.2 


29.7 


33-3 


38.9 


44.5 


50.0 


300.0 


6.0 


91.8 


7.5 


03.3 


09.2 


14.8 


20.6 


26.3 


32.1 


37-9 


43.5 


49.3 


55.0 


10 


9.0 


4.7 


100.9 


06.8 


12.7 


18.6 


24.3 


30.3 


36.2 


42.2 


48.1 


54.1 


60.0 


20 


91.5 


97.7 


103.9 


IIO.O 


116.1 


122.2 


128.3 


134.5 


140.6 


146.8 


152.8 


158.9 


165.0 


30 


4.5 


100.7 


07.1 


13-2 


19.6 


26.0 


32.2 


38.5 


44.9 


51.1 


57.2 


6"?. 8 


70.0 


40 


7.2 


03.8 


10.2 


16.7 


23.2 


29.7 


36.2 


42.5 


49.1 


55-5 


62.0 


68.5 


75.0 


350.0 


lOO.O 


06.6 


13.4 


20.0 


26.8 


33-3 


40.0 


46.6 


53.2 


60.0 


66.8 


73.4 


80.0 


60 


02.8 


09.6 


16.4 


23.2 


30.2 


37.0 


43.8 


50.7 


57.S 


64.5 


71.2 


78.1 


85.0 


70 


105.6 


112.S 


119.6 


126.8 


133.8 


140.8 


147.8 


154.8 


161.8 


168.9 


175-9 


'?^-? 


190.0 


80 


08.2 


15.S 


22.9 


30.0 


37.2 


44-3 


51.7 


58.9 


66.1 


73.4 


80.5 


87.8 


95.0 


90 


II. I 


18.5 


25-9 


33-3 


40.7 


48.1 


55.6 


63.0 


70.4 


77.8 


85.2 


92.6 


200.0 


400.0 



536 



OFFICE Practice 



Table 41 — Continued 
Distance Horizontal Sum of Areas Vertical Quantities in Cubic Yards 



28 


29 


30 


31 


32 


33 


34 

47-9 


35 
49.3 


36 

50.7 


37 


38 

53.5 


39 


40 


D'uble 
Areas 


39.4 


40.8 


42.3 


43.6 


45.1 


46.5 


52.1 


54.9 


56.3 


76.0 


40.4 


1.8 


3.3 


4.8 


6.2 


7.7 


9.1 


50.5 


2.0 


3.5 


4.9 


6.4 


7.8 


8 


1.5 


3.0 


4.4 


5.9 


7.4 


8.8 


50.3 


1.8 


3.3 


4.8 


6.3 


7.8 


^^•0 


80.0 


2.5 


4.1 


5.6 


7.1 


8.6 


50.1 


1.7 


3.2 


4.7 


6.2 


7.7 


9.2 


60.8 


2 


3.6 


5.2 


6.7 


8.2 


9.8 


1-3 


2.9 


4.5 


6.0 


7.5 


9.1 


60.7 


2.3 


4 


44.6 


46.2 


47.8 


49.3 


51.0 


52.5 


54-2 


55.7 


57-3 


58.9 


60.5 


62.1 


63.7 


6 


5.6 


7.2 


8.8 


50.5 


2.1 


3.7 


5.4 


7.0 


8.7 


60.3 


1.9 


3.5 


5.2 


8 


6.7 


8.3 


50.0 


1.7 


3.3 


S-o 


6.7 


8.3 


60.0 


1.6 


3.3 


S.o 


6.6 


90.0 


7-7 


9.4 


i.i 


2.8 


4.5 


6.2 


7.9 


9.6 


1.3 


3.0 


4.7 


6.4 


8.2 


2 


8.8 


50.5 


2.2 


4.0 


5.7 


7.5 


9.2 


61.0 


2.7 


4.4 


6.2 


7.9 


9.7 


4 


49.8 


51.5 


53.3 


55.1 


56.9 


58.7 


60.4 


62.2 


64.0 


65.8 


67.6 


69.4 


71.1 


6 


50.8 


2.6 


4.4 


6.3 


8.1 


9.9 


1-7 


H 


H 


l'^ 


8.9 


70.8 


2.6 


8 


1.8 


3-7 


5.5 


7.4 


9.3 


61. 1 


3-0 


4.8 


6.6 


8.5 


70.3 


2.2 


4.0 


lOO.O 


4.4 


6.4 


8.3 


60.3 


62.2 


4.2 


6.1 


8.1 


70.0 


72.0 


3.9 


5.8 


7.8 


05 


7.0 


9.1 


61.1 


3.2 


5.2 


7.2 


9-3 


71-3 


3.4 


5.4 


7.4 


9.5 


81.S 


10 


59-7 


61.8 


64.0 


66.0 


68.1 


70.4 


72.5 


74.5 


76.7 


78.8 


81.0 


83.1 


85.2 


IS 


62.3 


4.5 


6.7 


8.9 


71.1 


3.4 


5-5 


7.8 


80.0 


82.2 


4.5 


6.7 


9.0 


20 


4.8 


7.2 


9.5 


71.8 


4.1 


6.5 


8.8 


81.0 


3.4 


5.6 


8.0 


90.3 


92.7 


125.0 


7-3 


9.8 


72.1 


4.5 


J'^ 


9.4 


81.8 


4.2 


6.6 


9.0 


91.4 


3-9 


6.1 


30 


70.0 


72.S 


5.0 


7.5 


80.0 


82.5 


5.0 


7.5 


90.0 


92.5 


S.o 


7.5 


1 00.0 


35 


72.6 


75.2 


77.8 


80.5 


83.0 


85.6 


88.1 


90.7 


93.4 


96.0 


98.5 


lOI.l 


103.7 


40 


5-2 


7.9 


80. 5 


3.2 


5-9 


8.6 


91.3 


4.0 


6.7 


9.4 


102.0 


04.8 


07.5 


45 


7.8 


80.6 


3.4 


6.1 


8.9 


91.7 


4-5 


7.2 


lOO.O 


102.8 


05.6 


08.3 


11.1 


150.0 


80.4 


3.2 


6.2 


9.0 


91.9 


4-7 


7.6 


loo.s 


03.4 


06.2 


09.1 


12.0 


14.8 


55 


2.9 


5.9 


8.8 


91.8 


4.7 


7.7 


100.8 


03.8 


06.7 


09.7 


12.6 


15.6 


18.S 


60 

^5 


85.5 


88.5 


91.6 


94.7 


97.7 


100.9 


103.9 


107.0 


1 10.0 


113.1 


116.1 


119.2 


122.2 


8.1 


91.3 


4.4 


7.6 


100.8 


03.9 


07.1 


10.2 


13.3 


16.6 


19.7 


22.8 


26.0 


70 


90.8 


4.0 


7.3 


100.5 


03.8 


70.0 


•10.2 


13.4 


16.7 


20.0 


23.2 


26.4 


29.6 


175.0 


3.4 


6.6 


lOO.O 


03.3 


06.8 


iii.i 


13.4 


16.8 


20.0 


23.3 


26.7 


30.1 


33.4 


80 


6.0 


9.4 


02.8 


06.2 


09.6 


13.2 


16.5 


19.9 


23.4 


26.8 


30.2 


33.7 


37.1 


85 


98.6 


102.1 


105.6 


109.2 


112.8 


116.1 


119.7 


123.2 


126.7 


130.2 


133.8 


137.3 


140.8 


90 


101.2 


04.8 


08.4 


12.0 


15.6 


19.2 


22.9 


26.4 


30.0 


33.8 


37.2 


40.9 


44.5 


95 


03.7 


07.4 


11. 1 


14.9 


18.6 


22.2 


26.0 


29.6 


33.3 


37.0 


40.6 


44.4 


48.1 


200.0 


08.8 


12.8 


16.6 


20.6 


24.4 


28.4 


32.2 


36.2 


40.0 


44.0 


47.8 


51.6 


55.6 


10 


14.0 


18.2 


22.2 


26.4 


30.4 


34.4 


38.6 


42.6 


46.8 


50.8 


54.8 


59.0 


63.0 


20 


119.4 


123.6 


127.8 


132.0 


136.2 


140.6 


145.0 


149.0 


153.4 


157.6 


162.0 


166.2 


170.4 


30 


24,6 


29.0 


33.4 


37.8 


42.2 


46.8 


51.0 


55.6 


60.0 


64.4 


69.0 


73-4 


78.0 


40 


29.6 


34.4 


39.0 


43.6 


48,2 


53.0 


57.6 


62.0 


66.8 


71.4 


76.0 


80.6 


85.4 


250.0 


34.6 


39.4 


44.2 


49.0 


54.0 


58.8 


63.6 


68.4 


73.2 


78.0 


82.8 


87.8 


92.5 


60 


40.0 


45.0 


50.0 


55.0 


60.0 


65.0 


70.0 


7S.O 


80.0 


85.0 


90.0 


9S'0 


200.0 


70 


145-2 


150.4 


155.6 


161.0 


166.0 


171.2 


176.2 


181.4 


186.8 


192.0 


197.0 


202.2 


207.4 


80 


50.4 


55.8 


61.0 


66.4 


71.8 


77.2 


82.6 


88.0 


93.3 


98.8 


204.0 


09.6 


14.6 


90 


55.6 


61.2 


66.8 


72.2 


77.8 


83.4 


89.0 


94.4 


200.0 


205.6 


11.2 


16.6 


22.2 


300.0 


60.8 


66.4 


72.4 


78.0 


83.8 


89.4 


95.2 


201.0 


06.8 


12.4 


18.2 


24.0 


29.6 


10 


65.8 


71.8 


77.6 


83.6 


89.4 


95.4 


201.6 


07.6 


13.6 


19.4 


25.2 


31.2 


37-0 


20 


171.0 


177.0 


183.2 


189.4 


195.4 


201.8 


207.8 


214.0 


220.0 


226.2 


232.2 


238.4 


244.4 


30 


76.2 


82.6 


88.8 


95.2 


201.6 


07.8 


14.2 


20.4 


26.7 


33-2 


39.4 


45.6 


52.0 


40 


81.6 


88.0 


94.6 


201.0 


07.6 


14.0 


20.4 


26.8 


33.4 


40.0 


46.4 


52.8 


59.2 


350.0 


86.8 


93.2 


200.0 


06.6 


13.6 


22.2 


26.8 


33.6 


40.0 


46.6 


53.4 


60.2 


66.8 


60 


92.0 


98.8 


05.6 


12.4 


19.2 


26.4 


33.0 


39.8 


46.8 


53.6 


60.4 


67.4 


74.2 


70 


197.2 


204.2 


211.2 


218.4 


225.6 


232.2 


239.4 


246.4 


253.4 


260.4 


267.6 


274.6 


281.6 


1 
80 


202.4 


09.6 


16.8 


24.0 


31.2 


38.4 


45.8 


52.8 


60.2 


67.6 


74.4 


81.8 


89.0 


90 


07.4 


14.8 


22.2 


29.6 


37.0 


44.4 


S1.8 


59.2 


66.6 


74.0 


81.4 


88.8 


96.2 


400.0 



EARTHWORK 



537 



Table 41 — Concluded 
Distance Horizontal Sum op Areas Vertical Quantities in Cubic Yards 



41 


42 


43 


44 


45 


46 


47 


48 


49 


50 


75 I 


100 
140.7 




D'ubl 
Areas 


57.7 


59.2 


60.6 


61.9 


63-4 


64.8 


66.2 


67.6 


69.0 


70.4 


105-7 





76.0 


9.2 


60.7 


2.1 


3-6 


5.0 


6.4 


7.8 


9-3 


70.7 


2.3 


08.4 


44-4 


— 


8.0 


60.8 


2.2 


3-7 


H 


S'7 


8.2 


9.7 


71.2 


2.6 


4-1 


11.2 


48.1 


— 


80.0 


2.2 


3.8 


5.3 


6.8 


8.3 


9.8 


71.4 


2.9 


4-4 


5-9 


14.0 


51.8 


— 


2 


3.8 


5-4 


6.9 


8.4 


70.0 


71.6 


3.2 


4.7 


6.2 


7.8 


16.8 


55-5 


— 


4 


65.3 


66.8 


68.4 


70.1 


71.7 


73.3 


74.8 


76.4 


78.0 


79-6 


119-5 


159-2 





6 


6.8 


8.4 


70.1 


1.7 


3-4 


5-0 


6.6 


8.3 


9.8 


81.5 


22.3 


63.0 


— 


8 


8.4 


70.0 


1.7 


3.3 


5-0 


6.7 


8.4 


80.0 


81.7 


3-4 


25.1 


66.7 


— 


90.0 


9.8 


1.6 


3.3 


4.9 


^7 


o^-4 


80.1 


1.8 


3.5 


5-2 


27.9 


70.6 


— 


2 


71.4 


3.2 


4.8 


6.6 


8.4 


80.2 


1.9 


3.6 


5.3 


7.1 


30.7 


74-1 


— 


4 


72.8 


74.7 


76.4 


78.2 


80.0 


81.8 


83.6 


85.3 


97.1 


88.9 


133.4 


177.7 





6 


4.4 


6.3 


8.1 


9.9 


1-7 


3.5 


5.3 


7.2 


8.9 


90.8 


36.2 


81.6 


— 


8 


5-9 


o7-7 


„9-7 


81.4 


3-3 


5-2 


7.0 


8.8 


90.7 


2.6 


38.9 


85.1 


— 


lOO.O 


9.8 


81.7 


83.6 


5.6 


7-5 


9-4 


91.4 


93-4 


95-3 


7-2 


45-9 


94-4 


— 


05 


83.5 


5.6 


7.6 


9.6 


91.7 


93-7 


5.7 


7.8 


9-8 


IOI.9 


52.8 


203.7 


~— 


10 


87.3 


89.4 


91.6 


93.7 


95.8 


97.9 


lOO.I 


102.2 


104.4 


106.5 


159-8 


212.9 


— - 


15 


91.2 


93.4 


5.6 


7.8 


lOO.O 


102.2 


04.5 


06.7 


08.9 


11.8 


66.7 


22.2 


— 


20 


S-o 


7.3 


9-7 


101.9 


04.2 


06.5 


08.9 


II. 2 


13.5 


15.6 


73-7 


31.4 


— 


125.0 


8.8 


101.2 


103.6 


05.9 


08.4 


10.7 


13.1 


15.5 


17.9 


20^ 


80.5 


40.7 


— 


30 


102.5 


05.0 


07.5 


lO.O 


12.5 


15.0 


17.5 


20.0 


22.5 


25.0 


87-5 


50.0 


— 


35 


106.3 


108.9 


111.5 


114.2 


II6.7 


119.3 


121.9 


124.4 


127.1 


129.8 


194.5 


259.2 


— 


40 


11.2 


12.9 


1S.5 


18.2 


20.8 


23.6 


26.2 


28.9 


31.7 


34.3 


201.5 


68.5 


— 


45 


14.0 


16.7 


19-5 


22.3 


25.0 


27.8 


30.6 


33.4 


36.2 


38.9 


08.5 


77.7 


— 


150.0 


17.8 


20.6 


23.5 


26.3 


29.2 


32.1 


34.9 


37.8 


40.8 


43.6 


15-4 


87.0 


. — 


55 


21.5 


24.5 


27.4 


30.4 


33.4 


36.4 


39.4 


42.3 


45.2 


48.2 


22.4 


96.3 


— 


60 


25.3 


128.4 


131.5 


134.4 


137.6 


140.6 


143-8 


146.8 


149.8 


152.8 


229.3 


305-5 


— 


65 


129.1 


32.3 


35.4 


38.5 


41.7 


44-9 


48.0 


51.2 


54-3 


57-4 


36.2 


14.8 


— 


70 


32.9 


36.1 


39.4 


42.5 


45-8 


49.0 


52.2 


55-5 


58.8 


62.0 


43-0 


24.0 


— 


175-0 


36.8 


40.0 


43.4 


46.8 


50.0 


53-4 


56.8 


60.0 


63.4 


66.8 


50.0 


33.3 


— 


80 


40.S 


43.9 


47.4 


S0.8 


54.2 


57.7 


61.0 


64.5 


67.9 


71.4 


56.9 


42.6 


-~- 


85 


144.4 


147.8 


151.4 


154.9 


158.4 


161.9 


165.4 


168.9 


172.4 


176.0 


263.9 


351.8 


— 


90 


48.1 


51.8 


55.3 


58.9 


62.5 


66.2 


69-8 


73.4 


77.0 


80.5 


70.8 


61.1 


— 


95 


SI.8 


55-6 


59.3 


63.0 


66.8 


70.4 


74-1 


77-8 


81.4 


85.2 


77-7 


70.3 


— 


200.0 


59-5 


63.4 


67.3 


71.1 


75.0 


78.9 


82.8 


86.7 


90.5 


94-5 


91.6 


88.9 


— 


10 


67.0 


71.2 


75.2 


79.3 


83.4 


87.5 


91-5 


95.6 


99.7 


203.7 


305.5 


407.4 


"~~ 


20 


174-7 


^Z?-^ 


183.3 


187.5 


191.8 


196.0 


200.1 


204.4 


208.8 


213-0 


319.4 


425.9 


— 


30 


82.2 


86.8 


91.1 


95.5 


200.0 


204.5 


08.8 


13-3 


17.8 


22.2 


33-3 


44-4 


— 


40 


89.8 


94-5 


99.0 


203.7 


08.3 


13-0 


17-5 


22.2 


26.8 


^'1 


47-1 


62.9 


— 


250.0 


97.4 


202.3 


207.0 


11.9 


16.6 


21.6 


26.3 


3I-I 


36.0 


40.8 


61.0 


81.5 


— 


60 


205.0 


lO.O 


15.0 


20.0 


25.0 


230.0 


35.0 


40.0 


45-0 


50.0 


75.0 


500.0 


— 


70 


212.7 


217.8 


223.0 


228.2 


233.3 


238.6 


243.7 


248.9 


254.1 


259.2 


388.7 


518.5 


— 


80 


20.2 


25.6 


30.9 


36.3 


41.7 


47.1 


52.4 


57.8 


63.2 


68.5 


402.7 


37-0 


— 


90 


27.8 


33.4 


38.9 


44.S 


50.0 


55.6 


61. 1 


66.7 


72.3 


77.8 


16.5 


55-5 


— 


300.0 


35.4 


41.2 


46.9 


52.6 


58.3 


64.2 


69.8 


75-6 


81.3 


87.0 


30.4 


74-0 


— 


10 


43.0 


49.0 


54.8 


60.8 


66.7 


72.7 


78.5 


84-4 


90.4 


96.3 


44.3 


92.6 


— 


20 


250.6 


256.7 


262.8 


268.9 


275.0 


281.2 


287.2 


293-3 


299.5 


305.5 


458.2 


611.0 


— 


30 


58.2 


64.5 


70.7 


77.1 


83.3 


89.7 


95.9 


302.2 


308.5 


14.8 


72.1 


29.6 


— 


40 


65.7 


72.3 


78.7 


85.2 


91.7 


98.2 


304-6 


II. I 


17.6 


24.1 


85.9 


48.1 


— 


350.0 


73.3 


80.1 


86.7 


93.4 


300.0 


306.8 


13-3 


20.0 


26.7 


33.0 


99.8 


66.0 


— 


60 


80.9 


87.9 


94.6 


301.5 


08.3 


15.3 


22.0 


28.9 


35.8 


42.6 


S13.7 


85.2 


-~ 


70 

( 


288.S 


295.6 


302.6 


309.7 


316.7 


323.8 


330.7 


337.8 


344.8 


3SI.8 


S27.6 


703-6 


— 


80 


96.1 


303.4 


10.5 


17.8 


20.0 


32.3 


339-4 


46.7 


53.9 


61.1 


41.5 


22.2 


— 


90 


303-7 


Xl.X 


18.5 


25-9 


33.3 


40.7 


48.1 


55.5 


62.9 


70.3 


55.5 


40.6 


"■"■ 


400.0 



538 



OFFICK PRACTICE 





a 


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o 

H 




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w 

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1 


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1 


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lOvO t>»00 On 



OVERHAUL 539 

Overhaul. — If dirt must be hauled more than a stated distance 
(free haul) to place it in fill, the additional distance is called over- 
haul and is paid for at an agreed rate; the amount of overhaul is 
estimated as the (number of cubic yards that have to be overhauled) 
X (the distance beyond the free haul expressed in stations, that is 
units of loo ft.). That is, if 20 cu. yd. had to be hauled 3000 ft. 
when the free haul was 2000 ft., the overhaul would be expressed 
as 10 stations X 20 yd. 

Overhaul is to be avoided if possible, as it is a source of dispute 
between Contractor and Engineer. Where necessary it can often 
be computed from an inspection of the earthworks computation 
sheets. If the cut from which the dirt is drawn is short and well 
defined and the fill to which it is taken is likewise well defined, the 
position of the centers of gravity of both cut and fill can be located 
sufficiently close by inspection; however, if two or three cuts are 
hauled to one fill or one cut to more than one fill, the amount and 
length of overhaul can only be determined with accuracy by means 
of a mass diagram. 

In Fig. 132 an earthwork chart is given which was prepared for 
the Batavia-Buffalo road. State Route 6, Sections 10 and 11. 
This chart gives amount, location, direction, and length of haul 
for excavation at a glance, and as an example of overhaul has 
been illustrated on the diagram this will indicate the method. 

Explanation of Fig. 132, page 541. — i. The horizontal scale rep- 
resents stations along road: in this case 5 stations or 500 ft. to 
the inch. 

2. The vertical scale represents the algebraic sum of the exca- 
vation and embankment on whose vertical the amount is plotted. 
In this case 200 cu. yd. to the inch. 

3. Reading from left to right, all ascending lines indicate amount 
and location of excavation; all descending lines indicate amount 
and location of embankment. 

4. All embankment quantities in each balancing section were 
multiplied by the factor written above that section as "Balance 
Used." 

5. The excavation and embankment quantities at each station 
were added together algebraically, after the embankment quantities 
had been increased as specified; the algebraic sum so obtained was 
then added algebraically to the sum similarly obtained from pre- 
vious sections. 

6. This diagram indicates the amount of material that should 
be excavated or deposited at each station. 

7. The diagram indicates the direction of haul. 

8. To compute overhaul consider the section A B C D E A. 
Suppose free haul is to be 500 ft. Find where a line 500 ft. long 
will fit the section. B D is such a line. The material above B D 
will be hauled free. 

On material A B there will be paid overhaul. The average 
distance the material A B will be hauled will be the distance 
between the centers of gravity oi A B and D E respectively. 



S40 



OFFICE PRACTICE 



Let X represent that distance. Then X minus 500 ft. equals 
the average length of overhaul. 

9. The overhaul can also be computed from the area of the 
section A B D E A; this area represents the product of the material 
excavated in yards and. the distance hauled. Find the area of the 
section A B D E A by a, planimeter or otherwise. This area will 
be expressed as yard stations, and when divided by the ordinate 
G B in cubic yards will give the length of haul in stations. 

Suppose the area A B D E A equals 2.5 square inches. Each 
square inch represents 200 cu. yd. X 5 stations, or 1000 sta. yd. 
Therefore, an area of 2.5 square inches would represent 2500 sta. 
yd. According to the diagram the total amount of dirt hauled 
equals 280 cu. yd. as measured on the ordinate GB, Therefore 

the average haul for this 280 cu. yd. equals -^-7; \ = 8.9 

280CU. yd. 

stations. 

The free haul equals 500 feet, or 5 stations, therefore the overhaul 

equals 8.9 — 5 = 3.9 stations. The amount of overhaul equals 280 

cu. yd. X 3.9 = 1092 sta. yd. 



Table 43.^ Giving the Number of Pounds of Stone per 

100 Feet of Road for Different Depths of Loose 

Spread and Different Weights of Stone 







12-FOOT 


ROAD 






Weight of 

1 cu. yd. 

Stone, Loose 

Measure 


Depth of Loose Spread 


2|- 


3i- 


3|- 


5i'' 


6^" 


2250 
2300 
2350 
2400 

2450 
2500 
2550 
2600 


^20,800 
21,300 
21,800 
22,200 

22,700 
23,200 
23,600 
24,100 


26,000 
26,600 
27,100 
27,700 

28,200 
28,800 
29,400 
30,000 


32,300 

33>ooo 
33,700 
34,400 

35,200 
35,900 
36,600 
37,300 


43,700 
44,700 
45,700 
46,700 

47,700 
48,700 
49,600 
50,600 


54,200 
55,300 
56,600 
57,800 

59,000 
60,200 
61,400 
62,600 



1 Note. — The quantities in this table are figured by slide rule but are sufficiently 
close for the purpose to which the table is put. 



MASS DIAGilAM 



541 




O a «9 



542 



OFFICE PRACTICE 







Table 43. 


— Concluded 




14-FOOT ROAD 


Weight of 




Depth of Loose Spread 




I cu. yd. 
Stone, Loose 






















Measure 


2h" 


3i" 


zl" 


S\" 


6^- 


2250 


24,300 


30,400 


37,700 


51,000 


63,200 


2300 


24,800 


3 1 ,000 


38,500 


52,200 


64,600 


2350 


25400 


31,700 


39,300 


53,300 


66,100 


2400 


25,900 


32,400 


40,200 


54,400 


67,500 


2450 


26,400 


33,000 


41,000 


55,600 


68,900 


2500 


27,000 


33,700 


41,800 


56,700 


70,300 


2550 


27,600 


34,400 


42,700 


57,800 


71,600 


2600 


28,100 


35,100 


43,500 


59,000 


73,000 






15-roc 


)T ROAD 






2250 


26,000 


32,600 


40,400 


54,700 


67,700 


2300 


26,600 


33,200 


41,300 


55,900 


69,200 


2350 


27,200 


34,000 


42,200 


57,200 


70,800 


2400 


27,800 


34,700 


43,100 


58,400 


72,200 


2450 


28,400 


35,400 


44,000 


59,600 


73,800 


2500 


29,000 


36,100 


44,800 


60,800 


75,200 


2550 


29,500 


36,900 


45,800 


62,000 


76,700 


2600 


30,100 


37,600 


46,700 


63,200 


78,200 






16-FOC 


)T ROAD 






2250 


27,800 


34,700 


43,100 


58,400 


72,300 


2300 


28,400 


35,500 


44,000 


59,600 


73,900 


2350 


29,000 


36,300 


45,000 


60,900 


75,500 


2400 


29,600 


37,000 


45,900 


62,200 


77,200 


2450 


30,200 


37,800 


46,900 


63,600 


78,700 


2500 


30,900 


38,600 


47,800 


64,900 


80,300 


2550 


31,500 


39,400 


48,800 


66,200 


82,000 


2600 


32,100 


40,100 


49,800 


67,400 


83,600 



QUANTITIES 



543 



Table 44^ Giving the Number of Cubic Yards of Macadam 
PER 100 Feet of Road for Different Widths and Depths 





Dkpth 


Width 




of 
Macadam 






















2" 


2\'^ 


z" 


zY 


Ar" 


S" 


6* 


1" 


10' ... . 


6.17 


7.71 


9.26 


10.80 


12.34 


15.43 


18.52 


21.61 


12' .... 


7.41 


9.26 


11. 11 


12.96 


14.82 


18.52 


22.22 


25-93 


14;.... 


8.64 


10.80 


12.96 


15.12 


17.28 


21.61 


25.92 


30.25 


15' .-.. 


9.26 


11.58 


13.89, 


16.20 


18.52 


23.16 


27.78 


32.41 


16' .... 


9.88 


12.35 


14.81 


17.28 


19.76 


24.70 


29.63 


34.57 


18' .... 


II. II 


13.90 


16.67 


19.44 


22.22 


27.79 


33.34 


38-89 


20' .... 


12.35 


15-44 


18.52 


21.60 


24.70 


30.87 


37.04 


43-21 


i22' .... 


13-58 


16.98 


20.37 


23.76 


27.16 


33-96 


40.74 


47.53 




Table 45 


: Square Yards per 100 Feet and per Mile for Different 






\ 


^^IBTH 


OF SUI 


IFACE 









Width 


Number of Square Yards 


Width 


Number of Square Yards 


in 
Feet 


Per 100 Feet 


Per Mile 


_ Feet 


Per 100 Feet 


Per MUe 


8 
10 


88.889 
III. Ill 


4,693 
5,867 


26 
28 


288.889 
311. Ill 


15,253 
16,427 


12 
14 
15 


^33-333 
155-556 
166.667 


7,040 
8,213 
8,800 


30 
32 
34 


333-333 
355-556 
377-778 


17,600 
18,773 
19,947 


16 
18 


177.778 
200.000 


9,387 
10,560 


3(> 
3^ 


400.000 
422.222 


21,120 
22,293 


20 
22 
24 


222.222 
244.444 
266.667 


11,734 
12,907 
14,080 


40 
42 
44 


444.444 
466.667 
488,889 


23,466 

24,640 

25,813 
> 



j The other quantities figured are: length of road in miles. Table 
I 42 converts lineal feet to miles. 

Quantities of macadam, sub-base, concrete paving foundations, 
square yards of resurfacing, which are simple computations involv- 
ing length, width, and depth: Tables 43, 44 and 45 can be conven- 
iently used. 

Quantities of oil or other surface or penetration treatments, which 



544 OFFICE PRACTICE 

are usually specified as gallons, per square yard : Table 46 is devel- 
oped with this in view. 

Concrete for culverts or retaining walls. Where a large amount 
of work is done it generally pays to compile a table of quantities 
for standard culverts of different sizes and lengths. The quan- 
tities can then be picked from these tables sufficiently close for a 
preliminary estimate. There would be no object in including in a 
book of this character any table suitable for certain culverts, as each 
department has a different standard. 

Expanded metal and reinforcing bars, Tables 47 and 48 cover 
these features. 

Weights of cast-iron pipe: Table 49 can be used. 

Incidentals requiring ordinary arithmetical computations only. 

The quantity estimated being completed, the estimate of cost is 
made. This is considered in chapter XIV. 

Final Design Report. — On the completion of the design a report 
of this nature is filed for reference. 

Rochester, January 31, 191 6 

REPORT ON DESIGN AND ESTIMATE 

of the 

VARYSBURG- WARSAW PART II COUNTY HIGHWAY 

No. 1349 

WYOMING COUNTY 

(FORMERLY known as the Orange ville- Warsaw Road) 

Length, 4.74 Miles 

Tjrpe of Construction. — Top: From Orangeville Center to 
Corporation line Village of Warsaw (Sta. b + 00 — 249 + ^57) 3" 
waterbound macadam 14' wide. Imported limestone top and 
screenings, surface application of calcium chloride using 2 3^# per 
sq. yd. in two applications. 

Bottom: Orangeville Center Sta. + 00 to corporation line 
Village Warsaw Sta. 249 + 57, 5'' macadam 14' wide. Screened 
gravel local. 

Section: 26' wide with 18'' ditch. 

Estimated Cost $49,858.00 

Engineering and Contingencies 5, 042.00 

$54,900.00 
Cost per Mile $11,600.00 

Survey. — By H. TenHagen, rodman, Spring, 191 5. Weather 
conditions favorable. 

Design. — By F. W. Mills, Leveler. 

Field Inspection. — Bv George A. Wellman, County Assistant; 
F. W. Mills, Leveler, 



DESIGN REPORT 545 

Estimate. — By George A. Wellman, County xAssistant; George 
G. Miller, Chief Draughtsman. 

Status and Connections. — This road is a section of the old 
Cherry Valley Trail which is claimed to be the shortest highway 
between Buffalo and New York. It is the beginning of a system of 
improvements to connect the western part of Wyoming County 
with Warsaw. At Halls Corners (Sta. 145 + oo) it will connect by 
a proposed County System road with the east end of C. H. 1267. 
With the proposed Varysburg- Warsaw Part I Road and proposed 
Route 19 it will connect with Route 16 already built. It will also 
connect with the proposed County System road south through 
Johnsonburg, North Java, to Arcade. 

Foundation Soil. — Is for the most part clay loam and is very 
unstable when wet. This calls for an unusual estimate for sub-base. 

Traffic. — The heaviest traffic is eastward and down hill. It con- 
sists principally of wagon hauled farm traffic. There is considerable 
automobile traffic both ways. This will greatly increase as the high- 
ways West toward Buffalo are improved. 

Grades. — The ruling grade for eastbound traffic is 8% between 
Sta. 23+00 and 29 + 00. The ruling grade in the opposite 
direction is a short 8.54% at Sta. 149. 

Alignment. — The alignment is generally straight and curves easy. 
The minimum radius is 573' at Sta. 162 +00. 

Right-of-way. — No land taking is necessary. 

Tjrpe of Metaling. — The bottom course throughout the entire 
length of the road is to be of screened gravel as per B. R. sample 
G-2095 5" deep, to be obtained on the property of Henry Roth, 
one mile south of Sta. 145 + oo^ 

Top course is to be 3" imported limestone from Buffalo Crushed 
Stone Co. with screenings from same source. 

Drainage. — All existing culverts have been replaced by either 
concrete or cast-iron pipe structures. The former have been given 
■ preference wherever head room permitted. 

I The bridge at Sta. 15 + 40 is to be rebuilt by the Town of Orange- 
ville and that at Sta. 175 + 19 by the Town of Warsaw. 

MATERIALS 

j The materials suitable to be used in the work have all been tested 
and accepted by the Department. The filler for the bottom course 
j to be the fine material screened out at the pit. 

Sand for use in concrete has been accepted from the Roth pit, 
I one mile south of Sta. 145 + 00. 

' Unloading Points. — Erie R. R. at Warsaw Station siding, 1200' 
] from Sta. 249 + 57. Respectfully submit'ted, 

1-^ Perry Filkin, 

j^^ Division Engineer 

H. CONSTRUCTION PLANS 

^^^he construction plans should give sufficient information to show 
^ the contractor what he is expected to do and to enable the con- 
' structing engineer to stake out and to build the road. 



546 



OFFICE PRACTICE 



A finished set of plans consists of a map, profile, and cross-sections 
showing the alignment in relation to the preliminary survey line, the 
proposed grade elevations, the shape of the finished road, the widths 
and depths of road metaling, the crowns to be used, the existing 
structures and the proposed structures, and all the minor points of 
design. Each Department has its own method of giving this 



Pig. 133. 

information, and it makes little difference how it is shown so long 
as it is complete and clear. In general it may be said that the 
scales used are the same as in mapping the preliminary survey 
and that the size of sheets or rolls must be convenient to handle in 
the field; sheets larger than 24" X 30" are clumsy. 




Miscellaneous Points. — A point often overlooked in laying a 
grade line is the proper approach to a railroad grade crossing where 
the track is on a curve and has a superelevated rail. Where the 
road grade is level, or nearly level, the solution is comparatively 




Pig. 134. 

simple, as shown in Fig. 133; but where the grade of the road is in an 
opposite direction to the elevation of the rail it is more difficult 
and sometimes impossible to make an easy riding crossing. 

Also, where a road, on a steep grade, crosses the railroad track 
on a large skew angle, care must be taken to flatten the grade near 



GRADE CROSSINGS 



547 



the track to avoid distorting the road section due to the difference 
in the rate of grade of the track and road. See Fig. 134. 

Grade Crossing Eliminations. — In grade crossing elimination 
designs the following minimum clearances have been adopted, Div. 
5, N. Y. S. Dept. of Highways. 

Where a highway is to be built under a railroad the crown eleva- 
tion is made 13.5' below the bottom of the bridge girder, and the 
minimum right-angle distance between abutments is taken as 26 




548 



OFFICE PRACTICE 



feet. For solid floor railroad through girder bridges a clearance of 
13.5' below the bottom of the girder means a distance of from 16.5' 
to 17.0' below the top of the rail. 

The tables (pp. 547, 548) are taken from Spofford's "Theory of 
Structures," and a pamphlet issued by Heath & Milligan, of 
Chicago. They show the approximate weight of through girder 
railway bridges with the depth of floor system. They are useful 
for preliminary estimates of grade-crossing elimination. 




GRADE CROSSINGS S4Q 

The -weights given are for the steel only; the weight of the floor 
system must be added. For purposes of a rough preliminary esti- 
mate of cost the superstructure can be assumed to cost $80.00 
per ton in place including all erection costs. 

Where the highway crosses over the railroad a minimum clearance 
of 21.0' is used from the top of rail to the bottom of the highway 
bridge; the span varies with the number of tracks. In determining 
the length required it is best to get in touch with the railroad 
engineers. 

Alignment at Grade Crossings — New York State Regulations 

1. The alignment should be laid out so that approaches are 
on a tangent which is at least 400 feet long, 200 feet on each side 
of the crossing. The angle that the highway makes with the 
railroad should not be less than 60 degrees. The grade of the 
approaches should not be greater than 6 per cent'., and there 
should be a portion level or nearly so for a distance of not less 
than 100 feet on each side of the crossing. 

2. On the highway within 200 feet of the railroad, on each 
side, traffic should have a clear view of approaching trains for a 
distance of 1000 feet. (See Rule 5.) 

3. The width of the planked crossing shall not be less than 
24 feet, measured at right angles to the center line of the high- 
way. The ends of the pavement should be protected by an edg- 
ing of stone or concrete placed at a sufficient distance from the 
ends of the ties to allow for replacing them. 

4. A standard danger sign should be placed at each side of 
the crossing along the highway in a prominent location at least 
400 feet from the crossing. 

5. When the view of the railroad either way, as required in 
2, is less than 1000 feet, or when there is a great deal of traffic 
on either the highway or railroad, or when vision may be blocked 
by cars or trains as in the case of a railroad with two or more tracks, 
a flagman should be employed to warn highway traffic. 

Right-of-Way Computations. — The form of traverse computa- 
tion and closure was shown on page 334. 

The areas of rights of way are generally figured by dividing the 
parcel into rectangles, trapezoids, triangles, sectors, or segments, 
and figuring these shapes from the formulae given in Table 70. 
These areas are checked by planimeter. They are usually figured 
to the nearest o.oi acre. 

The method of double-meridian distances can, however, be used 
if desired. The following formula and example are given to illus- 
trate this method. It is not often necessary and is a tedious 
computation : 

The rule is: 

Twice the area of the figure is equal to the algebraic sum of the 
products of the double-meridian distances of each course multiplied 
by its latitude. 

In which the double-meridian distance equals the sum of the 
meridian distances of the two ends of each course referred to the 
meridian drawn through the most westerly point of the parcel, 



550 



OFFICE PRACTICE 



3 



CO 
CO 

J^ 

bo 
VO 

E 

.s 

c 

rC5 






(X 

B 
o 



o 

n 

O . 

B ^ 



H 



1 


1 :ii 1 

On 

M 


2 


CO CX) PO 

M I CO S 
00 CO 


Q 


VO lo oj 

00 6 d 00* 

(N CS to lO 

O lo to 


3 


T^ CO <N q 

lO CO t^ M 

vO On to t^ 
M 

+ 1 ++ 


^ 


lO cq 

1 1 CO to 

Tf to 


W 


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o6 4 1 1 

ON 


C/D 


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1 p 1 


^ 


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to t^ M 

VO ' to t^ 


s 


H COOC) C^* 

t^OO COVO 

Ov Tf tr> 


.1 


^0 "o ""0 "lo 

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o o O o 

COOO M C^ 
W t-*00 00 


O 3 


H o) CO T^ 



;^ «i 



':.<u 






r^ u 





^ s 


II ^ 


t>. 


. <1> 


o 


^^ 


II 




6^*0 




O 


d 




lO 


to »H 


M 
H 


CO 


M C^ 


x>. 


o" <1^ 


VO 


X 


co^ 




01 



I S II 



. CO 

^§ 

CO O" 
vO <U 






rn < 



CROWNS 



S5I 



and the latitude of each course is reckoned as plus if the course 
runs north and minus if it runs south. Take as an example the 
right of way parcel shown in Fig. 69, page 334, for which the traverse 
has been figured and refer the meridian distances to the meridian 
drawn through the corner 3.1' distant from station 194 + 71.7. 




Parabolic Crowns for Pavements. — It is often convenient to 
have the following data on parabolic crown ordinates in making 
templets for pavement work. 

Divide the distance from the center of the road to the curb or 
edging into ten equal parts and call the total crown i.o; the dis- 
tance down to the surface of the pavement from the crown elevation 
at each of these ten points expressed in terms of the total crown will 
be 

Center of Road, point No. o o . 00 

I o.oi 

2 0.04 

3 0-09 

4 0.16 

5 0.25 

6 0.36 

7 0.49 

8 0.64 

9 0.81 

Curb point 10 i .00 



PoirrHO 



Curb 




552 OFFICE PRACTICE 

Summary of Points to be Considered in Making an Economical 

Design 

Justifiable economy in grading is largely limited to the inter- 
mediate grades and to variations in the cross-sections. A well- 
designed road in these particulars may easily save $700 to $900 per 
mile over a careless design. 

Economy in widths of hard paving is attained by the selection of 
a width suitable to each particular road or part of road. A uniform 
width of 16 ft. for all roads is unnecessary and a waste of money 
both in first cost and in maintenance and renewal. For class I and 
II traffic nothing less than 18' or 15' should be considered; for 
class III and IV the widths may vary from 10' up. The cost per 
foot width per mile for different types is approx. as follows: 

Type of Road First Cost per 

foot width per mile 

Brick $1200 

Asphalt HOC 

Concrete 950 

Bituminous Macadam 750 

Waterbound " 650 

Economy in foundations is limited to utilizing local materials to 
their best advantage with short hauls. 

Economy in top courses lies in the selection of the cheapest type 
suitable to the traffic conditions and the use of the minimum 
thickness. 

Economy in maintenance is attained by preventing rather than 
by repairing damage. 



OIL QUANTITIES 



553 



1 

1 

g 

1 

n 

g 


d 


80.00 
100.00 
120.00 
140.00 
150.00 


160.00 
180.00 
200.00 
220.00 
240.00 


260.00 
280.00 
300.00 
320.00 
340.00 


88888 
v2cg8S^ 

tOtO '^''f ^ 


00 

d 


M On t>- •* to 
H 00 vO -^ to 

Hod vd ■4 fo 
t^oo M to 

M H M 


N OOOvO to 

cj q t>- *9 to 
w d i>- >o to 

Ttvo t^ a M 

M M H H Ci 


H Ov t^ ■<+ M 

M 00 vq Tj- <s 
Modvd 4 ci 

to ^vOOO 
W W Pt « to 


OoOvO CO »-• 

q t^ to CO M 

d t^ to to H 
« CO to t^ Oi 
CO to to CO to 


d 


C<00 to OM^ 
W t>. tOOO VO 

cJ t^ tood vd 

NO I^ M 


Tl- OVO M t^ 
Tt to MVO 

4 d to M vd 

d rt to 1>.00 
H H H H H 


woo CO 0> •* 
CS t^ COOO Tj- 

pi t^ rood 4 
w CO "*vo 
W W W CS M 


QvO M t^ « 

to MVO W 

d tA H vd « 

00 0> M « •»t 
W « CO to CO 


d 


d> ■4od to M 

to t^OO H 
H H 


N to to t^OO 
to to H Ov t^ 
od tood <N t^ 
w CO "<tvO t^ 


vq ^ w q 00 

Ov P» CO to 


r^ 0. M M 
vq rl- to M q 

vd M vd M to 

VOOO M « 
« W « CO to 


6 


to t^ (O 

too to q 
tovd d to d 

lOvOOO 

H 


t^ CO t>- 

VO covq q 
-vd d tcvd d 

<N CO -^vo 


CO t^ to t^ 

covq q tovq 
covd d tovd 
t-*oo M P< 

M M <N N CS 


8 ^vq q ^ 
d covd d CO 

Tf tovOOO 
P< C« M PI W 


d 


4 vovd t^ to 

Tj-»0\0 t^OO 


0> H <M to 

00 q H w CO 

od d H CN to 

00 H C» CO 

M H H H 


rfvo t^OO Ov 

-^ tovq t^oq 
rf tovo r>-oo 


200.00 

211. II 
222.22 

233.33 

244-44 


d 


VO ■* to <N 1^ 

»o ^ to <Nvq 
»o ■4 to cJ vd 

to ^«OvOvO 


M OvOO t^ 
W 000 t^vO 

M 


VO rh CO <^ M 

to -^ CO <N M 
to 4 to <N M 
M <N CO Tj- to 


dod t^vd 10 

vOvO t-00 





to "^ ID lOvO 

vq q -=1-00 »o 

W to "* 10 10 


VO t^ t-OO 0> 


Ov W M t^ 


CO CO -rl- tovO 
CO !>. M to q 

CO d od »A pJ 

CO -^ Tj- tovO 

M H M H M 


'^^^crXi "too 
Oi^o 4 M od 

tovO t^OOCJO 


<N t^ M to q 
vd CO M od to 





t^ to r^ 
vd fo dvd d 

«S to ''t ■<+ »o 


CO t^ CO 

to OvO CO 

J^^vS^S^cg 


t^ CO t^ CO 

vq CO qvq to 
vd CO dvd to 
00 o* H 


i^ to t^ 

q vq CO qvq 
6^ fr> 6'-6 

P< P« CO "^ ■^ 


d 


N tN. to OM>. 

« t^ rood M 
<N w to to "<t 


"+ VO H t^ 

•"t q to Mvq 
4 d to Mvd 

rf to tovOvO 


« 00 CO o> ■* 
w j>. cooq rt 
N !>. cood 4 

t^ t^OOOO 0* 


Q VO M t^ p* 

6 VOMVO P» 

d tA> Mvd N 

2 2 H H H 


6 


00 w r^ M to 
t^ <N vq M to 
t^ M \d M to 
M w « to to 


^8?c?? 

to d 4od CO 

to '^ rl- Tj-lO 


00 P< t^ HVO 

t^ «N vq M to 
t^ c^vd H to 
lovo VO t^ t>. 


q -^00 CO f^ 
d 4od CO t^ 
000000 Ov o> 


H 

6 


o» M tovO t^ 
00 M to>ovq 

od M to tovd 

M M H M 


00 p» "^t^. 
t^ d w 4vd 

M M 0» W M 


0> M fOvOOO 

00 H CO to tv. 

od M CO to f4 

« CO CO CO CO 


Q M *0vO 

q M CO tooq 
d H CO tood 

Tt Tt t '=i- -* 


1 


^1 


00 w rtin 

M M M M 


VOOO M Tj- 
M M tN « CS 


VOOO <N '* 
W cs CO to CO 


VOOO M -^t 
CO CO •^ -"t Tf 



554 



OFFICE PRACTICE 



I 

O 

hH 
H 

< 

U 

M 

»-; 

PM 

•< 

s 






P4 
O 

Q 

O 

o 






Z 
O 

)-) 
< 

o 



s 

H 

-< 
& 
C 

CO 

M 

S 

o 

H 
w 

s 

o 

g 
12; 


00 
M 


160.00 
200.00 
240.00 
280.00 
300.00 


88888 
8j8$=g 

CO to ^ -«<• ^ 


520.00 
560.00 
600.00 
640.00 
680.00 


720.00 
760.00 
800.00 
840.00 
880.00 


M 


M t^ Tj-fO 

MOO VO Tj- CO 

MOO vd 4 fo 

1000 c^OOO 


W OoOvO to 

cj q t^ 10 CO 
«N d f^ »o to 

-^ t^ M to 

CO to to -* Tf 


M 0> t^ Tt- M 
M 00 VO --t «H 

m' 00 vd 4 cJ 

<NVO Tt 
rt 10 lONOvO 


QOO VO to M 
q r>. to CO M 

00 M to 0\ to 
VO t>. t^ t^OO 




»0 Ov N t«^ 

00 10 ts d tC 

^00 <N liO t^ 
H M W « c< 


tOt^ M Tt- 

to to to Tt •"t 

sd to d t^ 4 

Ov to r-. ■* 
<N CO to 'it 't 


00 M 1000 N 
Tt to 10 tONO 

H M 10 pi d 
00 00 to Ov cs 
Tj- to to tOvO 


t^ tooo M 

Nq t>. t;. t^oq 
vd fp d t^ 4 

VO -"t l^ M 
NO t^t^ t^OO 


H 


NoO to 0> r^ 
<M r^ tooo VO 


T}- Q VO M t^ 

4 d »o Mvd 

00 rs 10 0> <N 
<N CO to to ""t 


NOO to 't 
CJ t>. COOO ""t 

c^ t^ tood 4 

NO Ov fOvO 
•<t rt to lOvO 


QvO M t>- W 
to MNO c« 

d tA M Nd c^' 

Tf r^ M "^00 

NO VO 1^ t-- t^ 


*? 


»0 t^ Q to Q 
fovo to q 
*ovd Q to d 

COvO to VO 
M M CS M CS 


r^ Q to t^ 

NO tovq q 
vd d tovd d 
VO too 

CN CO to to Tt 


CO t^ Q to t^ 

covq tovq 
tovd d tovd 

tOvO tONO 

Tt Tt to to to 


Q to t^ Q to 

q cono q CO 
d tovd d to 
toNO to 

NOvOvO t^t^ 




Tj-vo r-oo to 

^ lOvO t~- to 
rj- »o\d t^ to 

CS VrOO M fO 
M M M <N tM 


0» Q •-< <N CO 

00 q M p< to 

06 d m' r! CO 
•^00 M Tt 1^ 
CN CS CO to to 


rj-vo t^OO 0> 
Tt lONO t^OO 

4 toNd t^oo' 

tONO On M 

•* ■^ ■* ■* »o 


Q M W to Tt 

q M cj CO Tt 

NO 0- cl JoOO 
to lOvO NO vO 


to 
to 


N 1000 M (M 
lOM t-.Ttc^ 
00 00 t^ *^ N 


^l^ tovO 

q vq to q> up 
f^vd vd 10 10 
COVO a (N »o 

M M <N to to 


a «>« Tfoo M 
MOO "^ q t>. 
to 4 4 4 to 
00 M rt t^ 

CO 't -^ ■^ »0 


CO r^ c< to 

CO <><> CJOO 
CO cs pI cJ m' 
COVO Ov c>» to 
10 »0 tONO VO 


fO 

M 


VO -* to ts r^ 

»0 -^ CO (S VO 
to 4 to <N vd 
M Tt t^ M 
M M M <N CS 


M 00 l^vO 

M dod t^vd 

tOvOOO M Tt 
M <N CI to to 


NO Tf ro N M 
to "^ CO C< M 
to 4 CO <S M 

t^ tOvO o» 
to -* 't ^ ^ 


Q 000 l^vo 

000 t>.NO to 

doo* t^Nd tA 

W rl- t^ to 
10 to tONO VO 


H 


M 0> t^ rf to 
M 00 VO Tj- to 

Modvd 4-od 
M fovo o> 

M M M M W 


W 000 VO to 
W t^ to to 

<N d t^ »A to 

M »0 t^ to 
W CS CS to CO 


H M t^ t}- C« 

HOOVO ^ <N 

CO to 't -"t --t 


000 NO CO M 

q t;. to CO M 

d t^ to CO H 
<v« tooo M 
10 to to lOvO 


M 


t^ to i^ Q 

vq to qvq q 

"o ^vooo 

M M M M <N 


to Q t^ to Q 

to qvq to q 
to dvd CO d 

M '^VO Ov M 
W CS CS Cv« CO 


t>. CO t^ to 

NO to q VO CO 
vd to dvd to 

CO to Tf ""t rt 


t^ to 1^ 

qvq CO qo 

00 CONO 00 
•^ to to to to 


M 
H 


00 N t>. H to 

t^ cjvq M to 

t^ <Nvd M to 

0> «S Tft>.00 
M M W H 


VO -* Ov ro 
to -^00 to 

to d 4o6 to 

M <N C» W <N 


00 N t^ MNO 
t;. CSNO M to 
t"^ C^vd M to 
M Tj-vo 0^ M 
CO to to to 't 


Q rfOv tooo 
-^00 CO t>. 

d 4oo* toiA 

tJ-nOOO m CO 
rj- -"t •^ >0 to 


2 


0> M tovO l^ 

00 M to lovq 
00 M to tAvd 

00 H to lOvO 
M M M M 


00 N '^ l^ 

!>. q <N Tj-vq 
t-^ d <N 4vd 

t^ <N rl-vO 

M <N ^^ CH <M 


Oh COVO 00 
00 M to to t>. 

06 H to to t^ 

00 M CO to t>. 

W to to to to 


Q W •^ »^ 0» 

q (N -^Nooq 
d «N 4vdo6 

M -^VOOO 

"t Tt '^ Tt Tt 


Width 
in 


(2 


00 « ^to 

^ M M M M 


NO 00 N rt 
H H (N CS C4 


vOOO N •* 
C» W CO CO CO 


'^'^^^^ 



EXPANDED METAL 



555 



1 

k 

< s 

2c/3 

< 


Weight 

in Pounds 

per 

Sq. Ft. 


OvvO -^ On •^ O t^ lO M t^vo "*vO 

o 00 vo M -^ <N CO looq q fooq cj 
oddoodoooMMOM 




Note. — Expanded metal for small 
culverts is generally specified as 
weighing a certain number of pounds 
per square foot and having a mesh 
approximately the size shown on the 
plans. 


Sectional 

Area in 

Sq. In. per 

Foot of 

Width 


(NNMOwOMMCJrO'^f^rO 

ddddddddooood 


1 
'in 


H «^ COO CX3 OO 00 00 OO 00 00 «^ <N 

xxxxxxxxxxxxx 

Hlnnh* M <N cocOfO^OcOfO coO O 


U.S. 

Stand- 
ard 
Gauge 


OOMf^OvOOcsOOOt^'^'^ 


o 
< 

H 

w 




66666666666 


No. of 
Sq. Ft. 

in 8' 
Bundle 




No. of 

Sheets in 

Bundle 


1010»OU->0 lOlOlOCO^O COO »0 CO 
H 


0) 


*CJ *CN *<N "cN *N *<N *<N %S ^^) "(N .^ <N CS 
^MMHMHMMMHWO^MM 

Xooooooooooooo 

OoOOOOOOOOOOOOOOOOOOO 000000 

S xxxxxxxxxxxxx 

coo ■^invOvOvO "^l-O lo »o •^ lo «o 









1 


xxxxxxxxxxx 

COCO<NCS<N<NHHMHM 




Weight 

per 
Sq. Ft. 


rtOOOOOOOOOOOt^cN -tvO 
r^OO t^ »^ «^ »^\0 On <N CO q -^00 « 


Section 

Area per 

Foot of 

Width 


On »o i^vO cooO 00 t^O O O CO irioO 
O <N O VO 00 ^ t^O lO O O On rJ-vO 

«S<N<NMOMMC»CO -^O q <^i fO 

66666666666666 




Standard 

Light 

Standard 

Heavy 

Ex " 

Standard 

Heavy 

Old Style 

Standard 

Heavy 


1 

6 


O <N O N ^^VO ^ ^ ^ ^ JJ 


II 


00c00»«^O0000Ov0vO'^^ 

1 


1 

« s 


Hf^n-^-HN ^ fr>cocOcocOtOfO ^O O 



;s6 




OFFICE PRACTICE 






Table 48. Table of Round and Square Bar Weights 




Round Bars 


Plain Square Bars and Twisted 
Square Bars 




Diameter 


Area 


Weight 


Dimension 


Area 


Weight 




i 


.0491 


.167 


i 


.0625 


.212 




A 


.0767 


.261 


A 


.0977 


•332 




f 


.1104 


.376 


1 


.1406 


.478 




j\ 


•1503 


.511 


A 


.1914 


.651 




i 


.1963 


.668 


2 


.2500 


.850 




A 


.2485 


.845 


? 


.3164 


1.076 




f 


.3068 


1.043 


5 
8 


.3906 


1.328 




ii 


.3712 


1.262 


H 


.4727 


1.607 




i 


.4418 


1.502 


i 


.5625 


1-913 




H 


.5185 


1.763 


11 


.6602 


2.245 




i 


.6013 


2.044 


1 


.7656 


2.603 




U 


.6903 


2.347 


a 


.8789 


2.988 






.7854 


2.670 


I 


1. 0000 


3.400 




15 


.9940 


3.380 


ii 


1.2656 


4.303 




I4 


1.2272 


4.172 


ii 


1.5625 


5.313 






1.4849 


5.049 


If 


1.8906 


6.428 




^2^ 


1. 7671 


6.008 


ij 


2.2500 


7.650 





Diameters expressed in inches. Areas expressed in square inches. 

Weights expressed in pounds per foot of length. 

The twisted square bar is known as the Ransome Bar. 



RansomeBar. 



Kahn Cup Bar. 



Corrugated Bars. 
Diamond Bar. 



ThacherBar. 



STEEL BARS 



557 





c 
Pi 

Z 
& 

5 

o 
< 

< 
g 


1 

P 


1 


CSOOlOfOMOO tH 

<N '^00 CO o^^q "<^ CO 
dddwH csco to 




< 


c^ H O w CO^O O CO 
OM<NcOtOt>.0 to 

d d d d d d H h 




1 
1 


s 


VO Tt-M toGvl:^MvO rf 

M covq qv fooq ^ o ^ 
ddddiHHcicoco 




1 


Tl-OOOOOHIOHOO 
O MM (N rJ-lO-t^OvM 

66666666^ 




12 

1 

6 




KO CO to to vO 
00 Ov^ -^ CO 
d M cJ CO ^ 


00 


< 


to VO t>. O vO 
Ol lO tN. o to 

d d d H M 


a 
1 


1 


1 


c^<sOOOOOOO 
oi Ovt^to'itrt-toiO^"- 

^ ri-oq CO qvvq "^ ^ ^o 
dddHMoJco'^io 




c3 
(V 

< 


tovo O VO tovO O VO to 
csOOOcNtoOto<N 

VO Tj- to QvvO vO O vO vO 
O M cs cotot>»0 csvo 




t-l 

a 
M 
a 

u 


1 


<N CO tJ-oO CO O 00 CO 
O OvOvO coi>>M t^ 

tooq CO q '^ ^^ ^ 

ddHC^CSCO"<^tO 




< 


VO O vO tovo O VO to 
000<NtoOtoc» 

Tf to O^VO VO O VO vO 
M cs cotot^O csto 
OOOOOmmm 






H-*«laoHN«n|«n|'*«-|(» H|aOf-i|'* 
M M M 



.558 



OFFICE PRACTICE 



it 


1 

pin 

H 


1 


1 


MD p o o o 


O O O O O 
O to O O lo 

<N^ to q; CO t>. 

H M M CS W 


=88888 

CO vo t^ O^ cT 


1 


q q cooo t^ 

CXD lOCXD voO 
H <N CO to t^ 


O <N CO t^ W 

d doo M 6s 

O <N to On cs 

M t-i i-i t-t C^ 


^ 0. q q 
vd d to to d 

10 M CS to 

CO "^vo 00 0^ 

M 


•as 


00 w to 00 
Ti- lo tovq vo 


to <N OnVO <0 

t->.oo 00 q^ q 


yO t-^00 00 vO 
H CO to t^ 0^ 


> H 

< O 

1 


o 

M 


1 




TO O O lo O 

O OO CO <N lO 
(N (N rtvO OO 


I,IOO 

1,400 

1,725 

2,100 

2,500 


Q Q 
to to 

fOOO^ lOMD^ On 

CO '^VO'OO^ 0" 


1 


■M cooq w 00 

t^ CO to cs 6 

H CS CO to t^ 


t^ t^oO <o 

M vd CO tooO 

On M Tf t^ 

H H H CS 


CS 00 t^ CO 

28^^=8 

CS Tj- 10 t^ On 


ii 


tOOO H VO C< 
rt Tt to tOVO 



00 ""t t^ W 

X^-00 00 OS 


Tj- VO Th H 

^. • ^ ^ *^ 

H M M H H 




1 


R 

1 


J3 


rj- O to 

H Ol ■^ to l>- 


00 CO 

On <N^ to 00^ M^ 


2,800 
4,000 
5,450 
7,100 
9,000 


1 


<N !>. CO tooO 

VO M CO -t^ CO 
M <N CO "^O 


M to q q q 

CS o) to to 
00 c^ to t^ 

H M H M 


CO CO <N t^ 

CO CO -4 M d 

CO CO to On to 
CS CO ■^ to !>. 


it 

e3« 


<N tOOO M f^ 

^ ^ ^ lo to 


<N VO 10 

vO vO X>- <^00 


ON <0 1000 cq 

00 q M CS ^ 


8 

H 


i 

Pi 

§ 
9 


be 

1 




to O O *o to 

r^ ^ t^ H 00 
H <N CO too 


10 Q 
r^ t^ 10 
00 0^ «o ^00^ 


Q 
to 10 

Tt; to !>. H^ q^ 

cs' CO rf NcTod" 


^ 
£ 


to q 00 o H 

rj- 6 d oi !>. 

H cs CO rt" to 


tovq CO <^ q 
CS osod & d 
t-^00 <N to 

M iH hi 


CS !>. t^ to t^ 

rf M H CS 
On On M vo 
CS CS CO tovo 




On C^ "^vO O 
CO -^ 'it '^ to 


rt t^ '^ t^ 

to tovO vO 


NO 00 On NO 

t^OO On H CS 

H H 


l^mraoM 


COTj-vOOO O 

M 


C^ rt-vO 00 

M M M M C4 


rf NO CS 00 
CS CO CO "^ Tf 



CORRUGATED PIPE 559 

Table 50. — Weight of Corrugated Metal Pipe 



1 




Freight Classification 


Diameter 


LrSige ot 

Metal 


Weight per Foot 




1 






Riveted 


Nestable 


12''' 


16 II lb. 


2 


3 


15'' 


16 


i3>^ " 


2 


3 


18'' 


16 


16 '' 


2 


3 


21'' 


16 


18 " 


2 


3 


24'' 16 


22 '' 


2 


3 


30'' 14 


32 


I 


3 


36" 


14 


37 


I 


3 


42'' 


14 


44 


I 


3 


48'' 


14 


51 


I 


3 


Note. — In carload lots the freight classification is No. 4 for 


Riveted pipe, No. 5 for Nestable pipe. 





56o 



OFFICE PRACTICE 



Table 50A. — Approximate Weights, Dimensions, Etc. of 
Standard Sewer Pipe 



Calibre, In. 


Price 


Weight per 


Depth of 


Annular 


Thick- 


per Foot 


Foot, Lbs. 


Socket, In. 


Space, In. 


ness, In. 


3 


$ 0.30 


7 


i3^ 


H 


M 


4 


0.30 


9 


1% 


% 


M 


5 


0.4s 


12 


iM 


% 


5^ 


6 


0.45 


15 


iVs 


ti 


t^ 


8 


0.70 


23 


2 


l« 


M 


9 


105 


28 


2 


t^ 


13-16 


10 


105 


35 


2^ 


yg 


% 


12 


1.35 


45 


2M 


\i 


I 


15 


1.80 


60 


2y2 


yi 


i^ 


18 


2.50 


85 


2^ 


% 


iH 


20 


3.00 


100 


3 


^ 


1% 


22 


4.00 


130 


3 


yi 


i^ 


24 


450 


140 


3M 


^ 


i^^ 


27 


6. 50 


224 


4 


M 


2 


30 


7. 20 


252 


4 


M 


•2% 


33 


9.00 


310 


5 


iM 


2K 


36 


10.25 


350 


5 


iM 


2H 



Double Strength Pipe 



Calibre, In. 


Price 


Weight per 


Depth of 


Annular 


Thick- 


per Foot 


Foot, Lbs. 


Socket, In. 


Space, In. 


ness, In. 


15 


$r.8o 


75 


2% 


}A 


iM 


18 


2.50 


118 


2% 


Vi 


iH 


20 


3.00 


138 


3 


Vi 


1% 


22 


4.00 


157 


3 


H 


1% 


24 


4.50 


190 


3>i 




2 


27 


6.50 


26s 


4 


M 


2K 


30 


7. 20 


290 


4 


« 


^Vt 


33 


9.00 


335 


5 


iM 


2% 


36 


10.25 


375 


5 


iK 


2%, 



Discount about 74% off Standard. 

" 68% off Double Strength. 



PROPERTIES OF I-BEAMS 561 

Table 51. Properties of Cambria Standard I-Beams 



Depth of 
Beam 



Inches 



3 
3 
3 

4 
A 
4 
4 

5 
5 
5 

6 
6 
6 

7 
7 
7 

8 
8 
8 



9 
9 
9 
9 

10 
10 
10 
10 

12 
12 
12 



Weight per 
Foot 



Pounds 



5-50 
6.50 
7-50 

7.50 

8.50 

9-50 

10.50 

9.75 
12.25 

14.75 

12.25 
14-75 
17-25 

15.00 

17.50 
20.00 

18.00 
20.25 
22.75 
25-25 

21.00 
25.00 
30.00 
35-00 

25.00 
30.00 
35-00 
40.00 

31.50 
35.00 
40.00 



Area of 


Thick- 

ness of 

Web 


Section 


Sq. Inches 


Inch 


1.63 


.17 


I.91 


.26 


2.21 


.36 


2.21 


.19 


2.50 


.26 


2.79 


.34 


3.09 


.41 


2.87 


.21 


3.60 


.36 


4.34 


.50 


3.61 


'^3 


4.34 


'35 


5.07 


.47 


4.42 


.25 


5-15 


.35 


5.88 


.46 


5-33 


.27 


5.96 


•35 


6.69 


.44 


7.43 


.53 


6.31 


.29 


7.35 


.41 


8.82 


.57 


10.29 


.73 


7.37 


.31 


8.82 


.45 


10.29 


.60 


11.76 


.75 


9.26 


.35 


10.29 


.44 


11.76 


.56 



Width of 
Flange 



Inches 



2.33 
2.42 
2.52 

2.66 

2.73 

2.81 
2.88 

3.00 
3.15 
3.29 

3-33 
3.45 
3-57 

3.66 
3-7^ 
3-^7 

4.00 
4.08 
4.17 
4.26 

4.33 
4.45 
4.61 

4.77 

4.66 
4.80 

4-95 
5.10 

5.00 
5.09 
5-21 



For Fiber Stress 
of 12,500 lbs. per 
Sq. In. for Bridges 



Coefl5cient of 
Strength 



13.790 
14,950 
16,180 

24,850 
26,480 
28,110 
29,750 

40,300 
45,390 
50,490 

60,520 
66,610 
72,740 

86,260 

93,290 

100,430 

118,490 
125,400 
^33,570 
141,740 

157,260 
170,260 
188,640 
207,020 

203,500 
223,630 
244,050 
264,480 

299,740 
317,030 
341,540 



562 



OFFICE PRACTICE 







Table 51, 


— Continued 




Depth of 


Weight per 


Area of 


Thick- 
ness of 


Width of 
Flange 


For Fiber Stress 
of 12,500 lbs. per 


Beam 


Foot 


Section 


Web 


Sq. In. for Bridges 


Inches 


Pounds 


Sq. Inches 


Inch 


Inches 


Coefficient of 
Strength 


15 


42.00 


12.48 


.41 


5.50 


490,840 


IS 


45.00 


13.24 


.46 


5-55 


506,490 


15 


50.00 


14.71 


.56 


5.65 


537,130 


15 


55-00 


16.18 


.66 


5.75 


567,770 


15 


60.00 


17.65 


.75 


5.84 


598,410 


18 


55.00 


15.93 


.46 


6.00 


736,620 


18 


60.00 


17.65 


.56 


6.10 


779,440- 


18 


65.00 


19.12 


.64 


6.18 


816,200 


iS 


70.00 


20.59 


.72 


6.26 


852,970 


20 


65.00 


19.08 


.50 


6.25 


974,600 


20 


70.00 


20.59 


.58 


6.33 


1,016,490 


20 


75.00 


22.06 


.65 


6.40 


1,057,340 


24 


80.00 


23.32 


.50 


7.00 


1,449,460 


24 


85.00 


25.00 


•57 


7.07 


1,505,430 


24 


90.00 


26.47 


.63 


7-^S 


1,554,450 


24 


95.00 


27.94 


.69 


7.19 


1,603,470 


24 


100.00 


29.41 


.75 


7.25 


1,652,490 



Explanation of the coefficient of strength in the above table and 
examples showing use in practice. 

The coefficient of strength for each sized beam represents the 
maximum uniformly distributed load, in pounds, that will produce a 
fiber stress not exceeding 12,500 lbs. per sq. inch multiplied by the 
span in feet. 

If the load to be investigated is a concentrated load it must be 
changed to an equivalent uniform load in order to use the values 
given. This is done by multiplying the concentrated load by 2. 

Example: Suppose that it is required to determine the size I-beam 
that will carry a 40,000 lb. load in the center of a 15' span and a 
uniformly distributed load of 20,000 lbs. The coefficient of resistance 
for the concentrated load will be 2 (40,000) X 15 = 1200000 
Uniform load 20,000 X 15 = 300000 

1500000 

The required beam must have a coefficient of resistance of 1500000 
plus the coefficient due to its own weight. A 24" beam weighing 90 
lbs. per foot has a coefficient of 1,554,450. 

. The beam weighs 90 X 15 = 1,350. The coefficient for the beam 
weight is 1,350 X 15 = 20,250, which deducted from 1,554,450 gives a co- 
efficient of 1,534,200, which is slightly greater than required and 
is safe. 



TIMBER BEAMS 



563 



Table 52. — Condensed Table of Strength of Wooden Beams 

Based on a very complete table published in the Cambria Steel 
Handbook to which the reader is referred if he is using much data 
of this kind. 

This tabulation based on factor of safety of 6. 

Allowable fiber stress 1200 lb. per square inch. 

The loads given are the safe total uniformly distributed loads 
per inch width of beam for the span noted including the weight 
of the beam. 

This table applies directly to White Oak and Long Leaf Yellow 
Pine. 

For Hemlock use K of the load given. 

For Douglas Fir, Norway Pine, Cypress, Chestnut and Spruce, 
use % of the load given. 

Note. — The safe concentrated superimposed load is }4 of the 
total superimposed uniformly distributed load exclusive of the 
weight of the beam. 

For weight of timber see pages 950 and 805. 



Span 
in 








Depth of 


Beam 


in Inches 






























Feet 


4'' 


- 


8" 


10'' 


12'' 


14" 


16" 


18- 


20" 


22'' 


24" 


4 


535 


1200 




















6 


355 


800 


1420 


















8 


270 


600 


1070 


1670 


2400 














10 


215 


480 


850 


1330 


1920 


2610 












12 


180 


400 


710 


mo 


1600 


2180 


2840 


3600 








14 


150 


340 


610 


950 


1370 


1870 


2440 


3090 


3810 






16 


135 


300 


530 


830 


1200 


1630 


2130 


2700 


3330 


4030 


4800 


18 


120 


270 


480 


740 


1070 


1450 


1900 


2400 


2960 


3590 


4270 


20 


105 


240 


430 


670 


960 


1310 


1710 


2160 


2670 


3230 


3840 


22 


95 


220 


390 


610 


870 


1190 


1550 


i960 


2420 


2930 


3490 


24 


90 


200 


360 


560 


800 


1090 


1420 


1800 


2220 


2690 


3200 


26 




185 


330 


510 


740 


1000 


1310 


1660 


2050 


2480 


2950 


28 




170 


305 


480 


690 


930 


1220 


1540 


1900 


2300 


2740 


30 




160 


285 


440 


640 


870 


1 140 


1440 


1780 


2150 


2560 



Note. — If a deep beam is used for a shorter span than shown 
in the table figure the limiting load on the basis of shear along the 
neutral axis. By the formula 

TF = ^ 
3 
In which W — safe load in pounds uniformly distributed. 
d = depth of beam in inches. 
h — breadth of beam in inches. 

S = allowable shear in the direction of the grain 
in pounds per square inch.. 

White pine 100 lb. per square inch. 

Long leaf yellow pine 150 lb. per square inch. 

White oak 200 lb. per square inch. 



S64 



OFFICE PRACTICE 









G 


G G G G G 


G G 


G 




^ 










t^ 


to H lO M CO 


M H 


VO 




O^io G 


o 

H 






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vO 


r^ c< t^vo '^ 


CO <N 


CI 








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M M 




t^ 






fO 














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H ol 








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G G G G G 


G 


G 




^ 








^ 


t^OO 


c^ r>.oo t>- CO 


cj -in 


G 




Bxo^S c 


fO 








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■^ OnnO "^ CO 
H 


CS H 


00^ 

o 




















CO 




M d 








G G 


G G G G G 


G • 


G 




V 










VO CO 


CJ VO C^ lO CO 


00 • 


Tf 




t^.-^ G *^ 






o 




H t>. lO CO CS 


M 


On 




--->9 ^ 














CJ 




G <N 








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G G G G G 


~^ 




G 




^ 










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CO <N CI 00 G 






vO 




t-- "g ; 


N 






00 


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OnvO rj- c^ c< 






ON 

g" 








^ 












CI 




G M 






•s 










































a 




G G G 


G G G G 








G 




^ 






»— t 


V 


0\ M On 


On »0 G On 








r^ 




MD^ ^O VO 




a 


M 


CO M M 


NO -^ CO H 








H 
VO 




"^^^"^ 8 




.Q 














H 




G H 






^ 
















































CO 




G G G 


G G G 










G 




^ 






*t:! 




Tt G <N 00 


On M On 










CO 




o^ o o 




o 
43 


M 


00 to CO t^ 
VO cT m" 


Tt CO H 










G^ 

cT 




lO^Q »o ^ 




Q 
















M 




G H 




H 




G G G G 


G G G 










G 




.^ 




Kl 






G fOvO lO 


-^ H CI 










G 




On*. *b r^ 


-< 




CI 

M 


COOO On lO 


CO CS M 










ON 

oo" 




G H 






G G G G 


G G 












G 




.^ 


^ 






V 


M 00 G ^ 


G M 












ON 




QS^ \o ^ 






o 


00 M so CO 


CN» M 












00^ 




^O '^ 2 






CS M 














to 
































G M 








O to lo J>. 


G 














G 





^ 










vO <N MD On 


G 














t^ 




lo^ ^G S? 






i> 


t^ t^ CO H 


H 














t>. 




cs-^O O 








M 
















CO 




G H 






C 


> lO lO CO G 


















lO 




:: 








•- 


On lOvO 00 


















c< 




lo^ G t^ 






o °^ 


^00 fO H 


















On 




^O 9 t^ 






c< 


"5 


















H 




d M 


































"^« 




g 








































CO 








& 




























i^^ 




B 


rods 
w ste 
slab 






.s *^ 


Tt-vOOO G 


<N TfNO 00 G 


cs Ti- 


a^.^l 


»+H 








H 


H H H M C«< 


cs M 


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1 








Resisting 
slab in ft 
width of s 




ing of 
h belo 
ht of 














•4-1 

1 


in.) 
Spaci 
Dept 
Weig 

ft. 





CONCRETE SLABS 



565 



Table 53. — Condensed Table of Strength of Reinforced 
Concrete Slabs (Free End Supports) 

Safe Uniformly distributed superimposed load per square foot of 
slab for the span noted, exclusive of weight of slab. 
Factor of safety 5 which is very conservative. 
(Note. — For factor of safety of 4 add 34 to the tabular loads.) 
Concrete 1:2:4 mix. 

Allowable unit stress in concrete . . . 500 lb. per square inch. 
" " " " steel 14,000 lb. per square inch. 

Note. — ^The safe concentrated load is 3^ of the total uniformly 
distributed load. 



Table 5 3 a. — Recommended Thickness of Concrete Slabs 

When Used in Highway Bridges Under Different Depths of 
Earth or Macadam Fill (Conservative Practice) 







Depth of Fill Over Slab in Feet 




Span of Slab 
in Feet 


























i' 


2' 


4' 


6' 


8' 


ID' 


12' 


2 


6" 


6" 


6" 


6" 


6" 


6" 


6" 


4 


1" 


7" 


7" 


1" 


7" 


7" 


7" 


6 


9" 


9" 


9" 


. 10" 


10" 


10" 


11" 


8 


10" 


10" 


10" 


11" 


12" 


13" 


13" 


10 


12" 


T 0'^ 


Ti" 


14" 


15" 


16" 


17" 


i. Z 


'■O 


12 


14" 


14" 


IS" 


16" 


17" 


18" 


20" 


14 


16" 


16" 


17" 


18" 


19" 


20" 


22" 


16 


18" 


18" 


19" 


20" 


22" 


24" 




18 


20" 


20" 


22" 


23'' 


24" 






20 


22" 


22" 


23" 


24 









566 



OFFICE PRACTICE 



M ^ 



o 






B 
B 



O -M 

^ o 



X3 
O 



O 



;3 



M itj ^ 4h y ^ 







o o 


o O O O ^ 


o 


00^ XI 
<N to ^ 




V 


o a 


VO 00 M CS !>. CO 


o 




«D 


vo ^ 


CO CS Cl M 


CO 




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CO 

M 


o^d, 




o o o 


O O O O ^ 

t"^ O ^ 00 -"^ 




o 


(N \o *^ 






VO H VO 




o 




*« 


t^ lO CO <N <N M 




q^ 


w 


rt 








o" 

H 


d C 4 




0^^ o o o »o 









0^ £ 


1 


V 


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o 


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lO ro <N 


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1— 1 


fO 


- 








!>. 


<N 00 
CO 


















1 


*>• fO lo <N o • 








O 


t^^ 1— H 

M ^ 


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r-* 'Tt- t>- (N o t^ 








CO 


^ 


o 


CO CS M 


M 








q^ 


<u 


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o 














to 


CM C^l 
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CO 


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V t^ 


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4 


0:: 7J 




00 ^ 


5 C< M 














t> 


M 10 ^ 




















^ 


H 






















0^ j6 




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o 


^*\oS3 




f^ 1/ 


100 Tj- CS H 
















^ 




>-t H 


















t^ 


H <N 

H 




























:S 


































xj 




































































'B 


































4:3 


































(J 


































.S 


































M 




6 : 1 




























'k 


^ C^ . 




























cu 


73 . 




























jd 


? 60 




1? 
























4J 


-se § 




























.s 


.ssr 




G 
























1 


M^ " 




^ 


00 O cs r 


h O 00 O lo »o 








H H H 


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•-^ <u^ 










4J 

1 


1 (sq. 
m ste 
am i' 












IV <l> 










,s, 


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<L) 










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c3 5.bf 












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<S^ 



TIMBER COLUMNS 



567 



Table 55.- 



-Condensed Table of Strength of Timber 
Under Long Column Action 



Based on the Formula of the U. S. Department of Agriculture, 
Division of Forestry. 

"^ -^ 700 + 15C + C' 
P = ultimate strength in pounds per square inch 
F = '' crushing strength of timber 

C = J in which I = length of column in inches 
a 

d = least diameter in inches 

Safe load per square inch on the basis of a factor of safety of 
8 is given below. A factor of safety of 6 is often used in good 
practice. 



d 


Safe Load in Pounds per Square Inch 


White Oak 

and 

Long Leaf 

Yellow Pine 


Douglas Fir 

and 
Short Leaf 
Yellow Pine 


Red Pine, Spruce 
Hemlock, Cy- 
press, Chestnut 


White Pine 
and Cedar 


5 
10 

15 

20 
25 
30 


600 
560 
510 

450 
400 
350 


550 
500 
450 

400 
360 ^ 

320 •": ■■ 


480 

450 
400 

360 

^ 320 

280 


420 
390 
350 

310 
280 
250 


Note. — 


- over 30 is E 


Lot advised. 





(b) THE LOCATION OF NEW ROADS 

Detail Instructions compiled by the author for drafting room 
procedure in connection with the design of Mountain Roads. 

NOTES FOR DESIGNERS ON THE PREPARATION OF 
PLANS 

In the preparation of plans, the quickest and easiest methods 
which will be sufficiently accurate for the purpose should be used. 

In this connection, it should be borne in mind that, as a rule, 
graphic methods are to be preferred to computations wherever such 
methods are sufficiently accurate. This will probably occur in 
nine cases out of ten. 



568 OFFICE PRACTICE 

When you consider the methods which will be employed in con- 
structing mountain roads and in staking them out for construction, 
localized errors in paper locations are not important factors in 
determining the value of the design. 

A localized error in length of one foot or even two feet per one 
hundred feet on one curve will not materially afifect the accuracy of 
the layout or the quantity of excavation, particularly as these 
errors tend to balance and they are never cumulative. 

A localized error of o.i foot or even 0.2 foot on the profile grade 
line will not destroy the value of the plans or the value of the esti- 
mate as it is not cumulative. 

Careful graphic methods will not exceed these limits and the 
average error should be well within the necessary accuracy. 

A sample sheet of plan and profile using graphic methods is 
attached. See page 571. This shows a uniform method of pro- 
cedure which is to be followed wherever, in your best judgment, the 
method can be used. 

INSTRUCTIONS FOR DRAFTING ROOM 

It is necessary in drafting room work to keep all records and 
computations in as neat and orderly condition as possible. 

Have on your desk only as much material as you need for the 
work you are doing. Keep the rest in the files. 

At night clean off the tables completely and place your working 
material either in your table drawers or in the files. Cover tables 
with cover. 

All computations and maps must be marked plainly with the 
name of the job. 

All office computations which will become part of the permanent 
records are to be made on the forms provided or on letter sized 
sheets. 

The designing chief for each project will be responsible for the 
following notations on all records. 

Name of job on each separate sheet or roll of computations 
and plans. 

Name of computer on each sheet. 

Name of checker on each sheet. 

The methods employed in all work should be shown in enough 
detail to make it possible for anyone to check the results. 

DRAFTING ROOM SUPPLIES 

Tracing cloth, plain, 25" wide 1.7 yd. per mile 

Detail paper (36" wide) (i lb. = ^ of 36" paper) 

Mlb. '' " 
Cross-section paper (opaque) (used for profiles) 22" wide 

* 1 . 7 yd. per mile 
Transparent cross-section paper (22" wide) 6 " " " 

Cross-section sheets (18" X 24") 12 sheets per mile 

Cost per mile, office supplies, $1.50. 



DESIGN SPEED 569 

DETAIL INSTRUCTIONS 
Mountain Road Design 

These instructions have been prepared in detail as many of the 
men have no idea of the order of work or reasonable speeds on the 
various parts of the design and in many cases they waste time by 
needless work on the rough plans. The cost of design work is 
often high on account of the inexperience of the force. By a 
careful study of these instructions some improvement in speed and 
cost should be obtained. 

Speed of Work. — The following list of reasonable speed is based 
on a seven hour working day for the average man. If you are not 
equaling this rate ask the chief draftsman to see if he can help you 
find the cause. 

General Speed. — Two miles per month per man of completed 
plans when men are experienced. 

About I Jl miles per month per man when force is not used to 
road design. 



Detail Reasonable Speed 

Division of Work Approximate Miles 

per Day, per Man 

1. {a) Plotting, checking and inking base line 

and plotting topography 1.5 miles 

*{b) Base line profile complete 3.0 '* 

*{c) Plotting and checking cross-sections. . . . i .0 " 

(d) Inking cross-sections. 1.5 '' 

2. (a) Trial grade line 7.0 " 

*{b) Projecting grade contour on map 1.5 ^' 

(c) '^ final center line i . o '' 

3. *(a) New center line profile i .0 " 

*{b) Balanced section profile 1.5 " 

(c) Trial final grade based on balanced 

profile 1.5 " 

id) Drawing templets on sections 2.0 '' 

{e) Planimeter sections and compute quan- 
tities 0.8 " 

*(/) Determine final grade line and balance 

quantities 0.4 '^ 

(g) Ink final grade line 7.0 '' 

4. (a) Compiling estimate 2.0 '' 

5. {a) Tracing plans 0.6 " 

Note. — *Indicates work that can be done to advantage by two 
men working together. 



570 OFFICE PRACTICE 

Reasonable Cost 

General Cost 1 $40 to $50 per mile with experienced men 
Completed Plans / $80 to $100 " " " inexperienced men 

Detail Costs 

B ased on the following wages : 

Designer $150.00 per month 
Draftsman 110.00 " ^' 
Tracers qo.oo " '' 

Computers 80.00 " '' 

Cost per Mile 

1. (a) Detailed paper map $ 2.50 

(b) Base line profile i . 00 

(c) Plotting and checking cross-sections 3 00 

(d) Inking cross-sections 2 .00 

2. (a) Laying trial grade i . 00 

(b) Projecting grade contour 3 .00 

(c) Projecting final center line 8 . 00 

3. (a) New center line profile 3 . 50 

(b) Balanced section profile 4 . 00 

(c) Trial final grade based on balanced profile 4 . 00 

(d) Templets drawn on 3 . 00 

(e) Planimeter and computation of quantities 4.00 
(/) Determine final grade line and balance 

quantities 10 . 00 

(g) Ink in final grade line .50 

4. (a) Compile estimate 3 00 

5 . (a) Trace plans 5 • 00 ' 

Total $57-50 

DETAIL OFFICE DESIGN 
MANIPULATION 



DETAIL MANIPULATION 

General Note. — Get all information on rough plans and profiles 
needed by the tracer, but do not ink anything not Hkely to be 
erased during the design and do not attempt to print notes, etc. 
A great deal of time is being wasted every day by unnecessary 
work on the rough plans. We appreciate that good work has been 
done, but further improvement can be made. 




T.i s s 7 






AMPLE. SHEET.^ — 






COLO/tS FOH T/fACINS. 

8ovnJane&, Bast Line o-fSurvty and alt 
I ines, i effers andriqum n fating iv 
■ ■ ;. Also Btnchlfarks, Tiflts-T^lts, 
criptlons, Narth Points, ffc 



••10 '" * 

i' 



r| O-^^ ^M.,o:. ^ ^^^^\ 







{Between pages S70 and S7I.) 



DESIGN INSTRUCTIONS 571 

Be careful to mark the name of the road on all rolls, sheets, etc., 
before starting work. 

We do not expect you to follov/ these instructions absolutely but 
the system outlined has been proved in practice and it is expected 
that you will follow the principles, give the information called for 
and that you will eliminate useless work. 

Preliminary Work: 

I. {a) Map. (See Sample Map.) (One Man working alone.) 
The map is drawn on a roll of detail paper 18'' wide. 

Scale 1'' = 100'. In exceptionally hard locations use i" = 50' 

Order of Work 

1. Plot base line in pencil (6H) using vernier protractor or 
tangent method in plotting angles and careful scaling for distances 
between transit points. Plot bearing of each course from north 
line drawn through each transit point. 

2. Check this plotting. 

3. Ink in the base line with a fine solid black line and mark the 
transit points with small circles. 

4. Mark the even stations with a short ink dash and number 
every fifth station in black ink. Mark station of transit points in 
black ink. 

5. Mark true bearing or azimuth on each course in black ink 
and check. 

6. Show the location of each cross-section by a fine red ink line 
extending far enough from the base line to reach any center line 
shift and check. Do this work very carefully as your center 
line distances will be affected. 

7. Plot topography in pencil (4H) making the lines heavy and 
firm so it can be easily traced without inking. DO NOT INK. 
Write all notes, property names, etc., in large plain long hand. 
DO NOT PRINT, Use 4H pencil with a blunt point so tracer 
can read easily. 

I. (b) Base Line Profile. (See Sample Profile.) 

Use her-vy white paper roll 22 inches wide ruled in squares 10 

to the inch. 

Scales. — Use i" = 100' horizontal or i'' = 50' horizontal to 

agree with the map scale. Use 1" = 10' vertical. 

Order of Work 

1. One man mark even stations in pencil along upper margin. 
Use 4H pencil with blunt point and make the figures large and 
distinct, but don't be fussy. 

2. (Two men.) One man calling from notes. Other man write 
in pentil on profile the elevations of base line at even stations and 
pluses. 

Record these elevations in tens, units and tenths. Do not 
record hundreds and thousands. These can be easily determined 
by the datum on the profile and their omission saves time. 



572 



OFFIGE PRACTICE 



Also, write pluses of stationing on margin. Use 4H pencil, 
large plain figures, but do not be fussy. Check back these figures. 

3. (One man.) Plot profile points by referring to elevations 
marked in pencil. If reasonable care is taken in plotting this 
need not be checked. 

4. Ink in ground line with light firm black ink line. 
I. (c) Cross -sections. (See Sample Sheet.) 




Cross-sec+ions 

Ephraim-Onanoeville Road 

fian+i Na+ional Forest.U+oh. 

191 & 

tST/r 710*00 
t - we*9s 



EXC 1911 8 CU FT 

EMB IIS3 4 

« ST/t 709-t n 

t " 709'hi6 

i. 6R/JPE 32 5 

EXC 577 5 

EMB 2d3 5 

tST/7 709*00 

t " 10B*9S 

t 6fifOE 82 6 

EXC. 1095 

EMB Z482 

t ST/I 708*25 

t - 708*22 

i6/fffDE 83.1 

EXC 299.9 

EMB 857 t; » 

*. ST/} 708*00 

t " 707*95 

t6ff/rr>E 8*2 

EXC 821 5 
EMB. 679.5 
t ST/I 707*43 
t •• 707*42 
i.$R/IPE 84.7 



€ 5r/7 707*00 
t " 706*95 
i.QMD£ 85.5 



A 5T/7. 706*48 
t " 706*48 

i annoe 86.0 



4 STA 706*00 
t " 706 *00 
t 6ff/JPE 06 7 



SAMPLE. 



Fig. 136. 

Plot on transparent cross-section paper cut in sheets 22" X 36" 
and ruled i" = 10 parts or i" = 5 parts heavy and 5 sub-divisions 
lighter. 

Scale. — Use i" = 5' except for exceptionally heavy worl^ when 
i" = 10' may be used. 

Elevations, — Points must be plotted by their absolute elevation 
referred to the datum used for the Bench levels. The heavy lines 
outlining each square inch must be used as an even 5 ft. or io ft. 
of a-bsolute elevation. 



DESIGN INSTRUCTIONS 573 

Order of Work. (Two men work together) 

1. Mark base line verticals and use same vertical for all sections 
in each row. Generally two rows of sections can be placed on 
esch sheet. 

2. Plot ground line section points by dot surrounded by small 
circle and write in pencil, vertically, on the base line the elevation 
of the ground at the base line. Write on the right hand margin 
directly opposite and level with the intersection of the ground 
line and base line, the base line station and note it as B. L. Sta. 
123 + 20. 

3. Check all operations of plotting and recording by reading 
back from the actual plotted elevations. No corrections need be 
made for errors of o.i ft. Correct for any larger errors. It is 
extremely important that the cross-sections be accurately plotted 
and carefully checked as the design depends more on this phase 
of the work than on any other part. 

Elevation and distances farther than 40 ft. from B. L. should be 

•1 . S1-^ Elev. 
written m pencil, viz., - — . 

45 IJist. 

1. {d) Inking Cross-sections. (One Man.) 
Ink in checked pencil cross-sections. 

Use firm, moderately heavy line (black ink) for the ground line. 

Use large black ink heavy line letters and figures in marking 
Base Line elevations and station numbers. 

Note. — The Cross-sections must he inked before they are used 
in the design, 

DETAIL MANIPULATION 

Grade Line Design. — 2. (a) Trial Grade Line. (One Man, the 
Designer.) 

On the base line profile draw on a trial grade in pencil (6H) 
using fairly long straight grades and cutting every bump and filling 
every hollow. 

Remember that the object of the trial grade is to smooth out the profile 
on sidehill work by center line shift. It is fundamentally different 
from the final grade line which endeavors to follow the new center line 
profile as closely as possible. 

2. {b) Projecting Grade Contour on Map. (Two Men.) 

The grade contour should only be determined on sidehill work 
where the center line can be shifted to advantage. Designers are 
cautioned not to use the grade contour method in flat or rolling country. 
Never destroy good alignment in easy country. It is preferable to 
use an undulating grade. 

Order of Work 

I. On each cross-section determine the distance right or left of 
the base line where the trial grade line elevation for that particular 
section hits the ground line. Locate this by means of the absolute 
elevation of trial grade determined graphically from the grade 
profile. 



574 OFFICE PRACTICE 

Do not determine this point by the method oj base line profile, 
cut or fill as this later method introduces more chance of error. 

2. Note the location of these points by a Hght pencil vertical 
dash and write in pencil lightly the number of feet from the base 
line. 

3. Check this work. 

4. Plot these points on the detail map and mark them by a pin 
hole surrounded by a small red ink circle. 

5. Check this plotting. 

2. (c) Projecting Final Center Line. (One Man, Designer.) 

1. IDraw on map the proposed center line in pencil (6H) fol- 
lowing as closely as possible the grade contour marked with the 
red circles, considering the limitations of alignment imposed by 
reasonable engineering considerations and the type of road desired. 
This work should be very carefully studied and is a slow operation. 
The curves should be drawn with the standard office curves or 
compass and their radii noted in pencil. The approximate loca- 
tions of the P. C.'s and P. T.'s should be shown by short pencil 
lines perpendicular to the tangent. If possible short tangents 
should separate curves but this limitation must be used with 
judgment and is not intended to apply to extremely difficult or 
costly locations. 

Make this projection with sufficient care so that the center line 
is practically settled on at this point of the design. This is 
important. 

2. Mark the even stations on the new center line continuously 
by scaling. Use a standard scale on the tangents and the stepping 
method with dividers on curves. Check this. Do not use the 
stepping method on tangents as it generally introduces a cumulative 
error. Number every fifth station plainly in large figures. 

3. Mark lightly in pencil the new center line stationing where 
each base line cross-section line previously drawia in red on the 
map intersects the new center line. Check this^ 

4. Mark lightly in pencil at each of these cross-sections the 
distance from the new center line to the base line and check this. 
You are now ready to transfer the location of the final center line 
to the cross-sections and plot the final center line profile. 

3. {a) New Center Line Profile. (Two Men.) 

Order of Work 

1. Mark on cross-sections with a short vertical distinct pencil 
arrow the location of the adopted center line determined by the 
previously scaled and noted offset marked on the plan. Check them. 

2. Directly under the noted base line station on the right hand 
margin of the cross-section sheet write in pencil the new center 
line station for each corresponding base line station as previously 
determined and shown on the map. Check this. 

3. Mark in pencil the absolute elevation of the ground at the 
new center line. Check this. 

4. Plot the true center line profile using the true center line 



DESIGN INSTRUCTIONS 575 

horizontal distances and stationing, the true center line ground 
elevations as shown on the cross-sections and showing (as per 
sample profile) the equivalent B. L. stationing at each section. 

Use the same manipulation methods as regards pencil and ink as 
described for base line profile. 

3. (6) Balanced Section Profile. (Made by Designer and one 
Helper.) 

Note. — At this point eliminate from all further consideration 
the base line profile and trial grade. A great many men attempt 
to make the final grade similar to the trial grade which is absolutely 
the wrong principle except where a ruling grade governs. 

Order of Work 

1. Select the templet suitable to the cross-section under in- 
vestigation. 

2. Shift this templet up and down (with the center line always 
coinciding with the final center line location previously marked 
on the cross-section) till it reaches a point where by inspection 
you judge that the cut area will make the fill area as shown. Mark 
the center line elevation of the templet lightly in pencil with a 
short horizontal dash and write lightly the absolute elevation 
of this dash. 

3. Plot the center line elevations of these balanced templets 
on the new center line profile for each section by a pencil dash using 
the absolute elevation previously determined. Do not plot by 
phis or minus from the ground line as this introduces more chance 
of error. • 

4.. Check this plotting very carefully. 

5. Ink the short dashes with red ink but do not connect these 
points. 

Note. — This portion of the work is very important particularly 
on a fairly uniform profile. By the use of these balanced templet 
elevations the final grade can generally be balanced with less work, 
shorter hauls and from 10% to 30% less excavation than if a hit' 
or miss method based on ground line is used. I cannot over- 
emphasize the value of this part of the design. On an extremely 
rough profile requiring a succession of heavy cuts and fills it is not 
applicable nor advised. 

3. (c) Trial Final Grade Based on Balanced Templet Elevation. 
(Designer must do this personally.) 

Order of Work 

I. Lay grade line on center line profile (in fine pencil 6H) fol- 
lowing as nearly as possible the balanced elevations shown by the 
red dashes previously plotted on the profile. 

Except where a ruling grade is encountered or where a tangent 
grade wiU hit the majority of the indicated balanced elevations, a 
rolling grade is to be preferred, this can be laid out most econom- 
ically by a succession of vertical curves selected to fit the conditions. 



576 OFFICE PRACTICE 

These curves are drawn on the profile by the standard office railroad 
curve templets and the radius noted. There is no necessity of 
drawing the tangent grades to intersection as all the elevations on 
the vertical curves can be determined graphically. The tangent 
rates of grade should be laid out to some even tenth and figured 
between the ends of the vertical curves. 

2. Determine elevations of grade line at each point where a 
section occurs and write this elevation in heavy pencil above the 
grade line. Do not record hundreds or thousands in these eleva- 
tions. Determine these elevations graphically on vertical curves 
and by figuring on tangent grades. 

3. Check these elevations, 

4. Transfer each elevation to the cross-sections by recording it in 
pencil directly under the center line stationing on the right hand 
margin of the sheet. Check this transfer. 

3. {d) Drawing in Templets. (Designer should do this.) 
Note. — This work should be done by the designer as considerable 

judgment must be exercised in the selection and variation of the 

standard sections. 

Order of _Work 

I. Draw in proper templet making its center line elevation agree 
with grade elevation previously recorded under the station number. 
Use a 4H pencil with a fine point as many of these templets will 
have to be changed before the design is accepted. 

3. {e) Planimetering Areas. 

Methods: 

Various methods can be used depending on the kind of plani- 
meter. So long as care is taken and a double run is made to check 
the initial run any desired method will be satisfactory. 

With a fixed arm planimeter reading directly to square inches a 
double run divided by 8 is the usual practice for a 5' scale. 

With an adjustable arm planimeter it can be set to read square 
feet directly on the second run or can be set to read cubic yards per 
100 ft. directly. The last method is a great time saver. 

Order of Work 

1. Check the correctness of templet plotting by comparing 
templet elevation with grade elevation marked on the margin. The 
planimeter vian is responsible for checking the templet plotting, 

2. Test planimeter before using and at frequent intervals to 
see it is recording correctly. 

3. Planimeter the areas checking by a double run. 

4. Record the areas of cut and fill in pencil at the right of the 
sections to nearest ft. as C = 21 

F = 20. 



DESIGN INSTRUCTIONS 577 

COMPUTATION OF GRADING QUANTITIES 
Order of Work 

1 . (Two men.) Transfer center line stationing and areas for each 
cross-section to the standard computation sheets. Check this 
transfer. 

2. (One man.) Compute quantities. If areas are in sq. ft. com- 
pute quantities in cubic feet. This is an order; no discretion is 
allowed. The reason this is specified is because it has been deter- 
mined from practice that it is quicker and more accurate. The 
more or less prevalent method of computing each quantity in 
yards will not be allowed. The use of cubic feet keeps all work in 
full units and eliminates 90% of the transfers, feet to yards. We 
have proved from checking that too many mistakes are made in the 
decimal point on detail yardage quantities. 

3. Check Detail Computations. — This means check every phase 
of the computations, distances between sections, extensions, addi- 
tions, etc. 

3. (0 Balancing Final Grade Line. (Designer and one helper.) 
This portion of the design is very slow and requires more judg- 
ment than any other feature. 

(a) It is desirable to balance in as short sections as possible as 
this results in cheaper excavation methods. A continuous balance 
means plow and road machine turnpiking which is very cheap. 

Short balances mean scraper longitudinal haul and machine 
finish which is moderately cheap. 

Long balances mean wagon haul which is expensive. 

(b) It is desirable to balancewith a downhill haul on noticeable 
grades. 

(c) It is desirable to proportion the cut to fill so that dirt is not 
wasted. 

This last is entirely a matter of judgment. 

If the ground is bare and classed as common the following ratios 
will not be far out: 

Volume of Exc. Ratio Cut 

per Station to Fill 

30 yd. to 50 yd 1.30 to 1.25 

60 yd. to 100 yd i . 25 to i . 18 

Above 100 yd i . 15 to i . 10 

If the ground has a thick carpet of humus or a heavy stand of 
large trees the grading conditions can not be definitely determined 
until the clearing and grubbing is completed. In such a case the 
grade line should be noted as tentative and the resident engineer 
on construction will have to re-cross-section and re-design the grade 
after the mold and stumps are removed. The quantities in such a 
case can only be approximated and should be made on the safe 
side. 

(d) In balancing quantities it is usually desirable to reduce the 
larger quantity. 



578 OFFICE PRACTICE 

(e) It is often cheaper and more desirable to waste at places and 
borrow at others. This should be borne in mind. The ratio of 
borrow excavation from pits to borrow fill is generally taken at i.io. 

(/) In considering rock cuts and fills use Trautwines' figures, 
I cu. yd. solid rock makes approximately 1.7 cu. yd. rock fill. Where 
the fill is a mixture of earth and rock i cu. yd. rock will make i cu. yd. 
of fill. The order of work and detail manipulation for the portions 
of the grade line that have to be changed to accomplish a balance 
are the same as for the original grade line. 

3. (g) Inking Final Grade. After the grade line is balanced, ink 
it in with red ink on the profile so it can be easily traced. 

4. Estimate. — (Designer.) 

(i) Drainage. — From survey notes locate culverts on profile and 
draw them on the proper cross-section to determine length and in- 
vert elevations and outlet ditches if necessary. Do this work in 
pencil. Make notes clear and complete. 

(2) Bridges. — Use standard designs up to 25'; above that have 
design made by Department Bridge designer. 

(3) Compilation. — Compile data on forms provided, using center 
line station to locate all structures quantities, etc. 

(4) Unit costs will be determined by the Ofiice Engineer in charge 
of the Drafting Room and reviewed by the District Engineer. 

(6) Check all operations. 

5. (a) Tracing Plans. 

Size of Sheets: 

Outside 22'' X 36'' 
Border J^'' top, bottom and right. 
2" binding edge on left. 

All work in black ink. 

Make heavy and plain. 

Lay out as per sample sheet. 

Check all tracing. 

5. (b) Finishing Cross-section Sheets. Do not ink in final grade, 
templets, or center line ground elevation till contract is let and 
cross-section blue prints are needed in the field. This delay is 
advisable as it is often necessary to revise even after the original 
design has been accepted. 

EXPLANATION OF TABLE OF RELATIVE WEIGHTS OF 
OFFICE DESIGN 

To obtain the equivalent mileage of completed office design 
multiply the actual mileage complete to date of each sub-division 
of the work by the precentage shown. Add all these products 
which will give you the total equivalent mileage of completed 
design. 

Example. — Suppose at the time a report is due you have 10 
miles of map completed, 20 miles of base line done and 5 miles of 
cross-sections plotted, checked and inked. 
{Continued page 580.) 



PROGRESS RECORDS 



579 



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. 






58o OFFICE PRACTICE 

This work will be equivalent to the following mileage of complete 
office design: 

Item 

I. (a) Map lo miles X 5% o. 50 miles. 

I. (b) Base line profile 20 miles X 2% 0.40 •" 

I. (c) Cross-sections plotted and checked 5 miles 

X 10%. .^ 0.50 '' 

I. (d) Cross- ection inked 5 miles X 4% o. 20 '* 

Equivalent miles total Completed Plans 1.60 '* 

Suppose the project is 20 miles long. 

The per cent, completion office design is 1.6/20 = 8% complete. 

BASIS OF TABLE OF RELATIVE WEIGHTS OFFICE DESIGN 

General Speed. — Two miles per month per man of completed 
plans when men are experienced. 

About iJ4 miles per month per man when force is not used to 
road design. 

Assumed Speed per Man per Day on Various Divisions 
OF Work 

1. (a) 1.5 miles Detail map. 

* (5) 3.0 " Base line profile. 

* (c) i.o *' Cross-sections plotting and checking. 
{d) 1.5 '' Inking cross-sections. 

2. (a) 7.0 '' Trial grade 

* (&) 1.5 '' Grade contour. 

(c) 0.8 *' Center line projection. 

*3. (a) 1.0 " Center line profile. 

* (6) 1.5 " Balanced section profile. 
(c) 1.5 " Final grade line. 

{d) 2.0 ' ' Templets 

(e) 0.8 " Planimeter and quantities. 

(/) 0.4 " Balance quantities. 

(g) 7.0 " Ink final grade line. 

4. 2.0 '' Compiling estimate. 

5. 07 " Tracing plans. 

* Indicates work that can be done better by two men working 
together which will result in twice the speed shown. 



I 



SAMPLE ESTIMATE FORMS 
SAMPLE ESTIMATE FORMS 



581 



SHEET NO... 



Date- 



ESTIMATE SHEET (.Letter size:)' 

Computed by. 

Checked by. 



GENERAL SUMMARY 


ITEM 


QUANTITY 


UNIT 
PRICE 


ESTIMATED COST 








$ 








































































































— 






- 




— 




- 




— 








— 






= 




^ 




~ 




= 










































































































Lengrth. miles 

Cost per milcg.. 


Total cost 
+ 10S6for E^ 
Cftst 'to dat< 

Appropriati 


I Items 
g. Adv. 
for 

ey^s & 
)I1 


So 
PI J 


n 


n 







































SHEET NO... 



ESTIMATE SHEET 



Road Computed by ^V- 

JDate -Checked by- 



SUMMARY CLEARING & GRUBBING 


STATION TO STATION 


LENGTH 


I 

Q 


ACRES 


CLASSIFICATION 


PRICE 
PER 
ACRE 


ESTIMATED COST 














' Tl 




































































































































O'otals 
















Aver 


age 


Llnit 


?rice pec Acre 









S82 



OFFICE PRACTICE 



ESTIMATE SHEET 



Road- 
"Date. 



_Gomp"ate^ by.. 
-Checrked "by—. 



SUMMARY BORROW | 


SOURCE OF SUPPLY 
STATION 


WHERE USED 
STATION TO STATION 


HAUL 
DISTANCE IN STAS. 


QUANTITY 
CUBIC YARDS 



















































































ESTIMATE SHEET 



Road Computed 

Date Checked 1 


by 




3y __ _ 




SUMMARY OVTRHAUL 


LOCATION OF CUT 


LOCATION OF FILL 
STATION TO STATION 


NUMBER 
CUBIC YDS. 


LENGTH 
OF HAUL 
LIN.FT. 


AMOUNT OF 

OVERHAUL 

IN STATION YARDS 
























































■ 















































SAMPLE ESTIMATE FORMS 



583 



ESTIMATE SHEET 



Road^x-. 
Date 










Pr 


)mptrted by. 
lecked byL^ 










CI 




SUMMARY CONCRETE STRUCTURES | 


STATION 


STRUCTURE 


I 


>■ 


1 = 


CLASa OF CONCRETE METAL REINFORCEMEtil 


PAVING 


1st 

CU.YD5 


2nd 
CU. YDS 


3ro 
CU, fDS . 


MESH 
LBS. 


BARS 
LBS, 


DOWELS 
LBS. 









































































































































=^ 











































































































ESTIMATE SHEET 



Road- 

Date- 
















-Computed by 






SUMMARY PIPE CULVERTS 


STATION 


Ul 




CONCRETE PIPE 


CORRUGATED 


VITRIFIED 


LENGTH, LIN. FT. 


LENGTH, LIN. FT. 


LENGTH, LIN. FT. 


18'/ 


24'/ 


30'/ 


36// 


15'/ 


18'/ 


24'/ 


30// 


12// 


15// 


18'/ 


24// 















































































































































































































































































































S84 



OFFICE PRACTICE 



ESTIMATE SHEET 

Road Computed by^ 

Date Checked by 



SUMMARY MASONRY STRUCTURES 


STRUCTURE 


STATION TO STATION 


LENGTH 
LIN.FT. 


EXCAV. 
CU.YDS. 


BACK FILL 
CU.YDS. 


DRY RUBBLE 
CU.YDS, 


MASONRY RUBBLE 
CU.YDS. 












































































^=:^ 


r~~~-— —1 

































































QUANTITY SHEET 

*Road jCojnputed by. 3Date_ _ 

Section „ .Checlced by Date- _ 


0. 


CLASS IF ICA 
TION 


STATION 


DIST 


AREAS-SQ.FT. 


VOLOmE — CUBIC FEET II CC 


>MMON 


CUT 


FILL 


CUT 


FILL tl E^CA 


V-CU.FT. 










































































































































































1 


J 
























"' 


~ 






— 




" ~ 




















^ 





































































































































































CHAPTER XIV 
COST DATA AND ESTIMATES 

Author's Note. — In retaining the data in this chapter in its present form 
the author wishes to state that while the costs given are too low for the pre- 
vailing labor wage and cost of materials (191 8) the analysis of cost can be 
used by applying the prevailing wage and material costs. 

Undoubtedly the labor wage scale will remain permanently at a higher 
level than shown in the data given but it is not likely to remain at the 
present extreme height and until comparatively stable times prevail 
again, after the war, it would be. useless to attempt to revise the unit cost data. 

New methods of construction have so changed the cost of road 
improvements that engineers just going into this work, or those 
not familiar with present methods, are often handicapped in making 
estimates. 

The cost data given in this chapter has been gathered chiefly 
since 1907 and covers most of the items necessary for estimating 
the cost of any ordinary road improvement. Such data must be 
used intelligently or it will be misleading. Local conditions 
should always govern in making estimates, and in presenting 
costs it is best to describe the conditions under which the work 
was performed, leaving their special application to the one using 
the data. An engineer's estimate should represent the probable 
average bid price. In the following examples of actual cost those 
have been selected that are considered to be average cases. Con- 
tractors who have an unusually good plant and a well-organized 
force can often do the work cheaper than is shown; on the other 
hand, those new to the work will spend more. 

Where machinery is used it is more satisfactory to include the 
items of depreciation, repairs, and interest in a lump-sum item 
for the whole contract than to try to reduce it to a yardage basis. 
These charges will be considered under the heading of "Plant 
and Payroll." 

BITUMINOUS AND WATERBOUND MACADAM CON- 
STRUCTION 

Cost of Earth Excavation. — Table 56 shows the cost of earth- 
work on four roads in New York State, which represent easy, 
average, and difficult work. The cost per cubic yard includes 
excavation and placing in fill, shaping the sub-grade for the stone, 
and trimming the shoulders and ditches. For heavy fills with 
short hauls wheeled scrapers were used, but the largest part of the 
work was done by wagons. 

585 






5,86 COST DATA AND ESTIMATES 

Cost of Rock Excavation. — The writer has no reliable personal 
data on ledge rock excavation. Rockwork on roads is usually a 
small item; the cuts are small and consequently expensive. Per- 
haps there is no item more variable in cost than small rock cutting. 
It is therefore safer to take as a basis of estimate the bids of ex- 
perienced road contractors. The reports of the Massachusetts 
Highway Commission and bids on New York State work show that 
prices for rock excavation range from $1.50 to $2 per cubic yard, 
for quantities up to 200 or 300 cu. yd., and $1.25 to $1.50 for 
larger quantities. 

Cost of Unloading Broken Stone. — For making estimates of the 
quantity of stone required the following data on imported limestone 
used on Road 5021 will be useful. The approximate sizes and 
actual weights of stone on this work were as follows: 

No. I Screenings, ^i inch screen 25501b. per loose cu. yd. 

No. lA Dustless screenings, ^ in. screen 

with dust jacket 2350 '' " *' " '* 

No. 2, i}i in. screen 2470 " '' " '' " 

No. 3, 23^ *' '' 2350 " " 

No. 4, 3>^ " " 2420 " '' 

For purposes of estimating the cost of handling imported crushed 
limestone, the following weights for a cubic yard, based on railroad 
weights, will be used: No. i, 2600 lb.; No. lA, 2400 lb.; No. 2, 
2500 lb.; No. 3, 2400 lb.; No. 4, 2400 lb. 

Unloading Cars by Hand. — On Road 5021, with the author as 
engineer, a number of short time (lo-hr.) estimates made the cost 
of unloading per ton $0.12 to $0,135; and the cost per cubic yard 
$0.14 to $0.16. This work was in 1910, and labor cost $0,175 per 
hour. The shoveling was done from a steel platform, where it was 
dumped from hopper-bottom cars. When shoveled from inside 
the cars the cost may run as high as $0.20 per cu. yd. The cost 
of shoveling is usually estimated at $0.15 per cu. yd. 

The time of loading 1 3^ cu. yd. wagons by hand shoveling will 
range from 8 to 12 minutes. 

Unloading Cars with Continuous Bucket Conveyor Elevator 
Plant. — Where there is a large quantity of stone to be unloaded 
and it is not possible to install an elevator plant on the existing 
track, it often pays to put in a switch. Six car switches can be 
usually built for about $300.00 Where there are competing rail- 
roads no charge is usually made. 

The following data is from Road No. 5046, season of 1910, 
with labor at $0,175 P^r hour. The plant consisted of an ordinary 
continuous bucket conveyor operated by a 6 H.P. gasoline engine; 
the bin had a capacity of 100 tons. 

The average fuel consumption was five gallons of gasoline per 
day. Cost of fuel and oil averaged $1.00 per day. 

The average force at the elevator was one foreman and three 
helpers. 

A total of 4670 tons, or 3890 cu. yd., was unloaded at $0,084 
per ton, or $0,101 per cu. yd. 



EARTH EXCAVATION 



587 



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588 COST DATA AND ESTIMATES 

The cost was divided as follows : 

Setting up elevator at Scottsville $ 60 . oo 

" " '' " Mumford 40.00 

'' '' " "Wheatland 75oo 

Labor of operation 194 . 00 

Gasoline and oil. ...... 25 .00 



Total $394.00 

This method of unloading is not only cheaper than hand methods 
but also cheapens the cost of hauling, as no time is lost in loading 
the wagons. The time of loading a ij^ cu. yd. wagon from bins 
ranges from 45 to 55 seconds. There is also a saving in car demur- 
rage if the bin holds two or three car-loads. 

Elevator unloading saves about $0.04 per cu. yd. on team time 
and about $0.05 on the unloading, making a total saving per cubic 
yard of about $0.09. It usually costs about I150 to ship the plant 
and install it the first time, so elevator unloading is notvadopted 
unless there are, at least, 2000 cu. yd. of stone handled. 

Unloading Cars from Coal Trestle. — This data is taken from 
the Scottsville road repair work, Mr. Harold Spelman, Engineer, 
season of 19 10; labor at $0.20 per hour; average force, two or three 
men. A total of 4400 tons was unloaded. The cost divided as 
follows : 

Rent of trestle |i 25 . 00 

Labor 232 .00 



Total $357 00 

Cost per ton o . 081 

" '' cu. yd 0.098 

Unloading from Canal Boats. — The plant used consisted of^a 
portable bin and a horse-operated derrick; Road 5014; Mr. James 
Anderson, contractor. The average amount of stone unloaded 
per day was 150 tons. The cost was $0,115 per ton, or $0.14 per 
cubic yard, divided as follows: 

I team and driver $ 4.00 (lo-hour day) 

I foreman 2.50 '' " ^' 

6 laborers, at $1 .75 per day. . 10.50 " " ^' 

Total $17.00 " " " 

Cost of Hauling Broken Stone. — Table 57 shows the cost of 
hauling stone on good roads as for repair work. The wagons 
were loaded from bins, so no time was lost in loading. 



HAULING 



589 



Table 57. — Haul of Stone on Good Roads for Repair Work 



Road 
No. 



Engineer in Charge 



Harold Spelman 
Harold Spelman 
G. G. MiUer . . . 
G. G. Miller . . . 
G. G. Miller . . . 
G. G. Miller . . . 
G. G. Miller . . . 
G. G. Miller . . . 
G. G. Miller . . . 
G. G. Miller . . 
G. G. MiUer . . . 
G. G. Miller . . . 
G. G. Miller . . . 



Price per 
Hour of 
Teams 


Length 

of Haul, 

Miles 


$0.50 


1.8 


0.50 
0.62 


1.2 
2.0 


0.62 


1-7 


0.62 


I.I 


0.62 


0.6 


0.62 


0.2 


0.62 


3-0 


0.62 


2.75 


0.62 


2.5 


0.62 


2.0 


0.62 


1-75 


0.62 


i-S 



Cost 

per Ton, 

Mile 



$0.20 
0.24 

o;2o 

0.215 

0.23 

0.25 

0.50 

0.17 

0.175 

0.175 

0.19 

0.215 

0.23 



Cost 

per Yard, 
Mile 



$0.24 
0.288 
0.24 
0.26 

0.275 

0.30 

0.60 

0.205 

0.21 

0.21 

0.23 

0.26 

0.28 



Road No. I, lo-hour day. 

Roads No. 2 and 3, 8 hours per day. 

Note. — Cost per ton mile on Roads No. 2 and 3 equals the cost 
per yard mile, for teams at $0.50 per hour. 

For hauling on bad roads for new construction I have the fol- 
lowing personal data: 

Clover Street Road, Section i, season 1908; teams at $0.45 
per hour; dump wagons loaded from bins; no time lost. 
6000 cu. yd., 0.6 mile haul cost 26 ct. per ton, or 31 ct. per 

yard mile. 
4500 cu. yd., 0.6 mile haul, cost 24 ct. per ton, or 29 ct. per 

cubic yard mile. 

Scottsville-Mumford Road, season of 1911; teams, $0.45 per 
hour. 306 cu. yd., i mile haul (including a 5 per cent, sandy 

hill 1200 ft. long) cost $0.30 per yard mile. 
500 cu. yd., 0.5-mile haul (level road in bad condition) cost $0.30 
per yard mile. 

Hauling Field Stone and Filler. — This material was hauled 
from fields and pits where it was loaded by hand, and considerable 
time thus lost. 

On the Clover Street Road, Section i, season of 1908, with the 
author as Engineer, and teams at $0.45 per hour, 10,000 cu. yd. 
of field stone were hauled an average of one mile for $0.36 per yard 
mile. 

On the Scottsville-Mumford Road, season of 191 1, with the 
author as Engineer, and teams at S0.45 per hour, 500 yd. of 
field stone were hauled 0.2 mile at $0.14 per cu. yd., or $0.70 per 
yard mile. On the same work 200 cu. yd. of filler were hauled 
0.2 mile for $0.15 per cu. yd., or $0.75 per yard mile. 

For all short hauls under J4 mile the cost is high and practically 
the same on account of the larger percentage of time lost in loading. 



590 COST DATA AND ESTIMATES 

Mechanical Hauling. — This method has not come sufficiently 
into general use to be considered in estimating, in the writer's 
opinion, unless it is difficult to get teams. It rarely pays to use 
traction engines for less than a three-mile haul, even on a hard 
road. In case they are used a light engine or road-roller and a 
train of ordinary dump wagons are more satisfactory than a heavy 
engine and large 5 or 7 cu. yd. cars. For maintenance and repair 
work, however, automobile trucks are the most economical. Under 
favorable circumstances mechanical hauling will cost about 12 to 
15 cents per yard mile considering interest, depreciation, etc. 

Cost of Loading Local Fence Stone into Wagons. — Road No. 
5046, W. G. Harger, Engineer, season of 191 1, 
Labor $0,175 per hour. 
2200' cu. yd., boulders loaded at a cost of $0.14 per cu. yd. 

A gang of six men will take from 9 to 13 minutes in loading i^ 
cu. yd., depending upon the size of the stone. 

Road No. 495, E. E. Kidder, Engineer, season of 191 1, 
Labor $0,175 per hour. 
1080 cu. yd., boulders loaded at a cost of $0,184 per cu. yd. 

Road No. 492, E. E. Kidder, Engineer, season of 191 1, 
Labor $0,175 per hour, 300 cu. yd., loaded at $0,137 per cu. yd. 

COST OF SPREADING STONE AND BINDER 

Table 58, page 591, gives the cost of spreading broken stone on 
several New York State roads. 

The ratio of the loose to the rolled depths varies with the size 
of the fragments and the depth of the course. Table 59, page 
591, gives the averages of the results obtained from 1000 test 
holes made by the writer on three separate roads. The last 
column of the table also gives the weights of No. 3 and No. 4 
stone required to make a cubic yard of rolled macadam. The 
amount of filler or binder per cubic yard of rolled macadam is 
given in Table 60, page 591. 

The excessive amount of filler required for the 2-inch bitumi- 
nous macadam. Table 60, was due to a layer of screenings placed 
under the No. 3 stone, all of which did not act as a filler. The 
small amount required for the 3-inch bituminous macadam was 
due to the fact that the bituminous binder partially filled the voids 
before the screenings were applied. 

The ratio of loose to rolled depth for boulder sub-base is variable. 

If the size of boulders is practically the same as the depth of 
the course, that is, if there is only one layer of stone, the loose 
depth and the rolled depth will be the same. Where there are 
two or three layers of boulders the ratio is, approximately, i : 1.25, 
i.e., a 12-inch, rolled depth would require 15-inch loose depth for 
boulders averaging 5 to 6 inches in diameter. 

Cost of Loading Filler at Pit. — On the Clover Street Road, 
Section i, during the season of 1908, with the author as engineer 
and labor at $0.15 per hour, 400 cu. yd. of sand filler were loaded 
at a cost of $0.12 per cu. yd. On the Scottsville-Mumford Road, 



SPREADING STONE 



591 



with labor $0,175 P^r hour, 200 cu. yd. were loaded at a cost of 
$0.13 per cu. yd. 





Table 58.- 


-Spreading Stone 






Refer- 
ence 
No. 


Engineer 


Labor 
Wage 


Depth of 
Loose 
Spread 


Amount 
Spread 


Cost 
per Ton 


Cost 

per Cu. 

Yd. 


I 


Harold Spelman . . 


$0.20 


4 in. 


7000 tons 


$0,066 


$0.08 


2 


W. G. Harger 


0.175 


5iin. 


6000 cu. yds. 


0.05 


0.06 


2 


W. G. Harger 


O.I7S 


4 m. 


4SOO " " 


0.07 


0.083 


3 


W. G. Harger 


0.20 


6" 


1000 " " 




0.05 






Placing sub-base stone 






3 


W. G. Harger 


0.175 


7 m. 


100 " " 





O.IO 


3 


W. G. Harger 


0.175 


10 " gravel 


200 " " 


— 


0.04 


4 


E. E. Kidder 


0.175 


6 " 


267 " " 


— 


0.07 


H 


E.E.Kidder 


0.175 


6 " 


1082 " " 


— 


0.12 



Table 


59. — ^Ratio of Loose to Rollee 


► Depth 


Size of Stone 


Rolled Depth 


Loose Depth 


Ratio 


Weight per 

Cubic Yard 

Rolled Measure^ 


No. 4 

No. 4 

No. 3 

No. 3 


4 in. 

3 " 
3 " 

2 " 


5.2 in. 
3.8 " 
3-9 " 

2.4 " 


1.3 

1.27 

1.3 

1.2 


3120 lbs. 

30S0 ;; 

3120 
2880 " 



Table 60. — ^Amount of Filler 


AND Binder Required 


Kind of Course 


Kind of Filler 


Amount of Filler 

per Cu. Yd. of 

Rolled Macadam 


Weight of 
Screenings per 
Cu.Yd. of Roll- 
ed Macadam 


Bottom stone 

Waterbound top^ . . . 
3-in. Bit. mac. top^. 
2-in. Bit. mac. top 3. 
Sub-base 


Sand 

No. I 

Nos. lA and 2 

No. lA 

Gravel 


0.35 CU. yds. 
0.50 " " 

0.37 " " 
0.60 " '' 

0.33 " " 


1300 lbs. 
900 '' 
1440 " 





Cost of Spreading Filler by Hand from Piles Spaced 20' to 30' 
Apart. — On the Clover Street Road, Section i, during the season 
of 1908, with labor at $0.15 per hour, 400 cu. yd. of sand filler were 
spread at a cost of $0.10 per cu. yd. On the Scottsville-Mumford 



592 COST DATA AND ESTIMATES 

Road, with labor at $0,175 per hour, the cost of spreading 200 cu. 
yd. was $0.20 per cu. yd. This includes some hand brooming, 
but most of the brooming was done by a broom attachment on 
the roller. 

Cost of Spreading No. lA and No. 2 Stone for Bitiiminous Mac- 
adam Top Courses and Brooming Same. — A layer of No. lA, 
3^ inch deep, was spread over the bottom course. On this was 
spread 23^^ inches of No. 3 stone. After rolling bitumen was 
poured over this course and a %-inch layer of No. 2 stone spread 
and rolled; the excess of No. 2 was broomed off and a %-inch wear- 
ing coat of No. I A placed. 

The cost of spreading for a 2-in. top was as follows: 

Cost of No. ix\ and No. 2 per cu. yd $0. 282 

Cost per ton of No. i A and No. 2 o . 210 

Eight hundred tons of this material were handled with labor 
costing $0,175 per hour. 

For a 3-in. top course the procedure was the same, omitting the 
layer of No. lA under the No. 3 stone. The cost of handling 
400 tons for the 3-in. course was as follows: 

Cost per cu. yd. of No. lA and No. 2 $0.31 

Cost per ton of No. lA and No. 2 o. 26 

Cost of Spreading Screenings with Cross Dump Wagons. — Wet 

dust screenings for waterbound macadam can not be successfully 
spread in this manner. For spreading dry dust screenings, No. 
2 stone or dustless screenings for bituminous macadam, this method 
has proved the cheapest and most satisfactory. On Road 5046, 
season of 1910, a number of short-time estimates made the cost 
of spreading by this method about $0.06 per cu. yd. The cost of 
brooming is slightly increased over that required by the hand-, 
spreading method, but not enough to counteract the advantage in 
the use of the wagon spreading. On the Clover Street Road, season 
of 1908, 1000 cu. yd. of screenings were thus spread for about 
$0.07 per cu. yd. 

COST OF ROLLING 

In the following costs lubricating oil is not included, as no 
reliable data were obtained as to the quantity used. Gillette's 
** Handbook of Cost Data" gives this item as $0.30 per day; us- 
ing this amount would increase the costs given below from 0.2 to 
0.3 of a cent per cu. yd. The amount of coal used was variously 
estimated at from 450 to 500 lb. per day. As before mentioned, 
items of depreciation, repairs of plant and equipment, and interest 
are not included in the cost per cubic yard of stone consolidated. 

On Road 5025, under Mr. E. E. Kidder, Engineer, during the 
season of 1910, the cost of rolling 3400 cu. yd. of bottom stone 
and 1700 cu. yd. of top stone, loose measure, was as follows: 

Rollerman, 4 months, at $90 $360.00 

Coal, li, ton per day, at $2.70 per ton, 80 days .... 55.00 

$415 00 



CRUSHING STONE 593 

The time and cost were divided as follows: 

3^ on sub-grade $ 69 . 00 

J^ on bottom stone 4'' deep 138.00 

3^ on bituminous top stone, 2" deep 208.00 

There was no cost for water. The roller worked 80 days in 4 
months. The cost of rolling per cubic yard of loose material 
was: bottom stone, $0.04, and top (bituminous macadam) $0.12. 

On Road 492, Mr. E. E. Kidder, Engineer, season of 1910, 
the cost of rolling 3700 cu. yd. of 4-in. bottom course was $0.03 
per cu. yd., and for 3200 cu. yd. of waterbound top stone $0.05 
per cu. yd. Both quantities refer to loose measure. The roller 
worked 74 days in three months. The puddling was done by a 
pipe line and hose and brooms attached to the roller. The roll- 
erman's wages were $90.00 per month and coal $2.75 per ton. 

On Road 5021 the cost of rolling a 3-in. bituminous top course 
per cubic yard of loose material was $0.09; for a 2-in. top $0.11. 

On Road 5046 a roller working in days consolidated 1850 
cu. yd. of field stone sub-base, 4300 cu. yd. of bottom stone, and 
2150 cu. yd. of top stone, loose measure. The depth of the sub- 
base was 6 in. (rolled measure), the bottom course 4 in., and the 
top course 2j^ in., bituminous macadam. The roUerman's wages 
were $90 per month and coal cost $2.75 per ton for J:£ ton per day. 
There was no cost for water. The costs were divided as follows: 
sub-base, $0,035; bottom stone, $0,045; top stone, $0,105 per cu. 
yd., loose measure. 

COST OF CRUSmNG STONE 

As a basis for all cost estimates for crushing, it is necessary to 
know something of the percentage of the different sizes of the 
crusher output. Table 61, page 594, gives the results of tests 
made by Mr. Archer White during the season of 19 10 on ordinary 
limestone and sandstone boulders composing the average field 
stone. The crusher used was the largest Acme portable crusher. 
The tailings were recrushed and the stone divided into four grades : 
No. I, M-in. screen; No. 2, ij^-in.; No. 3, 2j^-in., and No. 4, 
3 J^-in. From these data it may be seen that i cu. yd. of field stone 
makes i cu. yd. of crushed stone, and that it takes approximately 
1.8 cu. yd. of field stone to make i cu. yd. rolled measure of sizes 
Nos. 3 and 4. The crusher toggle was set to produce both top 
and bottom stone sizes. 

The cost of labor was $0.20 per hour. The engineman of the 
crusher plant received $0.25 per hour and the foreman $0.30 per 
hour. The field stone was loaded from a pile near the crusher 
into small dump cars running on a movable track. The loaded 
cars were drawn to the crusher by a small hoisting engine. The 
cost of bringing the field stone to the crusher pile is not included. 
The force loading consisted of one foreman, eleven laborers, and 
one engineman. The force crushing consisted of one foreman, 
four laborers, and one engineman. In eight days 1500 cu. yd. 



594 



COST DATA AND ESTIMATES 







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CRUSHING STONE 595 

were crushed. The cost of the entire output per cubic yard of 
loose measure was divided as follows: 

Loading stone for crusher $0 . 133 

Hauling to crusher 0.013 

Feeding to crusher o. 061 

Engineer to crusher 0.013 

Fuel and oil o . 030 

Loading crushed stone from bins o.oio 

Total $0,260 

Crushing Granite Hardheads and Sandstone. — The following 
data is from the records of the Clover Street Road, Section i, 
season of 1908. Labor cost $0.15 per hour and the engineman 
received $3 per day. The crusher used was a 10'' X 20'' Climax. 
A total of 5000 cu. yd. of granite were crushed at a cost per 
cubic yard, loose measure, of $0.19; 7000 cu. yd. of sandstone 
boulders were crushed at a cost of $0,103 per cu. yd., loose measure. 
These figures are for the total output of the crusher and include 
the cost of feeding to the crusher, the pay of the engineman, 
coal, oil, but not the delivery to the crusher. On the Scottsville- 
Mumford Road under similar conditions the cost varied from $0.13 
for granite and sandstone to $0.19 for granite hardheads per cubic 
yard of loose measure. 

Crusher force on the Clover Street and Scottsville-Mumford 
roads as follows: 

I foreman $4 . 00 

5 men feeding crusher 2 . 00 each 

I man tending screen 2 . 00 

I engineer 3 • 00 

Fuel and oil 4 . 00 

Where bottom stone alone is being crushed from local material 
the crusher is set to produce a larger amount of No. 4 stone, and 
the proportion of the screenings to the No. 3 and No. 4 size is 
different than given in Table 61. 

In the following data from Road 5046, Scottsville-Mumford, 
mentioned above, the No. 3 and No. 4 and tailings were used as the 
bottom course stone, the tailings being broken into proper sizes 
after the stone was spread by knapping hammers. The cost of 
knapping will vary from $0.01 to $0.03 per cu. yd. of loose bottom 
stone, depending on the number of tailings produced. When the 
crusher is set correctly to deliver a good grade of stone for bottom 
course, this charge should not amount to over $0.01 per cu. yd. 
of total output and is properly chargeable against crushing, which 
increases the crushing costs given above from $0.13 to $0.14 
and from $0.19 to $0.20. 

The sizes of screens were ^^'', i}4='\ ^W and sW^- 



59^ 



COST DATA AND ESTIMATES 



Crusher Set-up, No. i.— 60% granite, 30% sandstone, 10% 
soft rock. 

Total screenings. No. i 240 cu. yd. 

" No. 2 no record 

'* No. 3, 4, and tailings 1500 cu. yd. 

Crusher Set-up, No. 2.-50% granite, 40% sandstone, 10% 
soft rock. 

Total screenings 350 cu. yd. 

'' No. 2 no record 

'' No. 3, 4, and tailings 2600 cu. yd. 

For this same road the amount of field stone required per loose 
yard of bottom stone is shown by the following figures. Approxi- 
mately 1.5 yard loads were drawn to and from crusher. 



Date 


Number Loads of 
Field Stone Crushed 


Number Loads of 

No. 3 and No. 4 and 

Tailings Drawn from 

the Crusher 


1911 
Anril 2zi 


114 
86 

87 
104 
lOI 

106 

99 

86 

107 

no 

102 


93 
70 
69 
84 
82 

85 
78 

72 

95 
80 
83 


'' 2q 


'' 26 


Mav ■; 


ATA«,jr ;) 

'< 6 


8 


" Q 


'' 10 


''. II 


" 12 


'' 13 


Totals 


1 102 loads 
1653 cu.yds. 


891 loads 
1336 cu. yds. 





On this work 1.24 cu. yd. field stone produced i cu. yd. loose 
measure bottom stone, and 1.61 cu. yd. field stone produced i cu. yd. 
bottom stone rolled measure. 

Table 61, page 594, gives 1.8 cu. yd. field stone to i cu. yd. 
rolled macadam, but this apparent difference is explained by the 
fact that the tailings were recrushed and the crusher set closer to 
produce top as well as bottom stone, consequently the per cent, 
of No. I and No. 2 is higher than for the data just given. 

Data obtained by Mr. Frank Bristow, First Assistant Engineer, 



CRUSHING STONE Sgt? 

New York State Department of Highways, indicates that i cu. 
yd. of field stone produces i.i cu. yd. crushed stone when separated 
by screens of }4," , i}i" 2}4.'\ and 2)W\ this is slightly more than 
the writer's experience has indicated. 

When local stone is crushed for bottom only, the screenings are 
used as filler for that course, and in a case of this kind it is necessary 
to know how much additional filler must be estimated. Take 
the case of the Scottsville-Mumford Road (crusher set-up No. 2) 
given above. Twenty-six hundred cubic yards loose measure will 
consolidate under the roller to approximately 2000 cu. yd. of 
rolled bottom stone. This will require 2000 X 0.35 = 700 cu. 
yd. filler. The amount of screenings produced in crushing 2600 
cu.-yd. of bottom was 350 cu. yd., showing that for cases similar to 
the one given, half of the total filler required must be obtained 
from other sources. 

Cost of Sledging Boulders. — A certain percentage of the fence 
stone must be broken to reduce them to a proper size for crushing. 
This is done by blasting or sledging; where the boulders need to 
be broken only two or three times to reduce it to a usable size, 
sledging is the cheaper method. The cost of both of these methods 
is so variable that any cases cited would not be of much value. 
As given on page 636, under|Standard Estimates, the author allows 
arbitrarily $0.40 per cu. yd. for all boulders actually sledged or 
blasted, and in making estimates the per cent, to be treated in this 
manner is approximated roughly. 

As a matter of interest Gillette, in his cost data on rockwork, 
gives the cost of sledging small sandstone boulders as approxi- 
mately 0.05 per cu. yd., and the cost of mud capping at about 
0.35 per cu. yd. 

COST OF CRUSHING (continued) 

The following data is taken from the Report of the Massa- 
chusetts Highvv^ay Commission and refers to work done in Newton, 
Mass. The crushed stone was divided into the following sizes: 

Tailings 205 cu. yd 17.5% 

23^" stone 692'' " 57.0% 

Screenings and i" . . . . 30 *' " 25.5% 

Totals 1 197 100.0% 

The material was cobblestones and labor probably cost $0.20 
per hour, teams, $0.45. The cost per cubic yard at the crusher 
was $0,445, or $0.33 per ton. 

The cost per cubic yard was divided as follows: 

Teaming to crusher. $0.314 70.6% 

Feeding to crusher 0.033 7-4% 

Engineer of crusher o . 029 6.5% 

Repairs, coal, oil, etc o . 045 10.1% 

. Watchman 0.024 5.4% 

Total $0,445 100.0% 



59^ COST DATA AND ESTIMATES 

Material, Conglomerate. 

Amount broken 1288 cu. yd. 

Amount broken per hour 8.9** '* 

Divided as follows: Weight 

per Cu. Yd. 
Loose 

Tailings, 378 cu. yd 29.3% 25491b. 

23^" stone, 668 cu. yd 51.9% 2368*' 

Screenings and i", 242 cu. 

yd 18.8% 2727 '' 

Cost per cu. yd. in bins at crusher $1,112 

Cost per ton in bins at crusher o. 885 

Divided as follows: Cost Per Cent. 

Powder and repairs $0,018 1.6 

Labor drilling 0.249 22.3 

Sharpening drills and tools o .023 2 . i 

Breaking stone for crusher o. 420 37 . 8 

Loading stone for crusher 0.127 11. 4 

Hauling stone for crusher 0.062 5.6 

Feeding crusher oo53 4-7 

Engineer for crusher o 038 3 . 5 

Coal, oil, and waste o . 050 4 . 5 

Moving and setting crusher 0.023 2 .1 

Watchman o . 049 4 . 4 

Total $1,112 100. o 

Material. Greenish trap. 

Amount broken 3155 cu. yd. 

Amount broken per hour 7 • 7 ** " 

Divided as follows: Weight 

per Cu. Yd. 
Loose 

Tailings, 1004 cu. yd 31 .8% 2457 lb. 

23^" stone, 1618 cu. yd 51 -3% 2383 " 

i" stone, 323 cu. yd 10.2% 2277 " 

Screenings, 210 cu. yd 6.7% 2585 " 

Cost per cu. yd. in bins at crusher $0 . 898 

Cost per ton in bins at crusher o . 745 

Divided as follows: 

Cost Per Cent. 

Labor, steam, drilling $0,092 

Coal, oil, waste, powder, etc 0.084 

Sharpening drills and tools o . 069 

Breaking stone for crusher o . 279 

Loading stone for crusher o . 098 

Hauling stone for crusher o . 072 

Feeding crusher o . 053 

Engineer of crusher 0.031 

Coal, oil, waste, and repairs of crusher . o . 079 

Other repairs 0.041 

Total $0,898 



10 


3 


9 


4 


7 


7 


31 





II 





8 





5 


9 


3 


4 


8 


8 


4 


5 


100 






STONE FILLS 599 

W. E. McClintock, Engineer, Chelsea, Mass., season 1887; 

Labor $0. 20 per hour 

Teams o . 45 " " 

Material. Trap rock. 

Amount broken 1718 tons 

Stone delivered at crusher by sub-contractor for $0. 75 per ton. 

Cost, Tools $0,013 

Oil, waste, etc 0.016 

Fuel o . 050 

Stone at crusher o. 750 

Crushing (labor) o . 194 

Total per ton $1 .023 

Dustless Screenings. — The construction of bituminous mac- 
adams requires a dustless screening product referred to in the 
beginning of the chapter as No. lA; it is obtained by rescreening 
the ordinary screenings (%'' product) to remove the dust; the 
percentage of dust in the ordinary screenings will vary according to 
the stone crushed and the setting of the crusher jaws. The author 
has no reliable data for small crushing plants, but through the 
courtesy of the Buffalo Cement Company the following data is 
given for their output of limestone screenings at Buffalo, N. Y. 

Size of screen opening for ordinary screenings. . . M" 
Size of dust screen openings J^" 

Cu. yd. of dust for i cu. yd. ordinary screenings 0.35 

" " *' dustless screening i cu. yd. ordinary screening. . . 0.65 

The same data from the Leroy plant of the General Crushed 
Stone Company gives : 

Size of screen openings for ordinary screenings ^" to ^Ke" 

" " dust screen openings J^" ** %6" 

Cu. yd. of dust per cu. yd. ordinary screenings 33 % 

" " " dustless screenings per cu. yd. ordinary screenings 67% 

Percentage of screenings to total output for Leroy limestone 
approximates 15%. 

The above furnished to the writer through the courtesy of the 
General Crushed Stone Company, of Easton, Pa. 

COST OF STONE FILL BOTTOM COURSE 

The following data is taken from Road 5021, season of 19 10; 
labor cost $0,175 per hour, teams $0.40 per hour. 

The amount placed was 10,000 cu. yd. rolled measure. The 
average rolled depth was i.i ft. The surface was carefully brought 
to line and grade, allowing a variation of i in. either above or 
below, which inequality was taken out with the top stone. A 
3 in. bituminous top course was placed directly on this fill. The 



6oo COST DATA AND ESTIMATES 

top layer of bottom stone was sledged to reduce all stones to 8 in. 
or under. Flint stone was used to fill the top 6 in. and to surface 
the rough fill. The bottom course was of fence stone, hauled, on 
an average, about one-half mile. I estimate that one cubic yard 
rolled measure requires 1.25 cu. yd. loose. The cost of the bottom 
course per cubic yards rolled measure was $1.03, divided as follows: 

Loading i .25 cu. yd $0.19 

Hauling 1.25'' '' }i mile o . 20 

Placing 1 . 25 " ^' and rolling o. 24 

Sledging 0.15 

Flint o . 10 

Cost of fence stone 0.15 

Total, per cu. yd $1 .03 

Cost of Sub-base Bottom Course. — Road 495, Parma Corners- 
Spencerport. E. E. Kidder, Engineer. 1082 cu. yd. placed, 
average depth 6". Not much sledging required. 

Cost of stone, i cu. yd $0 . lo 

Loading, per i " '' o. 184 

Hauling i mile o . 30 

Laying, sledging and spreading filler o. 136 

Rolling 0.02 

Superintendence 0.02 

Cost of filler in pit nothing (gravel used) .... o . 00 

Loading 3^^ cu. yd o. 04 

Hauling }i cu. yd. i mile o. 10 

Total o. 90 

COST OF APPLYING BITUMINOUS BINDER 

The following data is taken from Road 5021, season of 1910. 
Bituminous macadam, penetration method: 

Labor. 

Kettleman $0 . 20 per hour 

Spreaders o . 20 " '* 

Plain labor o. 175 " " 

Teams 0.45 *' ^' 

Apparatus, 

4 bbl. kettle (coal burner) Bitumen heated 

2 bbl. " (wood burner) to 400° F. 

1 2 ton Kelly roller 

Spreading pots having a vertical slot J^" wide. 

Organization. 

RoUerman acting as foreman 
I Spreader 
I Kettleman 
3 Laborers 



BITUMINOUS BINDER 6oi 

Average speed 350 ft. of 16 ft. road, per day. 
Quantities. 

16,850 gal. laid in one coat covered 13,330 sq. yd., or 1.26 
gal. per sq. yd. 

Cost per gal. Unloading and hauling J^ mile $0.0015 

Heating 0.0032 

Spreading 0.0032 

Rolling and supervision 0.0051 

Total... $0.0130 

Bituminous material f.o.b. Caledonia 0.0950 

Total per gal $0 . 1080 

Second quantity. 

Forty-two thousand gallons covered 24,000 sq. yd. in one coat, 
an average of 1.75 gal. per sq. yd. 

Cost per gal. Unloading and hauling 1% miles $0.0032 

Heating o .0040 . 

Spreading c . 0039 

Rolling and supervision o . 0042 

Total $0.0153 

Bituminous material f.o.b. Caledonia 0.0950 

Total per gal $0.1 103 

Cost oj Applying Bituminous Binder. Road 5046, Penetration 
Method, 

18,890 gal. spread on 12,378 sq. yd. in one coat, of 1.52 gal. 
per sq. yd. 

Apparatus. 

5 2 bbl. kettles (wood burners) Fuel. Used bbl. staves and 

some extra wood. 
I lo-ton Buffalo Pitts Roller. 

Spreading hods. 

Organization. 

Per Hour 

1 Foreman $0 . 30 

2 Pourers, each 0.25 

5 Kettlemen, each o . 20 

2 Spreaders of No. 2, each 0.20 

4 Helpers, each o • 1 75 



602 COST DATA AND ESTIMATES 

Labor of Placing. Cost per gallon. 

Fuel $0,001 

Kettlemen o . 005 

Pouring ^o . 003 

Helpers o . 007 

Supervision o . 002 

Total I0.018 

Material f.o.b. Scottsville 0.093 

Total per gal $0,111 

Kentucky Rock Asphalt. — I have the following data from the 
Clarence Center Road, Mr. John D. Rust, Engineer, collected 
during the season of 1910. In this work an 8-ton tandem roller 
was found to do better than a 6-ton tandem. The cost of handling, 
spreading, and rolling this material, from data of five days selected, 
varied from $0,033 to $0,036 per sq. yd.; the average being $0,034. 
The following may be taken as a typical analysis of this cost: 

Abbreviations. L. Laborers. 
F. Foreman. 
T. Teams. 
E. Roller engineer. 

Asphalt $10.25 P^r ton f.o.b. unloading point. 

Run of July 20, 1909. 
69.22 tons hauled and placed. 
1730 sq. yd. covered. 
80 lb. asphalt per sq. yd. 

5 L. at cars, 10 hours, at $1 . 50 each $ 7 . 50 

}/2 F. at cars at $2 . 25 per day $ i . 12 

5 T. haul 2 miles at $4 . 00 per team 20 .00 

5 L. on wheelbarrows, 11 hours, each $0. 15 per hour 8.25 

I T. at shredding machine 4 . 40 

3 L. on rakes, 11 hours at $0.15 per hour 4.95 

3 L. shoveling, 11 hours, at $0.15 per hour 4.95 

I F. at shredder, 11 hours at $0. 225 per hour 2 .48 

I E. on roller, 1 1 hours at $0 . 30 per hour 3 . 30 

Total $56.95 

Cost per square yard, $ 0.033. 

PUDDLING WATERBOUND ROADS 

There are two methods of puddling: 

First, by Pipe Line and Hose. 

Second, by Sprinkling Carts. 

In the first method a 1 3^-in. or 2-in. pipe is laid along the road 
with taps every 200 to 300 feet. The road is wet down by a hose 
fastened to these taps and sprayed on by a nozzle, or the hose is 
fastened to a sprinkling attachment on the roller, which throws 



PUDDLING 603 

the water directly onto the wheels; this method is cheaper and 
more satisfactory than using sprinkling carts, but to work well 
a pressure of 125 lb. should be maintained at the pump, which 
requires a better pumping apparatus than contractors usually 
have. A very satisfactory plant, used near Rochester, N. Y., 
consisted of a Gould Triplex Pump, operated by a 6-H.P. gasoline 
engine; the relief valve at the pump was set at 120 lb. 

The cost of such puddling on Road 492 for 3000 cu. yd. of 
top course was $0.05 per cu. yd.; on Road 294 for 4000 cu. yd. 
of top course it was $0.06. This cost includes pumping, helper 
tending hose, and roUerman. Brooms on the roller were used 
which materially reduced the cost of brooming the screenings. 
No charge for water, no allowance made for laying the pipe line; 
this last charge is included in the lump-sum item of installing 
plant for a waterbound road, page 631. 

Gillette, in his handbook, gives sprinkling by carts approxi- 
mately $0.10 per cu. yd. of top course, which includes sprinkling 
the sub-grade as well as puddling the top course. As the sub- 
grade is rarely sprinkled, his data reduced to the conditions cited 
on roads 492 and 294 would give approximately $0.06 per cu. yd. 
of top course. To this is added the cost of rolling, or about $0.04, 
which makes the cost of puddling by this method about $0.10 to 
$0.12, or about twice the amount of the first method. 

Mr. E. A. Bonney, on the Hamburg-Buffalo road, from a metered 
supply of water, states the amount required to first puddle a 3 -in. 
top course varies from 50 gal. to 55 gal. per cu. yd. of top course, 
and the amount needed for the second puddle will be considerably 
less. ^ 

Mr. H. P. Gillette states, in a monograph on the Economics 
of Road Construction, that 30 gal. of water per cu. yd. will puddle 
a road. Mr. E. E. Kidder states that approximately 80 gal. are 
required per cu. yd. of top course for two puddles. The author^s 
experience agrees with the larger quantities. 

McClintock Cube Pavement. — The general costs of this experi- 
mental pavement were given in chapter VI. We here . give the 
detailed cost of the vitrified clay cubes and clay-ash cubes only, 
as the concrete cubes have not worn satisfactorily. 

Vitrified Shale Cubes. — During 1909, 74,000 2j^-in. vitrified 
shale cubes manufactured at Reynolds ville. Pa., were laid at a cost 
as follows: 

^Teams at $0.50 per hour 

74,000 cubes f.o.b. Reynoldsville $231 . 25 

Freight 68.41 

Carting 67 . 00 

Laying 20 . 00 

Total $386.66 

Note. — 331 sq. yd. were covered at a cost of $1.17 per sq. yd. 

Clay and Ash Cubes. — In 1910, cubes made of a local clay mixed 

with ashes and burned were tried in the effort to get a cheap, 



6o4 COST DATA AND ESTIMATES 

tough clay product. As far as known, this is the first time bricks 
made in this way have been used on road work. 

The ash-clay process has been worked out and patented by 
Karl Langenbeck, of Boston, Mass. Many local clays used for 
ordinary brick or farm tile will not stand up under vitrification 
without the addition of expensive, imported refractory clays; 
but the substitution of coal ashes for the more expensive clays 
has a similar effect and the cost is materially reduced. Some of 
the local clay was sent to Mr. Langenbeck, who turned out a few 
cubes that compare favorably in toughness with the best paving 
bricks on the market. 

The Standard Sewer Pipe Company, of Rochester, N. Y., under- 
took to furnish 400,000 2 -in. cubes of this description for Mr. Mc- 
Clintock. It was necessary for them to experiment to determine a 
practical method of molding, the correct temperature to use, and 
the best proportion of ashes, which naturally raised the price above 
ordinary practice. In molding they used a modification of the 
ordinary pipe-molding machine, which produced a hollow square of 
cubes, at the rate of 30,000 cubes per hour. The scoring knives 
were so set that the cubes were nearly cut apart, leaving just 
enough uncut clay to hold them together during the burning, 
after which a light blow separated them cleanly. The toughness 
of the resulting cubes can probably be increased by further experi- 
ment; but the product was good, although not up to the standard 
of the sample cubes made by Mr. Langenbeck. 

The cost of the ash-clay cubes was as follows: 

400,000 cubes f.o.b. Rochester, N. Y. $1200.00 $0,711 per sq. yd 

Carting, six miles 247.75 o-i47 *' 

Filler 27.00 0.016 '' 

Labor of laying 191 -77 0113 *' 

Roller 12.94 0.008 '' 

Total $1679.46 $0,995 " 

Note. — 1688 sq. yd. covered 

Labor, $0.22 an hour \ r ■, - 1 .- 

Teams! fo.50 an hour | ^°' '^^'"2 ^""^ ^^'^'""S- 

Mr. McClintock has stated, in discussing the cost, that in large 
quantities he believes the cubes can be delivered f.o.b. at the 
plant for $1,50 per 1000, which would reduce the cost as shown 
above to about $0.60 per sq. yd., and that the high cost of laying 
was due to the irregular shape of the first batch, due to not scoring 
the cubes deely enough. 

Amiesite Cost Data. — Road 13 19, Honeoye Village, Season of 
1 91 5. H. W. Baker, Eng. in charge. 4700 sq. yd. laid 16' 
wide 2^" deep. Laid in two courses. Bottom course 2j^" thick 
coarse material; surface 3^" thick fine material. 

Material 

588 tons @ $4.00 per ton f.o.b. plant $2352 .00 

588 tons freight $0.54 per ton 341 .04 

Total cost materials $2693 .04 



AMIESITE 60s 

Labor 
Force at cars unloading 

6 Laborers @ $2 . 00 per day $1 2 . 00 

I Foreman @ $2 . 50 per day 2 . 50 

I Fireman @ $3 . 00 per day 3 . 00 

I Night Fireman @ $2 . 50 per day . , 2.50 

$20 . 00 

Equipment at Cars 

I boiler and pipe line per day 8 . 00 

J^ ton coal and oil 2.50 

Total daily cost of unloading $30 . 50 

Hauling % mile 

4 teams @ $5 . 00 per day $20 . 00 

Spreading and Compacting 

I Asphalt raker 3 . 00 

4 Laborers @ $2 .00 per day 8.00 

I Rollerman 3 . 00 

per day $14 . 00 

Equipment 

I roller (10 ton tandem) 10 .00 

Coal, oil, etc o . 80 

Daily cost spreading and compacting ........ $24.80 

Summary Daily Force Account 

Unloading 30 • 50 

Hauling T 20 . 00 

Spreading and compacting 24.80 

$75.30 

Number of days worked, 15 

Total labor 15 days $1129.50 

*' materials cost 2693 .04 

Total cost $3822 . 54 

Cost per sq. yd . . o . 81 

Bid price sq. yd o . 85 

Conditions 

This work was done under bad weather conditions the night tem- 
perature being below freezing and only two days with an air 
temperature above 55® F. 

It was necessary to keep a night fireman at the cars to keep up 
steam and to move the steam pipes to different parts of the cars to 
insure the amiesite being in a condition to loosen and shovel in the 
morning. The material was loosened by bars and sledges to the 
bottom of the cars steamed 10 to 30 minutes and then shoveled 
into dump wagons, covered with canvas and hauled to the street. 

Under favorable weather conditions the cost of unloading from 
the cars would probably be reduced 40%. 

. Table of Amounts of Amiesite required for different thicknesses and 
materials J page 606. 



6o6 



COST DATA AND ESTIMATES 



Id 


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in 

g 

C/3 



HASSAM CONCRETE 



607 



TOPEKA MIX 

The following data on output and organization is quoted from 
E^igineering Contracting. 

The wearing surface mixture was prepared in a Cummer standard 
I -car portable paving plant of 2000 sq. yd. of 2-in. top per day 
(10 hours) rated capacity, having a twin-pug mill (10 cu. ft.) 
capable of handling a looo-lb. batch of material. The total weight 
of this plant ready for transporting is 100 tons. 

When the plant is working at its full capacity, 3 tons of coal are 
required per day. 

The organization at the plant is as follows: 
I Foreman. 
Engineer. 

Fireman and i blacksmith. 
Men at scales weighing materials. 
Men feeding stone to elevator to drier. 
Men feeding sand to elevator to drier. 
Men shoveling stone from car. 
Men shoveling sand from car. 
Men stripping barrels, etc. 

Man with horse, conveying sand from pile to elevator. 

Man with horse, conveying stone from car to elevator. 

On a good day's work (8 hours) the following quantities of 

material were used: 16 tons of asphalt, 132 tons of stone, 47 tons 

of sand, 11 tons of dust or filler, making a total of 206 tons of 

mixture. 

Hassam Concrete Pavement. — Cost of Grouting, Road No. 
5529. Lyell Ave., Spencerport. Season 191 5. E. E. Kidder, 
Eng. in charge. Road 16' wide 5" deep compacted measure and 
approx. 6 miles long. 9880 cu. yd. of Hassam were grouted in 
71 working days with the organization shown in the figure below. 

Inspeeton 
]A(lui8itiT» Natlres Ylston Eto. 




71 days @ $36 . 25 per day 

Amxount grouted 

Cost of labor per cu. yd. . . 



$2573-75 
80 cu. yd. 
$0.26 



Conditions, — Administration and superintendence good. Temper 
of crew rather bad as they were not receiving the wages that they 
expected to get for the first half of the job. Could have made a 
better record. 

Speed oj Work, — Averaged 450 lin. ft. per day. 



6o8 COST DATA AND ESTIMATES 



Materials 

Cement. — 8500 bbl. used or an average of 0.86 bbl. per cu. yd. 
of Hassam. This varied from 0.75 in the beginning to 0.95 during 
the latter part of the work when a liberal spread of stone was used 
to compensate for rough grading and a desire to end the work before 
winter. 

Sand. — Royalty on sand was $0.30 per load or $0,052 per cu. yd. 
of Hassam. Cost of haul corresponds to average costs given in 
previous cost data. 

Stone. — 16,050 tons of limestone i^H' to 3J^"in size were used. 
This amounts to 3250 lb. per cu. yd. compacted measure which is 
high for this grade of stone. This was due to a liberal use of stone 
over poorly shaped sub-grade and to excess depth where wet 
material was removed. 

Water. — Metered supply. 70 gal. per cu. yd. of Hassam*; this 
includes water for engines, leakage in a long line and considerable 
waste at the grout mixer. 

Concrete Roads 
Cost Data. — Rd. 5423, Hartland Medina Pt. 2. Season 1914. 
F. W. Bristow, Eng. in charge. 9550 cu. yd. i : iK -3 concrete 
pavement laid 16' wide 6" deep. 

Materials and Equipment 

Cement. — Knickerbocker @ $1.18 net bags returned f.o.b. 
siding. 4 mile average haul. 

Sand. — Excellent local sand. 1%, mile haul. 

Stone. — ^Local crushed stone (Medina Sandstone and granite J^'' 
to 2%" in size) 34 mile haul to crusher, i mile haul crusher to road. 

Concrete Mixer. — Koehring with boom and bucket delivery % cu. 
yd. batch. 

Speed of Work. — 500 to 550 lin. ft. of road or 148 to 165 cu. yd. 
mixed and placed per 10 hour day. 

Actual Amount of Materials Used 

Cement 1.85 bbl. per c. y. concrete 
Sand 0.4 c. y. per c. y. concrete 
Stone 0.80 c. y. per c, y. concrete 
Joints 

Wooden joints used for J^ the work. 

Steel and felt joints used for J^ the work. 
Labor Cost of Mixing and Placing Concrete 

Labor $1.75 per lo-hour day. 

The force at the mixer comprised: 

1 Foreman. 

2 Laborers setting forms. 
10 " shoveling stone. 

3 " " sand. 

6 '' on stone wheelbarrows. 
" sand 



CONCRETE PAVEMENTS 609 

I Laborer passing cement. 
I " emptying *' 
i^Mixer runner. 

1 " fireman. 

4 Laborers placing concrete. 

2 " on screed. 
2 " floating. 

I " preparing joints. 

I " sprinkling, brooming, etc. 

The cost of setting forms, mixing, placing and finishing the con- 
crete including coal ranged from 0.48 to 0.51 per cu. yd. 

This does not include overhead or plant charge. 

The water cost per cu. yd. concrete was approx. $0.04 and in- 
cludes laying pipe line and pumping from creeks. 

The overhead charge per cu. yd. of concrete was approx. as 
follows: 

Bond $0 . 036 per cu. yd. 

Employers Compensation Insurance $2.92 per 

$100 payroll 0.096 " '' " 

Public Liability Insurance o .016 '' '' '' 

Machinery and tools, freight hauling, erection, 
. interest, depreciation and repairs 0.600 " " " 

$0,748 
Say $0.75 per cu. yd. 

COST DATA, CONCRETE ROADS 
Materials 

' Stone. — Cost of stone varied greatly during the year, from 62^ to 
S$^ per cu. yd. at the Blissville docks. To obtain a low voidage 
contractors ordered a mixture of No. 2 and No. 3 stone. This mix- 
ture weighed approximately 2700 lb. per cu. yd.; therefore, cost 
of stone f.o.b. car at destination would be 

I cu. yd. stone at Blissville (say) $0 . 80 

Transfer (17^^ per ton), i .35 X 0.17 0.23 

Freight (63^^ per ton), i .35 X 0.63, (rate to Patchogue) 0.85 

Total $1 . 88 

Note. — ^Arrigoni paid $1.81 delivered f.o.b., on rate made in 1 914, 
before stone raised. Freight rate to Patchogue then 60^. 

Haul variisd from i2f!^ per yd. mile using tractor-roller and 5 cu. 
yd. trailers (3), to as high as 35^ per yd. mile with teams. 

Transfer from cars to wagons 15^ to 20^ per cu. yd. dependent 
mostly on rate of wages; therefore, cost on job, with stone as per 
above, and a two-mile haul would be approximately $1.88 + 0.60 
+ 0.20 = $2.68 per cu. yd. 

Gravel. — Cost of same at bank, screened, and in bin varied from 
4Si' to 85^ (dependent mostly on per cent, of gravel). Haul: same 
as stone. 

{Continued page 612.) 



6io 



COST DATA AND ESTIMATES 






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1200 
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COST DATA AND ESTIMATES 



Sand. — Cost of same at bank (in wagons. Screening unnec- 
essary) varied from 35$^ to 60 1!^. 

Haul: 25^ to 35^ per yd. mile. 

Note. — ^When obtained from same pit as gravel I would consider 
its cost in bin as }i the cost of all material leaving the plant, gravel 
in this case % of same total (say 25^ [sand] and $0^ [gravel] where 
gravel would be 75^ + were all sand wasted). 

Cement, — Cost of cement varied greatly during the year; a good 
average was $1.20 per bbl. net. Actual practice with graded stone 
has shown 1.75 bbl. per cu. yd. of concrete a safe factor. 

Haul varied from ^^i^ (truck) to 5^ (wagon) per bbl. mile. 

Handling: average 2^ per bbl. when handled direct from car to 
job. 



W 



^ Bridge 



W 



Screed 



E 



■*E *E 
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03 









Organization 
Concrete l-l>^-3, 4 bag batoh 

.H 

better Position Kumbe 

=j A Foxeioaii B 

B Engineer 

^ C Fireman. 

^ D Chute 

E Placing cone 

f F Screeding 
4 

Floating 



G 
H 



a 



K 



Brooming and 
general help 
Cement (to hoixpex) 

Cement (getting 
ready ) 



L Stone (barrows) 

^M Stone (shoveling) 

N Sand (barrows) 

Q Sand (sho.v&ling) 

P Forms 

R Pump 

T Trimming grade 



1 

1 

1 
3 
t 

I 
1 
2 

I 

4 or 5 

8 

2 or 3 

3 

2 

1 

3 



W Watchmen, covering 2 
and wetting down 

Also charge H Supt. and }i timekeeper 

Trimmers "T" place expansion joints 



Rate 

4.00 
3.00 

2.50 

2.00 

2.00 

2.00 

2.50 

1.85 

2.00 

1.85 
1.85 
,1.85 
1.85 
1.85 
2.00 
2.25 
1.85 
1.85 



IR 



CONCRETE PAVEMENTS 613 

Plant, — Exclusive of forms and water-line. 

I Mixer^4 bag mix, i-iJ^-3, at least 20 cu. ft. capacity. 

I Screed — 19' by 4" by 12", with }i'^ iron plate. 

I Bridge— 18' X 3" X 12". 

3 floats — (one split); and one trowel. 

I doz. Forks — close tined for stone. 
10 Square Shovels. 
16 Wheel-barrows (2 or 2}^ cu. ft. capacity). 

1 Canvass — 160' X 20' — with frame. 

2 Tampers. 

I Template to test sub-grade. 

I doz. Pins to hold expansion joints (or special template for that 
purpose). 
Small tools, other than noted. 

I Straight-edge, 24' X 10" X 4", for extra width on curves. 
Total cost of above approximately $2300.00. 

Manipulation 

Exclusive of water, forms and trimming sub-grade. 

Supt. (K) 3-00 

Time keeper (3^) i . 00 

Foremen (2) (see Fig., page 612) 7 .00 

Engineer(i) ( " ^' , page 612) 3.00 

Fireman (i) ( " '' , page 612) 2.50 

Mason (i) ( " " , page 612) 2.50 

Laborers (8 at 2.00) (see Fig., page 612) ... 16.00 

Laborers (21 at 1.85) ( " '' , page 612) ... . 38.85 

Total $73-85 

Based on an average day's work of 182 cu. yd. (lo-hour day), 
the manipulation of a cubic yard of concrete would cost with the 
above organization, $0 . 406. 

Note. — The above organization has laid over 780 lin. ft. of i6j^ 
ft. pavement (outside dimensions), in a lo-hour day. (The 182 cu. 
yd. is based on a length of 600' of pavement with a cross-section of 
8.2 sq. ft.) 

Water 

Plant should be capable of supplying 30 gallons per minute. 

Pipe : 10,000 (at least) lin. ft. 2" pipe, galvanized at 16 

cents $1600 . 00 

Black, at 14 J^ cents 1450.00 

35 "Ts" for same (one each 300') at 50^!^ 17 ■ 50 

Pumps: 3 to 25 H.P., dependent on conditions. For lower 
power, gas engine O. K.; for higher, steam the best (latter, best for 
surety of supply). 

Outfits $150.00 to $1000.00. 

Where wells were necessary, 2" supply pipe. Driving same $1.40 
per ft. for depths not greater than 40'; $1.50 to 70' depth. This 
includes pipe and point. 



6 14 COST DATA AND ESTIMATES 

Shaughnessy paid a lump sum for water from Bayshore to Islip 
($300,00, I believe) from hydrants. On 5 23 2 a, water was bought 
from private parties for part of the work at $3.00 per day. 

Cost of running steam pump located at well or surface water 
supply, including operator, varies from $5.00 to $8.00 per day de- 
pendent on weather conditions. 

200' of rubber hose at $0.34 per ft. necessary for connection with 
mixer and sprinkling road. Of this a 15-foot section should be con- 
nected on intake pipe of mixer, with which to sprinkle sub-grade. 

Forms 

1. d" Channel forms (steel) 32^^ per ft. including pins, 8' sections. 

2. Patent steel forms with bevel, 24^^ per ft. Pins for same $1.00 
each, one necessary for each section. Sections 12' long. 

3. Wooden forms with bevel about 12 cents per lin. ft. 

Cost of placing same, 2 men at $2.00 per day, $4.00 per day (see 
''P," Fig., page 612). 

At least 1 200 ft. of forms necessary, so that 600 lin. ft. of road can 
be built without forms being moved. Based on (2) forms would 
cost 

1200' of forms $288.00 

Say no pins 110.00 



Total $398.00 

Trimming Sub -grade 

Three men generally necessary at $1.85 per day (see T, Fig., page 
612). 

General 

A steam roller ($2200.00) might justly be, partially at least, 
charged to concrete. Cost of operating same, including rollerman, 
not greater than $12.00 per day if owned by contractor. 

CONCRETE COST DATA 

Name of Road, Main Street, Sec. Ill, County Highway No. 130. 
(Erie County, New York State) 
Length, 3 . 68 miles. Thickness, average 7" parabolic crown. 
Width, 16'. Proportions of mix, i-iJ^-3. 

Total No. Cu. Yd., 7038. 

1. Labor, exclusive of water supply, including supervision. 0.6818 

2. Plant forms and tools 0.3091 

r Steel plates 0.1782] 

3. Expansion joint material -{ Tarred paper 0.02 95 \ 0.2077 

I 0.2077J 

4. Water supply, including labor 0.0625 

5. Cement placed on roadside ready for mixer 2 .3379 

6. Sand '' " " " " " 0.8359 

7. Stone '' " " " ^V " 1. 0518 

8. Reinforcement, if any o. 0000 

Total cost per cu. yd - 5-4867 



CONCRETE PAVEMENTS 615 

Labor, rate per hour, i6J^^; Teams, rate per hour, 50^; Hours in 

day worked, 10. 

Remarks: Work done by State day Labor. Materials unloaded 
by hand. Plant Charges included proportionate to life of plant. 
Seven- tenths mile average haul. 



Name of Road, Huntington- Amity ville, Pt. 2, No. 12 19 (Suffolk 
County). 
Length, 4.69 miles. Thickness, 4%'' and 6%" = av. 5%". 
Width, 16'. Proportions of mix, 1-13^-3. 

Total No. Cu. Yd., 7409. 

1. Labor, exclusive of water supply, including supervision. . . $0.52 

2. Plant forms and tools o . 58 

3. Expansion joint material o .05 

4. Water supply, including lahor ,. . o. 10 

5. Cement placed on roadside ready for mixer 2 .36 

6. Sand '' '' " " '' " 0.23 

7. Stone Gravel " " " " " i .05 

8. Reinforcement, if any o. 00 

Total per cu. yd $4 . 89 

Contractor's Bid Price 5 . 30 

Labor, rate per hour, 20^; Teams, rate per hour, 55^^; Hours in day 

worked, 10. 

Remarks: Auto truck for most of haul. Gravel furnished by 
large screening and washing plant accounts for high plant cost. 
Only proportionate part charged for this plant as it is to be used to 
produce commercial output. 

Road No. 1 201 — Nassau County 

(i) Sand: 

In bins Heling Bros, per cu. yd $0.15 

Haul by auto (contractor owner) 2}^ mi. at o. 15 0.38 

Sand on road per cu. yd o. 53 

Gravel: 

In bins Heling Bros, per cu. yd o. 85 

Haul by auto (contractor owner) 2}4 mi. at 0.15 0.38 

Gravel on road per cu. yd $1 . 23 

Cement: 

Cement stored at $1 .00 per day for 150 days. ... $150.00 
Approximately 11 70 bbl. stored. Storage per bbl. o. 13 

F.o.b. Farmingdale (est.) i . 30 

Handling and hauling (o. 10 est.) double handling 

in most cases o.io 

Cement per bbl. on road $1 • 53 

This price also approx. cost of cement bought from 
Parker, Hassam Co. 



6i6 COST DATA AND ESTIMATES 

Plant: 

(2) I auto truck (Sauer) $6,500.00 

1 Concrete mixer 1,200 .00 

2 doz. shovels. 21 .00 

2 teams at $700, 2 bottom dumpers at $400. . . 2,200.00 

Forms (wooden) 800 lin. ft 40 .00 

8 barrows 24 . 00 

2 doz. picks 42 . 00 

I bucket conveyor, loader 600 .00 

I Screed iS • 00 

Incidentals 20 . 00 

$10,672 .00 

(3) Pressure water from fire plugs 

Pavement per cu. yd. cone. o. 10 $100.00 

1500 ft. (lin.) 2" pipe at 0.08 120.00 

100 ft. 2" rubber hose 50 .00 

300 ft. 1" rubber hose 45 -oo 

$315.00 

(4) Manipulation per cu. yd. in place, This does not 

include covering, uncovering, sprinkling $0.92 

(5) Forms: 

Setting and re-setting forms per Hn. ft. of road . $0 . 03 

3 X 1.75 X 20 days 

9 '-^ ^= 0.03 

3093 

(6) Trimming: 

Per cu. yd. of concrete $0. 28 

6 men @$ i . 75 20 days = $210 
roller @ 12.00 6 '^ = 72 

$^ Q 

= 0.28 

990 

cu. yd. of cone. 

Expansion joints at 40^ apiece every 30 ft. 

Covering and uncovering and wetting concrete 
during curing season 

2 men to cover (g $1 . 75 $3-50 

2 men to uncover at $1 . 75 3 • 5° 

I man to sprinkle i . 75 

$8.75 

-^-^ = $0.18 per cu. yd. cone. 

990 

Road No. 1203 — ^Nassau County 

(i) Sand: 

In Pit of Mr. Bennett per cu. yd $0.15 

Screening and loading (estimated) 0.22 

Haul 2 mi. (auto truck) contractor owner @ o . 1 2 0.24 

Cost per cu. yd. on road $0.61 



CONCRETE PAVEMENTS 617 

Trap Rock (Imported) 

F.o.b. Baldwin $1 . 59 per cu. yd $1 . 59 

Unloading 15^ 0.15 

Haul 1 .6 mi. at 25 j^ teams and auto truck. ... 0.40 

m^ Stone per cu. yd. on road $2.14 

W^ Cement: 

^ " F.o.b. Baldwin per bbl $1.38 

Handling and hauling per bbl. 0.05 o. 05 

Cement per bbl. on road $1 43 

(2) Plant: 

I Screed $ 20 . 00 

I Concrete Mixer 1800. 00 

I Steam Roller 3000 . 00 

1 doz. Wheelbarrows 36 .00 

2 doz. Shovels . 21 . oo 

3 Teams at $700, 3 Bottom Dumpers at $400 3300.00 
■ I Auto Truck '. 5000 . 00 

2 doz. Picks 42 .00 

Forms (wooden $20.00; steel $126.00) 146.00 

ft Incidentals 50 . 00 

P Water Wagon 400 . 00 

$13,815.00 
Water: 

Pressure line fire plugs, total $100 .00 

4000 ft. 2'' pipe .06 240 .00 

100 '' '' rubber hose 50.00 

300 '' 1" " '' 45.00 

$435- 00 

(4) Manipulation: 

Includes all works, sprinkling, covering, uncover- 
ing, in place complete per cu. yd $0.67 

(5) Forms: 

Setting and resetting forms per lin. ft. of road. . 0.05 

(6) Trimming (Sub-grade) 

Per cu. yd. concrete in place o. 24 

Expansion Joints at 40^. apiece every 30 ft. 

Road No. 121 9. — Suffolk County 

(i) Sand: 

In bins Heling Bros, pit cu. yd $0. 10 

Haul by auto (contract) i . 5 mi. est. o . 30 0.30 

Cost per cu. yd. on road $0.40 

Gravel: 

In bins Heling Bros, pit cu. yd $0. 75 

Haul by auto (contract) estimated o . 30 0.30 

Cost per cu. yd. on road $1 05 

Cement: 

Bbl. f.o.b. Farmingdale $1.27 

Handling and hauling 0.08 

Cement on road per bbl $1 • 35 



6i8 COST DATA AND ESTIMATES 

(2) Plant: 

Same as on No. 1218 

(3) Water: 

Cost of water $700 . 00 

I mile 2" pipe at 0.06 per ft 320.00 

100 ft. 2" rubber hose 50 :oo 

400 ft. i/' '' " 60.00 

I pump and gas engine (est.) 1000 .00 

$2130.00 

(4) Manipulation: . 

Includes all work; sprinkling, covering, unco^^er- 

ing, in place complete per cu. yd $0 . 50 

(5) Forms, setting and resetting per lin. ft. of road . . 0.02 

(6) Trimming: 

Per lin. ft. of road o . 06 

Expansion joints at 40^ apiece every 30 ft. 



Road No. 12 18— Suffolk County 

(i) Sand: 

In bins Heling Bros, pit cu. yd $0.10 

Haul by auto (by contract) i . 7 mi. approx 0.40 

Sand per cu. yd. on road $0 . 50 

Gravel: 

In bins Heling Bros, pit cu. yd $0. 75 

Haul by auto (by contract) approx o . 40 

Cost per cu. yd. on road $1.15 

Cement: 

F.o.b. Farmingdale $1.27 

Handling and hauling o . 08 

Cement on road per bbl $1 • 35 

(2) Plant: 

Gravel and sand screening complete, including 

various set ups , $15,000 .00 

I Concrete Mixer 1,800 .00 

I Roller 2,800 . 00 

1 Screed 20 . 00 

18 Wheelbarrows 54 00 

2 doz. Shovels 21 .00 

3 teams @ $700, 3 bottom dumpers @ $400. . . 3,300.00 

2 doz. Picks . 42 . 00 

I rd. Planer and Scarifier 600 .00 

Forms (steel) 630 . 00 

Tarpaulins 100 . 00 

Incidentals 75 .oo 

$24,442.00 



I 



CONCRETE PAVEMENTS 619 

(3) Water: 

Total paid for water approx $130 .00 

I mile 2" pipe at o . 06 320 . 00 

100 ft. 2'' rubber hose 50 .00 

400 ft. i'' ^* '' 60.00 

$560.00 

(4) Manipulation: 

Includes all work, sprinkling, covering, uncover- 
ing, in place complete per cu. yd $0. 54 

(5) Forms: 

Setting and resetting forms per lin. ft. of road.. . 0.02 

(6) Trimming: 

Per lin. ft. of road o . 06 

Expansion joints 40^ apiece every 30 feet. 

COST DATA 

Name of Road, Huntington Town Line-Farmingdale, Part i 
(Suffolk County) 

Length, i .27 miles. Thickness, 5" & f = Av. 6". 

I Width, 16'. Proportions of mix, I -I J^ -3. 

j ^ Total No. Cu. Yd. 2051. 

j I. Labor, exclusive of water supply, including supervision. . $0.56 

I 2. Plant forms and tools o . 61 

I 3. Expansion joint material o .06 

t 4. Water supply, including labor 0.12 

' 5. Cement, Placed on roadside ready for mixer 2 . 13 

1 6. Sand, '' " " '' " " 0.22 

J 7. Stone, " /' " ^ " " 1. 01 

\ 8. Reinforcement, if any o . 00 

' Total per cu. yd $4.71 

Contractor's Bid Price 5 .30 

Labor, rate per hour, 20j!f; Teams, rate per hour, ssi'j Hours in day 
' worked 10. 
I Remarks: Auto truck for most of haul. Gravel furnished by 

large screening and washing plant accounts for high plant cost. 
{ Only proportionate part charged for this plant as it is to be used to 
j produce commercial output. 



(Road No. 1202 — Nassau County 

(i) Sand: 

Estimated at o. 10 per cu. yd. in bins $0. 10 

Haul (by contract) estimated at 0.40 per cu. yd.. . . 0.40 

$0.50 
Gravel: 

Stiff leg derrick set up (in bins) $2 . 00 

Haul (by contract) estimated at o . 40 per cu. yd . . . . o . 40 

ist set up per cu. yd. on road $2 . 40 



620 COST DATA AND ESTIMATES 

Drag line set up per cu. yd $i . 20 

Haul (by contract) estimated 0.40 per cu. yd 0.40 

2nd set up per cu. yd. on road $1 .60 

Imported gravel per cu. yd. scow L. I. City o. 85 

Unloading from scow L. I. City 0.15 

Freight L. I. City to Central Park o. 78 

Unloading at Central Park o. 10 

Haul (by contract) at o . 20 per cu. yd 0.20 

Cost per cu. yd. on road $2 .08 

Average cost per cu. yd. on road $1 .92, 
Cement: 

Bbl. f.o.b. Central Park { t^'"^^^, } f i . 20 

Haul by contract per. bbl 0.06 

Handling 0.02 

Per bbl. on road $1 . 28 

(2) Plant estimated $12,000.00 

(3) Water: 

Cost of water $1 ,000 . 00 

4 mile 2" pipe at $0.06 per ft . 1,270.00 

100 ft. 2" rubber hose at $0. 50 '. 50.00 

400 ft. I " '' '' $0.15 60.00 

I pump, boiler, etc 1,000.00 

$3,380.00 

(4) Manipulation: 

Includes all work, sprinkling, covering and uncover- 
ing; in place complete per cu. yd $0.64 

(5) Forms: 

Setting and taking up per lin. ft. of road 0.04 

(6) Trimming: 

Per lin. ft. of road o-07S 

Expansion joints at 40^ apiece every 30 ft. 

COST DATA 

Name of Road, Little Valley-Cattaraugus, Part i (Cattaraugus 
County) 

Length, 5.3S miles. {3900 lin. ft. ^x^6 ft. I 

T,, . , / 6" & 8" = Av. 7". \ 

Thickness, I ^i^„ g^ ^„ ^ ^^^i^^.„_ I 

2 . 575 miles completed. 

Width, 16 and 14. Proportions of mix. i-iJ^-3. 

Total No. Cu. Yd. 8280 — This cost covers 4165 cu. yd. 



CONCRETE CULVERTS 



621 



1. Labor, exclusive of water supply, including supervision. . 0.423 

2. Plant forms and tools, o. 662 + o. 158 for coal 0.820 

3. Expansion joint material o .045 

4. Water supply, including labor o .030 

5. Cement, placed on roadside ready for mixer i .984 

6. Sand, '' '' " '' " " 0.522 

7. Stone, " " '' " . " '' 1.505 

8. Reinforcement, if any 0000 

Total cost per cu. yd 5-324 

Contractor's bid price 6 . 30 



Labor, rate per hour, i8j^^; Teams, rate per hour. None used; 

Hours in day worked, 10. 

Remarks: Industrial Ry. Plant delivering sand, stone and 
cement into hopper of concrete mixer, clam shell unloader used to 
take material off cars. Material delivered alongside mixer in 
buckets proportioned for one batch size. 

For plant layout see illustration 







-28 Stafriotts - 
14 Foot 



Track 



' ^^^/^/^^^^^f^r. 






.,,ger,8.ta... 



Sketch 

Showing Layout of Plant 
on Boad 1209 



COST OF CONCRETE WORK 

The following data will help in estimating the cost of small con- 
crete jobs, such as culverts, walls, etc. This data was collected by 
Mr. E. E. Kidder during the season of 1908. Table 62 contains the 
theoretical proportions of cement, sand, and stone required for the 
three ordinary mixtures of concrete. These values were found by 
experience to agree with actual proportions very closely for J^" to 
iJ4"-3tone. (Continued page 623.) 



622 



COST DATA AND ESTIMATES 







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CONCRETE CULVERTS 623 

Table 62. — Materials Required for i Cu. Yd. of Concrete 



Mixture 


Cement 


Sand 


Stone 


i-ii-3 •••• 

1-2-3 

1-2-4 

1-2^-5 • • • 

1-3-6 


1 . 9 bbls. 

in 

1.0 " 


0.42 CU. yds. 

0.52 " " 

0.4S " " 
0.46 " " 

0.47 " " 


0.85 CU. yds. 

0.77^^ " 
0.90 " '' 
0.92 " '' 
0.95 " " 


) 

The amount of water used per cu. yd. of concrete will vary 
greatly. A plastic mixture usually requires about 30 gals, per 
cu. yd., according to Baker, 40 gals, according to Barnes. 

Where boulders are embedded in the foundations and side 
walls of small culverts similar to Plate 15, less cement, sand, and 
stone are required; our experience with work of this kind shows 
that only 0.8 to 0.9 bbls. of cement are needed per cu. yd. for the 
total amount of concrete in these culverts including cover and 
parapets. For all classes of work where boulders cannot be em- 
bedded these proportions are about right. 



'Cost Data Small Culverts 



Per Cu. Yd. 

Forms (labor) $0.58 

Lumber _ o . 50 

^Labor, mixing, and placing i . 18 

^Foreman o . 20 

^Broken stone, at crusher o . 90 

^Hauling stone, one mile o . 30 

Sand at pit at 65 cts. per cu. yd 0.32 

Hauling sand six miles o-75 

^Taking down forms o . 10 

Cement at culverts 2 . 00 

Total $6.83 

Labor, fo . 15 per hour. 
Concrete, hand-mixed. 

200 cu. yd., placed in small culverts, averaging 12 to 15 cu. 
yd. each. 

Note. — The labor of placing the concrete is customarily sublet to 
masons for $2.00 per cu. yd. 

Small Culverts 

Java Center Road. George A. Wellman, Engineer. 

One hundred and sixty-one cu. yd. of concrete in culverts, 
averaging 12 to 20 cu. yd. each. 

Boulders were embedded in the third-class concrete. Water 
only had to be hauled for 30 cu. yd. of concrete. 

1 Items accurate; other items approximately correct. 



624 



COST DATA AND ESTIMATES 



Materials 

Item Total Unit Total 

Quality Cost Cost 

Cement 138 bbl. $1.12.. $154.56 

^Sand 60 cu. yd. i.oo.. 60.0c 

Crushed stone 130 " " i-55- 201.50 

Lumber 3M 30.00.. 90.00 



Amt. per Cu. Yd. 
of concrete 

Material Costs 
0.86 bbl. $0.96 
0.37 CU. yd. 0.37 
0.80 " '' 1.24 
0.56 



Total $3.13 

Costs are f.o.b. unloading point; teaming of material included 
in the labor cost given below, except for sand, which cost $1.00 
delivered on the job. Concrete mixed and placed by hand. 



Cost of Labor and Teaming 



Item 



Total 



Foreman $93 . 00 , 

Labor, unloading stone from cars 20.00. 

Mixing, placing concrete, and removing forms 204.00. 

Carpenters, building forms 75 00, 

Teaming 182.00, 



Per Cu. 
Yd. of Con- 
crete 

. ..$0.58 
. . . 0.12 
. . . 1 . 27 
• • • 0.47 
• •• I 13 



Total Labor $3 57 

Total Material 3.13 



Total $6 . 70 



Labor $0,175 per hour 

Teams. o. 50 *' " 

Carpenters.. 0.25 " ^* 

Foreman o . 30 " '* 

Small Span Concrete Arch. — The following information of 
cost of 19-ft. span concrete arch was given by Mr. Charles M. 
Edwards, First Assistant Engineer, New York State Depart- 
ment of Highways. Arch was built at Pembroke, N. Y., by 
a contractor who was crushing stone at a quarry about one-half 
mile from the work. Cement was hauled three-quarters of a 
mile. For the concrete a mixture of one part Portland cement, 
two parts sand, and four parts stone was used. The old masonry 
abutments and wings were left in place and faced with 8 inches 
of concrete held by dowels. The quantities were: Concrete, 120 
cu. yd.; steel bars, 4500 lb.; pipe railing, 200 lin. feet. The 
cost of the work was as follows: 



1 The sand on this job cost practically nothing but we have placed the cost 
at $1.00 in order to avoid a misleading item. 



GUARD RAIL 625 

Lumber, including arch centers ... $156.00 on job 

Steel . 106.00 *' '' 

Cement 137 • 00 on siding, f.o.b. 

Stone 240 . 00 on job 

Dust and sand 90.00 

Railing 78.00 f.o.b. siding 

Labor 300 . 00 



Total $1107.00 

Omitting the cost of railing this figure gives a cost of $8.57 
per cu. yd. of concrete, including steel. This cost does not in- 
clude salvage of lumber or overhead expenses of any kind. The 
contractor received $1500.00 for the work, including the earth 
filling, for which he used quarry stoppings. This filling cost 
about $50.00. 

Guard-Rail. — In the following data the labor cost alone is 
given, for the materials will vary so much at different times and 
places that any quotations would be of little value. 

The style of rail erected is similar to sketch, page 216. Road 
715, 9760 lin. ft. were built at the following cost, according to 
S. O. Steere, engineer in charge: Post-hole auger-diggers and 
ordinary shovels were used; the holes were dug in medium hard 
clay; labor at $0.20 per hour, foreman $3.00 per day; unskilled 
labor used in painting fence. 

Digging post holes, setting posts, nailing on rails (erecting fence 
complete) : 

Cost. r. $0.0428 per lin. ft. 

Painting three coats 0.0094 " " " 



Total for erecting and painting $0.0522 " " " 

Road 5046, W. G. Harger, as Engineer. 2448 lin. ft. Built 
by subcontractor, Max Weller. 

Force: Max Weller acted as foreman. In this data he has 

been arbitrarily allowed salary of $4.00 per day $4 . 00 

I helper 2 . 50 

I 2 . 00 

I " ;■• 1-75 

Cost of erecting and painting complete, per lin. ft. $0,066. 
Guard-Rail Paint 

25 to 30 lb. white lead and ij^ gal. oil to paint 100 ft. guard- 
rail 3 coats. 

In Report of 1901 the Massachusetts Highway Commission 
gives the following costs for repainting guard-rail: 



626 COST DATA AND ESTIMATES 

Lineal feet of guard-rail painted 350,330 

Cost of paint per gal. (freight not included) $1.05 

Cost of paint per lin. ft. of guard-rail 0.0084 

Cost of paint and painting per lin. ft. of guard-rail 0.0165 

Lin. ft. of guard-rail painted per gal 134 • 4 

No. gal. of paint used per lin. ft. of guard-rail 0.0077 

Time required to paint one foot, in decimals of an hour. . 0.0269 

Concrete Guard-Rail. — Style of rail shown in sketch on page 
217, chapter on Minor Points. 

Labor, $0,225 per hour. 

Cost of manufacturing 1233 lin. ft. of- rail of the above de- 
scription. Taken from the Report of the New York State Highway 
Commission of 1910. 

Lumber $ 32 .46 $0,026 per lin. foot 

Steel 139.64 0.114 '^ '' *' 

Cement 57.62 0.046 " " " 

Gravel 10.00 0.008 " " '' 

Metal cores 77.00 0.063 "■ " " 

Labor 231.83 0.188 '' " 

Miscellaneous 5.35 0.004 *' " " 



Total $553.90 0.449 

This data applies to small quantities; if manufactured on a 
large scale the cost should be reduced to about $0.30 per lin. ft. 

The cost of setting the above rail varied from $0.09 to $0,125 
per lin. ft.: labor $0,225 per hour. This does not include haul- 
ing from the factory to the intended position on the road. 
Cobble Gutter. — Road 5046, W. G. Harger, Engineer. 

Labor, $0,175 per hour. Foreman, $3.50 per day. 

Cobbles averaged 6 in. in size; no sand cushion required, as 
gutter was built in a sand cut. Gutter was laid by ordinary 
laborers using paver's tools; tamped with a paving rammer, and 
the top voids filled with No. 2 stone crushed on the job. 

430 sq. yd. were laid at the following cost per sq. yd. : 

Cobbles, free $0 .000 

Loading J^ cu. yd. of cobbles o .030 

Hauling Vq " '' '' '' K mile o .024 

Laying and tamping o . 080 

Filler. — Cost of 0.05 cu. yd. No. 2 stone at crusher bin, 

approximately o . 030 

Hauling 0.05 cu. yd. i mile 0.015 

Spreading and brooming, 0.05 per cu. yd. No. 2 stone.. . . . o.oio 

Total $0,189 

PRICES OF VITRIFIED PIPE 

The discounts vary, but if no quotations of current prices are 
available the following list will serve for an approximate estimate: 



PLANT AND PAYROLL 



627 



^Eastern List 191 2 
Size Discount 

3" to 24" 88% 

24'' and 30'' . .80% 

33" and 36" 75% 

At these discounts the net prices per foot in car-load lots f.o.b. 
factory are : 



Size 


Price 


j Size 


Price 


f 


$0,024 


20" 


$0,270 


a" 


0.030 


21" 


0.325 


s" 


0.036 


22" 


0.360 


6" 


0.048 


24" 


0.390 


8" 


0.066 


2f 


0.900 


10" 


0.096 


K 


1. 100 


12" 


0.120 


33" 


1.560 


K 


0.162 


36- 


1.750 


18'' 


0.227 


— 


— 



PLANT AND PAYROLL 

Table 6;^, page 628, shows in a convenient form the value of 
plants and the largest weekly force account of two months' dura- 
tion on fourteen roads in New York State. From this and other 
information it is reasonable to assume that a contractor has tied 
up, outside of money on plant and materials, from $5000 to 
$8000 for the full length of time that the work is in progress, 
and for short periods he may have as high as $15,000 or $20,000 
invested. 

Interest, Depreciation, Repairs, etc. — To the best of my 
judgment the following estimates show about the amount of 
money required on the different styles of construction noted. 
These data are based on an outfit which would be capable of a speed 
of about 0.7 mile per month, or five miles in a season. 

Charge for bond M of 1% total contract in 19 16. There is 
considerable fluctuation in this and the liability insurance rates. 
Use the prevailing rate for your conditions. The rates given in 
the following estimate forms are for New York State conditions 
in 1916. 

1 Engineering News^ April 4, 19 12. 



628 



COST DATyV AND ESTIMATES 



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DEPRECIATION 

Adopted Value of Plant Items 



629 



Item 



Value 



Life 



Annual 
Repairs 



lo-ton roller 

Brick roller 

Traction-engine 

Crusher 

Elevator 

Bin and screen 

5 H.P. gasoline engine 

Gas engine and pump 

6000 ft. of pipe 

Wagons 

Hand tools . . 

Plows 

Road machine 

Tar kettle 

Wheel scraper 

Slush scraper 

10- ton roller used for hauling 
Hauling traction-engine .... 



$2700 
1800 
1200 
900 1 
200 \ 

500 J 
250 
200 
600 

115 
150 
100 
200 
$125-200 
70 
6 
2700 
2200 



20 yrs. 
20 



5 

say 10 

6 

I 

3 

5 

5 

5 

10 



$70.00 

40.00 

100.00 

400.00 

50.00 • 
50.00 
10.00 
10.00 



10.00 

^ 10.00 

10.00 

200.00 
200.00 



1 Including new tank every three years. 

6% Interest and Depreciation on Plant Items 



Item 



Interest 


Depreciation 


$162.00 


$135.00 


72.00 


150.00 


54.00 


100.00 


12.00 


30.00 


3.00 


50.00 


30.00 


40.00 


15.00 


30.00 


12.00 


40.00 


36.00 


60.00 


6.00 


20.00 


9.00 


150.00 


6.00 


30.00 


12.00 


10.00 


120.00 


— 


108.00 


100.00 


5.00 


15.00 


162.00 


^ 270.00 


132.00 


300.00 



Roller 

Traction-engine 

Crusher 

Elevator 

Screen 

Bin 

Gasoline engine ....... 

GasoUne pump 

6000 feet 1 1" pipe. .... 

Wagons 

Hand tools. 

Plows 

Tar kettle .^ 

Concrete mixer 

Brick roller 

Wheel scrapers 

Slush scrapers 

Roller used for hauling 
HauHng engine ./..... 



Charge for bond H of i % total contract in 19 16. There is considerable 
fluctuation in this and the liability insurance rates. Use the prevailing 
rate for your conditions. The rates given in the following estimate forms 
are for New York State conditions in 1916.J 



630 



COST DATA AND ESTIMATES 



PLANT FOR WATERBOUND MACADAM IMPORTED STONE 

Elevator unloading plant, provided more than 2000 cu. yd. 
of stone is to be unloaded. 



Item 


Interest 


Depreciation 


Repairs 


Elevator 


$12.00 
30.00 
15.00 

162.00 

36.00 

12.00 

9.00 

6.00 

12.00 

5.00 

80.00 


$30.00 
40.00 
30.00 

135-00 
60.00 
40.00 

150.00 
30.00 
40.00 
15.00 

300.00 


$50.00 
50.00 
50.00 

70.00 
10.00 
50.00 

10.00 
10.00 

150.00 


Bin 


5 H.P. gasoline engine 


I roller with broom and sprink- 
ling attachment 


6000 ft. I ^" Dine 


Gasoline engine and pump 

Hand tools 


Plows 


Road machine 


2 wheel scrapers 

2 slush scrapers 


I K waETons 




Totals one season's work 5 miles 
Total per mile 


$379.00 
76.00 


$870.00 
174.00 


$450.00 
90.00 





Force account money out: Allow six weeks out continually for 
length of job at }^% interest per month. 

Allow $6000 out, or $40.00 interest per mile on force account. 

Bond charge: J4 of 1% contract price; approximately $25.00 
per mile. Insurance charge: $2.00 per $100.00 total force 
account, approximately $100.00 per mile. 

Allow for moving plant on job, $500.00 lump sum. 



Plant for Waterbound Macadam Local Stone 



Item 


Interest 


Depreciation 


Repairs 


I traction engine 

I crusher and bin 


$ 72.00 

100.00 

10.00 

12.00 

322.00 


$150.00 

220.00 

50.00 

30.00 

770.00 


$100.00 

400.00 

80.00 

20.00 

300.00 


I steam drill and bits 


I small boiler for drill 

Roller, pipe, gasoline engine and 
pump, hand tools, plows, road 
machine, scrapers and wagons 
as for imported stone plant. 
Total of these items 


Total for season, 5 miles .... 
Total per mile 


$516.00 
103.00 


$1220.00 
245.00 


$900.00 
180.00 



PLANT CHARGES 



631 



Force account slightly larger on local stone roads. Approxi- 
mately $7000.00 out. 

Interest on force account $50.00 per mile 

Bond charge 20 . 00 " " 

Insurance 1 20 . 00 " " 

Moving plant on job, $500.00 lump sum. 

Plant for Bituminous Macadam Imported Stone 



Item 


Interest 


Depreciation 


Repairs 


Elevator unloading plant 

2 rollers 


$60.00 

320.00 

36.00 

112.00 


$100.00 
270.00 

535-00 


$150.00 

140.00 

30.00 

170.00 


3 tar kettles 


Hand tools, plows, road machine, 
scrapers and wagons as for 
waterbound macadam. Total 
of these items 




Total for season, 5 miles 

Total per mile 


$528.00 
106.00 


$905.00 
181.00 


$490.00 
98.00 





Interest on force account $ 40 . 00 per mile 

Bond charge 30.00 " " 

Insurance 100 . 00 " " 

Moving plant on job, $500.00 lump sum. 

Plant For Bituminous^ Macadam Local Stone 



Item 


Interest 


Depreciation 


Repairs 


I traction engine 


$72.00 

100.00 

10.00 

12.00 

468.00 


$150.00 

220.00 

50.00 

30.00 

805.00 


$100.00 

400.00 

80.00 

20.00 

340.00 


I crusher outfit 


I steam drill and bits 


I portable boiler for drill 

Rollers, hand tools, plows, road 
machine, scrapers, wagons, and 
tar kettles as for imported 
stone. Total of these items . . 


Total for the season, 5 miles . . 
Total pe^ mile 


$662.00 
132.00 


$1255.00 
251.00 


$940.00 
188.00 





Interest on force account $50.00 per mile 

Bond charge 25 . 00 " " 

Insurance 1 20 . 00 " *^ 

Moving plant on job, $500.00 lump sum. 



632 



COST DATA ANt> ESTIMATES 



FORMS FOR ESTIMATES (Macadam Roads) 

The following forms of estimate have proved very satisfactory. 
The item of 6% on materials is used to cover demurrage and 
interest on money tied up on freight and stone. The other items 
of profit are what we consider a reasonable return for the risk of 
such contract work. Mechanical hauling is not considered, 
because few contractors own plants that make it possible. The 
total item of interest, depreciation, repairs, and interest on force 
account money for the whole job is charged against top and bottom 
stone, as the construction quantities of the macadam will vary less 
from the estimated quantities than any other classes of work. 

Standard Estimates. — Figured on the basis of 20% profit on 
labor, 6% on materials, 6% on money invested, and an allowance 
made for depreciation on different plants, as previously given. 





Labor at $0. 175 per hour 






Teams at So . 450 '' '' 




Earth Excavation. 






Class 


Amount per Mile 


Price per Cu. Yd. 


Easy 




5,000-10,000 cu. yds. 


$0.40 


Easy 




3,000- 5,000 CU. yds. 


0.45 


Easy 




1,500- 3,000 '' " 


0.50 


Average . . . 




3,000- 5,000 " ''• 


0.50 


Average . . . 




1,500- 3,000 '' '' 


0.60 


Hard 




3,000- 5,000 *' '' 


0.60 


Hard 




1,500- 3>ooo " 


0.70 



Rock Excavation. 

Large boulders (for which 10 cu. yd. a mile 

are allowed on all estimates) $1 . 50 per cu. yd. 

/ Steam drillwork, limestone $0.80 to i . 25 " " " 

^* \ '' '' granite 0.80 to 1.50 '' '' " 

/Hand '' limestone... 2.00" '* " 

^' \ '' " granite 2.00 '' '' '' 

1. Large quantities. flll 

2. Small quantities. ^H 

Field Stone Sub-base. ^^ 

A sub-base course 6 in. deep made of the usual size fence stone 
requires i cu. yd. loose for i cu. yd. rolled; 12 in. deep requires 
1.25 cU. yd. loose. 



FORMS FOR ESTIMATES 633 



Cost of cobbles per loose cu. yd. $0. 10 

Loading cobbles per loose cu. yd 015 

Hauling cobbles i mile per loose cu. yd. 0.35 
Placing cobbles per loose cu. yd o . 10 

Rolling cobbles per loose cu. yd o . 05 

Filler (see below) — 



Multiply these 
items by 1.25 for 
1 2 -in. depth of 
sub-base. 



Total $ — 

20% profit — 



Estimate $ 

FiUer. 

}i cu. yd. per cu. yd. rolled sub-base. 



Loading }i cu. yd 0.05 

Hauling J^ cu. yd. i mile o . 10 

Spreading }i cu. yd o .04 

Total $ — 

Sub-base Bottom Covirse. 

Same relation of loose and rolled quantities as for sub-base. 

Cost fence stone per loose cu. yd $0.10 

Loading fence stone per loose cu. yd 0.15 

Hauling i mile per loose cu. yd o . 35 

Placing and sledging o. 20 

Rolling o. 05 

Filler (see below) — 



Total 

20% profit. 



FiUer. 



Estimate $ — 

3^ cu. yd. per cu. yd. rolled sub-base. . 

Cost 3^ cu. yd. at pit or crusher $ — 

Loading o . 05 

Hauling 0.33 cu. yd. filler per mile o. 10 

Spreading and brooming o . 08 



Total $ — 

Imported Bottom Stone Materials. 

3" course, 3050^ lb. f.o.b. crusher '. . . $ — 

4" '' 3150 " '' '' .. — 

6% profit — 



Total .. 

Freight on stone to delivery point. 



Total, No. I 

1 These weights are for limestone. See page 591. 



634 COST DATA AND ESTIMATES 

Labor. 

Unloading 

Under 2000 cu. yd. (shoveling) $0. 15 per cu. yd. 

Over 2000 cu. yd. (elevator) o. 10 " *^ *' 

Hauling (Teams) 

Bad conditions 0.35 ^' " *' 

Average conditions 0.30 " *' *' 

Good conditions o. 25 '' ^' " 

Mechanical hauling 0.15 *' " '' 

Spreading 

S}i in. loose depth 0.06 ^' '' ** 

4 in. loose depth 0.08 " '' " 

Rolling 0.05 '' ^^ '^ 

At this point total up and add 30% of the total to change the 
estimate from loose to rolled measure. 

Filler (see below) 

Labor, total $ — 

20% profit. — 

Total, No. 2 $ — 



FiUer. 

Cost of 0.35 cu. yd. at pit or crusher $ — 

Loading 0.35 '' " 0.05 

Hauling 0.35 '' '' i mile @ I0.35 per yd. mile. . . 0.12 

Spreading and brooming o. 35 cu. yd 0.07 

Filler, Total $ — 



Summary. 

Total No. I (materials) $ — 

Total No. 2 (labor) . -— 

Interest and depreciation (see page 630) — 

Estimate $ — 



Imported Top Stone Waterbound Macadam Materials. 

I4450 lb. stone f.o.b. (limestone) $ 

6% profit 

Total ^ $ 

Freight on stone to delivery point 

Total No. I $ 

1 These weights are for limestone. See page 591. 



FORMS FOR ESTIMATES 635 

Labor. 

Unloading (same as bottom) $ — 

Hauling (same as bottom) $ — 

Spreading o. 08 

Rolling o . 04 

Puddling 0.06 

Total, loose measure $ — 

Add 30% — 

Total rolled measure $ — 

Screenings. (See below) — 

Total $ — 

20% profit — 

Total No. 2 $ — 

Screenings. 

^Unloading o. 5 cu. yd So . 07 

Hauling 0.5" " i mile 0.15 

Spreading 0.5 " '' by cross dump wagons 0.03 

'' 0.5 " '' hand 0.07 

Total $ — 



Summary. 

Total No. I (materials) $ — 

Total No. 2 (labor) — 

Interest, depreciation, etc — 

Estimate $ — 



IMPORTED TOP STONE BITUMINOUS MACADAM. 
PENETRATION METHOD 

Materials (per consolidated cu. yd.). 

2" course, 4350 lb. stone and screenings, f.o.b. crusher $- 

3" ". 4050 '' ^'' " '' '^ " - 

gal. bituminous binder, f.o.b. plant - 

6% profit - 



Total $- 

Freight on materials to delivery point - 

Total No. I (materials) $~ 

1 Screenings are usually unloaded by hand. 



636 COST DATA AND ESTIMATES 

Labor. 

No. 3 stone (2^^'^ size) 

Unloading i cu. yd. (same as given page 634) $ — 

Hauling i cu. yd. " '* '' — 

Spreading i cu. yd. " " ^' — 

Rolling I cu. yd o . 09 

Total $— 

Add 20% for 2" course, 30% for 3" course. . . — 



Total No. 2 



No. lA, No. 2, and Bitumen. 
Unloading 0.6 cu. yd. for 2" course (same as given) 

0.37 " " " 3" " " " " 

Hauling at the rate of $0.30 per yd. per mile 

Hauling bitumen at rate of $0,002 per gal. per mile 

Spreading and brooming No. i A and No. 2 at rate of $0 . 30 

per cu. yd 

Manipulation of heating and spreading bitumen at $0,015 

per gal 



Total No. 3 $— 

Total No. 2 — 



Total 

Add 20% profit 



Total No. 4 

Summary. 

Total No. I (materials) . . 

Total No. 4 (labor) 

Interest, depreciation, etc. 



Estimate $ — 

LOCAL STONE MACADAM 

Field Stone. 
I cu. yd. field stone = i cu. yd. crushed. 
1 .8 cu. yd. field stone = i cu. yd. No. 3 and No. 4 rolled. 

Cost of field stone $0 . 10 per cu. yd. 

Blasting or sledging, per cu. yd. actually blasted 

or sledged o . 40 

Loading field stone 0.15 

Hauling field stone i mile 0.35 

Crushing — 

Sandstone (soft) $0.10 

Limestone o. 15 

Granite and trap rock o . 20 



l( IC (( 


n ii a 


U U 11 


ii ii ii 

ii ii ii :. 


ii ii it I 
ii ii ii 



FORMS FOR ESTIMATES 637 



Total cost in bins (loose including Nos. i, 2, 3, 

and 4 stone) per cu. yd $- 

Quarried Stone. 

Limestone, quarrying, small quarries. $0. 50 '' 

Conglomerate, " '' " o. 75 " 

Trap, " " , " 0.65 " 

Crushing (same as above) — " 

Total cost in bins $ — '' 

The crushing does not include repairs to crusher. 
The crushing is taken from previously given data. 
The item of quarrying includes delivery to crusher. 

Estimate of Bottom Stone. 

Cost in bins, per cu. yd $ — 

Loading, per cu. yd.. o.oi 

Haul (same as bottom, page 634) — 

Spread (same as bottom) — 

Rolling (same as bottom) — 

Total (loose measure) $ ■ — 

Add 30% — 

Total rolled measure $ — 

Filler (same as bottom) — 

20% profit — 

Total, No.T $ — 

Interest and depreciation ■ — 

Estimate $ — 

Local Top Stone. 

Cost in bins, per cu. yd $ • — 

Manipulation same as for imported stone . . — 

Total $ — 

20% profit — 

Total No. I $ — 

Interest and depreciation — 

Estimate $ ■ — 

Imported No. 2 Stone, Estimated Loose 

Material 

2400 lb. stone, per cu. yd $ — 

6% profit — 

Total No. I $ — 



(( t( 



638 COST DArA AND ESTIMATES 

Unloading (same as bottom) — 

Haul (same as bottom) — 

Spreading o . 10 



Total 

20% profit. 



Total No. 2 $ — 

Total No. I (material) $ — 

Total No. 2 (labor) — 



Estimate 

Local No. 2 Stone 



Cost per cu. yd. in bins. . 
Haul same as above. .... 
Spreading same as above 

Total 

20% profit 




Estimate $ — 

The following is a7i example of the 7nethod of using these standard 
forms. 

Estimate for Local Fence Stone Crushed Macadam Bottom 

Course 

Assume that stone will cost $0. 10 per cu. yd. in the fences. 
" }/2 raile average haul to crusher. 
" 20% of the stone has to be sledged or blasted. 
'' M of a mile average haul from the crusher. 
'* that filler costs $0.15 per cu. yd. in the pit. 
*' average haul of J:4 mile for filler. 

'' that the interest and depreciation charge for the total job, 
say 4 miles, is distributed over 6000 cu. yd. of macadam. 
Use Standard form for Local Bottom Stone, given on page 636. 

Cost I cu. yd. field stone $0.10 

Blasting and sledging J^ cu. yd. stone o. 08 

Loading i cu. yd. field stone 0.15 

Hauling i cu. yd. field stone J^ mile o. 18 

Crushing i cu. yd. (Mixed granite and sand- 
stone) 0.15 

I cu. yd. Total cost in bin. ... $0.66 

Cost I cu. yd, crushed stone in bins $0.66 

Loading on wagons, per cu. yd o.oi 

Haul to road, average conditions, ^ of a mile 0.22 

Spreading $}/^" loose, per cu. yd 0.06 

Rolling o . 05 

Total $1.00 



SAMPLE ESTIMATE 639 

Add 30% 0.30 

Per. cu. yd. rolled measure $1 . 30 

Filler (see below) 0.31 

Labor, total $1.61 

Add 20 % profit , 0.32 

Total, No. I $1 . 93 

Interest, depreciation, etc. (see below) 0.56 



Estimate per cu. yd. rolled in place $2 . 49 

say $2 . so. 

Filler. — As mentioned on page 597, the screenings produced in 
crushing bottom only, as in this case, will amount only to 50% of 
the required filler, therefore two estimates must be made for filler 
as below: 

Screenings for Filler. 
Cost of 0.35 cu. yd. screenings in bin @ $0.66 per cu. yd. $0. 230 

Loading 0.35 '' " '' from bin 0.003 

Hauling 0.35 " '' " % of a mile 0.077 

Spreading and brooming 0.35 cu. yd 0.070 

Total , $0,380 

Sand Filler. 

Cosf of sand in pit o . 35 cu. yd $0 . 05 2 

Loading 0.35 cu. yd ^. .^. 0.050 

Hauling 0.35 " " J4 milfe (short-haul figures) 0.060 

Spreading and brooming 0.35 cu. yd 0.070 

Total $0. 232 

Average these costs as the screenings must be utilized to use up 
the total output of the crusher. Average filler $0.31. 

Interest, Depreciation, etc. — From page 630, using value adopted 
for, say, waterbound macadam roads, the following charge for a 
4-mile road is figured: 

1 Interest on plant 4X103.00 $412.00 

I Depreciation on plant 4X245.00 980.00 

* Repairs on plant 4X180.00 720.00 

I Interest on payroll 4 X 50 . 00 200 . 00 

] Bond charge 4 X 20 . 00 80 . 00 

Insurance * 4X120.00 480.00 

Moving plant on job 500 . 00 

Total $3372.00 

to be spread over 6000 cu. yd. of macadam. 

3372 

: 6000 =0.56 cents per cu. yd. 



640 COST DATA AND ESTIMATES 

The cost of an improved highway generally depends on the item 
of top and bottom stone in place complete. Many of the minor 
items have standard prices. Such items as cast-iron pipe, the vari- 
ous sizes of tile, pipe railing, mesh reinforcement steel, etc., will 
hardly vary in price throughout the Eastern States. A table of these 
standard prices as used by the New York State Highway Com- 
mission is given below. 

It will be noted that all of these items have little bearing on the 
total cost, and that the items of Earth Excavation, Sub-base, or 
Sub-base Bottom Course, Macadam Bottom and Top Course, Con- 
crete Foundation, Brick Pavement, etc., which of necessity are not 
standard in price, determine whether or not the road is to be 
expensive. 

Unit Prices Minor Items (Date 191 5) 

Overhaul on excavation $0.01 per yd. sta 

Third-class masonry cement joints. . . 6.00 per cu. yd. 

Second-class concrete 9 .00 " '' " 

Third-class concrete (stone) 7.00 " *' ** 

(gravel) 5.50 '' '' " 

Pointing old masonry o. 75 '' sq. " 

Riprap i . 50 '' cu. " 

Paving cement joints i . 50 '^ sq. '' 

Cobble gutter o. 50 '' ^' " 

Expanded metal 0.08 '' "ft. 

Guard-rail o . 30 '^ lin. ft. 

2" pipe rail i . 50 " " " % 

Concrete guard-rail i .00 '' *' " 

Cast-iron pipe in place 35 00 " ton 

6" V. T. P. in place 0.30 '' lin. ft. 

12" V. T. P. " " 0.60 " '' " 

15" V. T. P. " " 0.90 " " " 

18" V. T. P. " " i.io '' " '' 

24" V. T. P. "^ " 2.00 '' " '' 

Relaying old pipe . o. 10 " " " 

4" farm tile under drain in place o. 10 '' " " 

Steel in place 0.05 " lb. 

Oak timber in place 50.00 '' M.B.M. 

Hemlock timber in place 40.00 '' M.B.M. 

Danger signs 2 . 00 each 

Guide-board posts 6.00 " 

Highway No. signs i . 00 ** 

Guide signs per letter 0.15 '' 

The item of Earth Excavation as shown in Table 56 may vary 
between 40^ and 65 ^. In extreme cases where material is difficult to 
handle, it may be estimated still higher. A particular instance of 
costly excavation where 70^ was estimated occurs on a road near 
the Lackawanna Steel Plant at Buffalo. This road had been filled 
with slag from time to time. 



HAUT. 641 

In the remaining variable items the length of haul is a governing 
factor and three actual conditions of determining the average haul 
are given here before proceeding farther with the estimate data. 

The following cases i, 2, and 3 show also the New York method 
of estimating where interest and depreciation are not directly 
considered. 

Case I 

The simplest possible conditions. Perry Village County High- 
way, Wyoming County, N. Y. Imported stone, delivery at middle 
- of road — coal trestle available for unloading — no dead haul to road. 
Road 16 feet wide throughout. 

Railroad at Station 60, Station o + 00 = beginning of ^"contract 

106 + 23 = end of contract 
For ease of computation, say stone runs 10 yd. to mile. 
Station o -}- 00 to 60 
I.I miles average 0.55 miles 0.55 milesXn yd. = 6.05 yd. miles 
i Station 60 + 00 to 106 + 23 

' ^ ., .1 0.44 miles X 8. 7 yd. =3.83 yd. miles 

, 0.87 miles average o . 44 miles — ^ . , — 3 w^^ T" 

Total yd. 19 . 7 9 . 88 yd. miles 

j Total 

j 9 . 88 yd. miles ., , , 

; ^ = 0.50 miles average haul 

I 19. 7 yd. 

I Completion of Perry Village Estimate. 

j Stone from Rock Glen Quarries Stone $0.65 per ton f.o.b. 

Cu. yd. = 24001b. Freight 0.40 '' |' |' 

Sub-base Stone 0.50 '' " " 

I Bottom Top Screenings Sub-base 

i Stone 78 .78 .78 .60 

Unloading .15 .15 15 15 

Average haul }i mi. at 

0.35 175 -175 .175 .175 

Manipulation 30 .25 .20 . 20 

I 305 
Consolidation (plus >^) .468 .451 -4+/^ -22 

.5220 
Filler (3^ cu. yd. sand Screen- 

at$l.Oo) 50 ings .522 Sand -SO 

Profit (20%) 474 465 -369 

Freight (40 + o . 08 + (40+ • o8-|- (40+08 

0.16) 64 .16+192) .832 +.096) .576 

6% interest on freight 
to cover demurrage, 

etc . .038 .05 .034 

Manipulation of Bi- 
tuminous Material. 60 

$3,525 $4-275 $2,824 

Use $3.55 Use $4.30 Use $2.80 



642 COST DATA AND ESTIMATES 

Case II 

The Walker-Lake Ontario Road, Monroe County, N. Y. Road 
extends from Station o -f 00 to Station 197 + 45- 
Local stone; — mostly fences. Because of location of stone as 
determined by engineer's inspection, it was determined to make 
three set-ups of crusher, at Station 40, 104 -\- 50 and at Station 

157. 

The hauls from stone piles to these crushing points were figured 
in the regular manner. From the crusher to road, the hauls were 
arranged, 

From Station 40 — haul stone o + 00 to 77 -f 00 

" " 104 -j- 50 haul stone 77 + 00 " 130 + 00 

l" 157 " '' 130 + 00 '' 197 + 45 

Care was taken to see that enough stone was available near each 

crushing point to furnish macadam between stations supplied from 

that set-up. 

The widths of road were as follows: 

o + 00 to 40 + 00 — 12' wide 
40 + 00 '^ 66 + 60 — 16' wide 
66 + 60 '' 129 + 50 - 14' '' 
129 + 50 " 197 + 45 - 12' '' 
Use 10 yd. per mile for 12' road 
proportionally 11 . 7 yd. mile for 14' road 

Haul on road from Station 40 + 00 

12' wide o + 00 to 40 + 00 

0.76 miles average .:i,Z .38 miles X 7.6 yds. = 2.89 yd. miles 

16' wide 40 + 00 to 66 + 60 

.50 miles average .25 .25 miles X 6.6 yds. = 1.65 yd. miles 

14' wide 66 + 60 to 77 + 00 

.20 miles average .1 

plus dead haul .5 

.6 .6 miles X 2.3 yds. = 1.38 

16.5 5.92 yd. miles 

Haul on road from Station 104 + 50 

14' wide Station 77 + 00 to 129 + 50 (say 130) 
77 + 00 to 104 + 50 

.52 miles average .26 .26 miles X 6.1 yds. = 1.59 yd. miles 
104 + 50 to 130 

.48 miles average .24 .24 miles X 5.6 yds. = 1.34 yd. miles 

1 1.7 yds. 2.93 yd. miles 

Haul on road from Station 157 

12' wide Station 129 + 50 (say 130) to 197 + 45 
130 to 157 

.51 miles average .26 .26 miles X 5.1 yds. = 1.33 yd. miles 
157 to 197 + 45 

.76 miles average .38 .38 miles X 7.6 yds. = 2.89 yd. miles 

12.7 yds, 4.22 yd. miles 



I 



SAMPLE ESTIMATE 643 

Average haul for entire road 

From Station 40 16.5 yd. 5.92 yd. miles 

" 104+50 II. 7 " 2.93 " " 

" 157 12.7 " .4.22 '' '' 



40.9 . 13 07 

13-07 "^40-9 =0-32 miles 

say 0.3 miles average haul 



Sub-base Bottom Course 

Stone $0.15 

Sledging, blasting, and sorting 30 % of stone at 0.35 per yd. o . 105 

Loading into wagons 0.15 

Haul to crusher at Stations 40, 104 -j- 50 and 157. One 

mile at 0.35 0.35 

Haul on road 0.3 mile at 0.35 o. 105 

Manipulation 0.20 

Consolidation (plus J^) 0.212 

Filler {}4 cu. yd. sand at o . 80) o. 40 

Profit (20%) 0.334 



$2,006 
Use $2 . 00 

Local Stone Top Course — Bituminous Binder 

Top Course Screenings 

Stone 0.15 o. 15 

Sledging, blasting, and sorting 6o5^ of stone at 

0.35 0.21 0.21 

Loading into wagons 0.15 0.15 

Haul to Crusher at Stations 40, 104 + 50 

and 157. 1. 1 miles at 0.35 0.385 0.385 

Crushing 0.35 0.35 

Haul on road 0.30 miles at 0.35 0.105 o. 1C5 

Manipulation 0.20 o . 20 

Consolidation (plus H) 0.517 1.55 

X0.4 



Filler (o . 4 cu. yd. of screenings) o . 620 o . 620 

Profit (20%)........^ ^ 0.537 

Manipulation Bituminous Material c.6o 

$3-824 
Use $3 . 85 

Case III 

The Obi- Cuba Highway, #965, Allegany County, N. Y. 
9.93 miles long. 

From a field inspection of this road, it was found that stone was 
available at both ends of road, but not in the middle. An ample 



644 COST DATA AND ESTIMATES 

supply of good gravel was found in the middle section, and it was 
determined to build a concrete base with bituminous top, this type 
of road being the only one which could be built using local material. 
The hauls and freight charges on imported material would make the 
cost prohibitive. 

The road was divided into three sections as follows: 
Station o + oo to 330 local field stone concrete 

Station 330 + 00 ^' 460 " gravel *' 

Station 460 + 00 "524 + 14 " quarry stone '^ 

Haul on stone o + 00 to 330. Crusher at 146, 220, and 285. 

■ These crusher set-ups were determined upon more by reason of 

nearness of stone supply and grade of haul than to equalize the 

hauling distance. The haul to the crusher was figured for the 

separate sources of supply and found to average i J^ miles. 

Haul from crusher on road. Station 146 to Station 0+00 
(12' wide use 10 yd. per mile) 2 . 76 miles, average i .38 miles. 

Station 146 to 170 1.38 miles X 27.6 yd. = 38.09 yd. mile 

0.5 miles, average o. 25 miles o. 25 " X 5 '' = i . 25 " 

Station 220 to 170 
1 .0 miles, average 0.5 miles 0.5 '* X 10 '' =^50 " 

Station 220 to 245 
0.5 miles, average . 25 miles 0.25 "X 5 *' =1.25 '' 

Station 285 to 245 
o. 8 miles, average o . 4 miles .4 " X 8 '* = 3.2 '' 

Station 285 to 330 

. 86 miles, average o . 43 miles o . 43 '' X 8.6 '^ =37 '^ 

Total for ist section 64. 2 yd. 52 . 49 yd. mi. 

52.49 -r 64.2 =0.82 mile, average haul for ist section. 

Haul from gravel pit to road. Station 330 to 460. 
Bank station 385 at side of road — no dead haul great enough to be 

figured. 

Station 385 to 330. 

1 . I miles, average haul 0.55 miles 0.55 miles X 1 1 yd. = 6 . 05 yd. mi. 
Station 385 to 460 

1 . 4 miles average haul o. 7 miles 0.7 '' X14 '' =9.8 " " 

Total 25 yd. 15.85 yd. mi. 
15.85 H- 25 = 0.63 miles Say 0.65 average haul 

Haul from quarry in Village of Cuba % mile from end of road. 
Station 460 to 524 + 14 

Station 460 " 500 14' wide (use 11 . 7 yd. per mile) 

Station 500 " 524 -f- 14 16' wide (use 13.3 yd. per mile) 
Station 460 to 500 

o . 8 miles, average o . 4 mi. 

Station 524 + 14 to 500 dead haul 0.5 " 
Quarry to 524 + 14 " '' 0.75 '' 

1.65 " 
1 . 65 miles X 9 . 36 yd. = 15 . 44 yd. mi. 



SAMPLE ESTIMATE 645 

Station 500 to 524 + 14 
o . 5 miles, average haul o. 25 mile 
Quarry to 524+ 14 dead haul .75 mi. i mile X 6.67 yd.= 6.67 yd. mi. 

1. 00 mi. Total 16.03 22.11 " " 
22.11 -T- 16. 03 — 1.38 Say 1 . 4 miles average haul 

Haul on Sand Pits at Stations 26 and 385 

Station 26 to 0+00 
o . 5 miles, average 0.25 mi. 0.25 miles X 5 

Station 26 to 330 
5 . 76 miles, average 2 . 88 mi. 2 . 88 

Station 385 to 330 
1 .04 miles, average o. 52 mi. o. 52 

Station 385 to 460 
1 . 4 miles, average o . 7 mi. o . 7 

Station 460 to 500 
0.8 miles, average 0.4 mi. 
385 to 460 dead haul i .4 mi. 

Total 1.8 "1.8 " X 9.36 " = 16.8 

Station 500 to 524 + 14 

0.5 miles, average 0.25 mi. 

460 to 500 dead haul o . 8 mi. 

385 to 460 '* '' 1.4 mi. 

Total 2.45 mi. 2.45 " X 6.65 yd. ==16.3 



X 5 


yd. 


= 1.25 yd. mi, 


X57.6 


u 


= 165.89 " " 


X10.4 


(( 


= 5.4 " " 


X140 


it 


= 9.8 " " 



103.01 215.44 

215.44 -f- 103.01 = 2.1 miles average haul. 

Haid on Cement 

Cement delivered at Cuba and Portville. 

Station 0+00 to 160 Say 10 bbl. to mile 

3 miles, average i . 5 mi. 7 . 5 ■milesX3o bbl. = 225 bbl. mi. 

dead haul, Portville 6 . o mi. 

to 0+00 7.5 mi. 

Station 160 to 460 

5.68 miles, average 2 . 84 mi. 

460 to 524+14 dead 1.3 mi. 

Penn. R.R. to 524+14 0.2 mi. 

4 • 34 mi. 

4 . 34 mi. X 56 . 8 bbl. = 246 . 5 bbl. mi. 
Station 460 to 500 
0.8 miles, average o . 4 mi. 

500 to 524 + 14 dead 0.5 mi. . 
Penn. R.R. to 524+14 0.2 mi. 



I . I mi. 

I.I mi. X9. 36 bbl. =10.3 bbl. mi. 



646 COST DATA AND ESTIMATES 

Station 500 to 524 + 14 

0.5 average o.S'S mi. 

Penn. R.R. to 524+14 0.2 mi. .45 mi. X6.65 bbl. = 3.0 bbl. mi. 



0.45 102.81 484.8 bbl. mi. 

484.8 4- 102.81 =4.7 miles, average haul. 

Having the haul figured for stone, gravel, cement, and sand, it 
was decided to obtain a composite price for the aggregate of the 
concrete instead of presenting an estimate with three prices for 
concrete foundation. This was done as follows: 

Field Stone. 

Stone $0. 10 yd. royalty 

Blasting 0.35 '' 

Loading o. 15 " 

Haul to crusher 1.5 @ 40c. 0.60 '* 40c. yd. mile used as haul 

^Crushing 0.30 ^' was off steep hills and 

Haul to road 0.8 mi. @ 35c. . 0.28 '' hard grades 



$1.78 yd. 

Gravel. 

Gravel (royalty) $0 . 50 

Stripping o . 05 

Loading (by hand) 0.15 

Haul to Station 385, o. i mile @ 35c 0.03 

Haul on road, o . 65 miles ©350 o . 23 

$0 . 96 

Stone at Cuba Quarry, 

This stone bought from quarry owner at flat rate of 75c. in bins: 

Stone $0.75 

Haul 1.3 @ 35c 0.455 

$1,205 Say $1.21 

Sta. 0+00 to 330 = 6.25 miles @ 10 yd. = 62.5X$i.78 = $iii .25 

330 " 460 = 2.46 '' '' 10 " =24. 6X 0.96= 23.62 

460 " 500 = 0.8 '^ '' II. 7 '' = 9.36X1.21= 11.33 

500 to 524+14 = 0.5 '' "13-3" =6.65X1.21= 8.05 



103. II $154-25 

$154.25 -^ 103. II = $1.49 composite price 
Sand 

Sand (screened) $1 . 00 yd. royalty 

Loading o. 10 " 

Haul to road o. i @ 40c. ... 0.04 " 40c. used because of steep 
Haul on road 2 . i miles @ 35c o . 735 hard grade 

$1,875 Say $1.88 

1 This item is higher than noted in the previously given cost data, as this 
estimate is made according to the N. Y. S. method, which does not consider 
interest and depreciation as a separate item. 



BRICK PAVEMENTS 647 

Cement 

Delivered at Cuba or Portville $1 .05 per bbl. 

Haul o. 188 tons X4- 7 miles Xo. 29 per ton mile 0.25 '' '' 

$1.30 

Concrete. — Inasmuch as gravel must be screened and sharp sand 
supplied, the proportions for stone concrete, ratio i — 23^ — 5, 
were used in place of standard gravel proportions. This is Fuller's 
rule for proportions of cement, stone, etc., for one cubic yard of 
concrete. A table of these ratios for different mixtures is found 
on page 623. 

Stone $1.49 X 0.92 = $1.3708 

Sand 1.88 X 0.46 = 0.8648 

Cement i .30 X i . 21 = i .573 

$3 . 8086 

Mixing $0. 40 

Spreading o. 20 

Profit 20% . 0.8817 

$5 . 2903 
Say $5 .30 per cu. yd. 

Note. — This method of estimating does not consider deprecia- 
tion directly. See other method of estimating in the standard 
estimate forms. 

The method of estimating thejop course for a Concrete Bitumi- 
nous Top road does not vary^from an ordinary bituminous top course, 
except that under the present New York State specifications the 
course is figured for loose measure. Therefore the items for con- 
solidation and filler would be omitted. 

Brick Cost Data on Country Roads. — The cost of brick pavements 
on country roads differs somewhat from similar work on city streets. 
There is not much data available for this class of work, but through 
the courtesy of Mr. Wm. C. Perkins, First Assistant Engineer, 
New York State Department of Highways, the author is able to 
give some unusually reliable data obtained from fifteen miles of 
brick paving averaging 14 ft. wide, built near Buffalo, N. Y., in 
1 910. Mr. Perkins' method of estimating, as given on page 651, 
assumes that 20% profit on both materials and labor will take 
care of the plant and payroll charges and give a reasonable profit. 
The method of estimating is different from that given on macadam 
roads. His results are good. 

Excavation. — Wliere brick pavement is built on an ordinary un- 
improved country road, the excavation is of the same class and will 
cost the same as given for macadam roads. 

Where pavements are built over macadam roads and the old sur- 
face must be cut into two or three inches and reshaped, the excava- 
tion is much more expensive. For this class of work see page 658 
(scarifying and reshaping). 



648 COST DATA AND ESTIMATES 

Labor Manipulation for Different Items of Brick Pavement Laid 
During 1910, in the Buffalo Residency.— These items figured from 
force accounts kept by the different engineers in charge of roads. 

Labor averaged $0,175 per hour. 

Concrete Base, 5'' thick (exclusive of edging). 

Machine-mixing, laying same in place, including labor of tamp- 
ing, etc. 

Road No. 2-R, Buffalo-Hamburg. . . $0.0853 P^r sq. yd. 

Road No. 128, Buffalo- Aurora 0.0991 '' ** '* (gravel 

concrete) 

Road No. 863, Blasdell Village o. 1228 '' '' '' 

Road No. 87, Main Street, Sec. 2. 0.1129 '' *' '' (3'' base) 
Road No. 862, Hamburg Village. . . 0.0655 '' " "• (28' and 

30' wide) 

The excessive cost on Blasdell Village due to a poor concrete 
mixer (gasoline) which was constantly breaking down. 

On Main Street, Sec. 2, poor organization and too high priced 
men; also, lack of water, causing delays. 

On Hamburg Village low price due<to width of base 28' and 30', 
allowing work to progress faster. 

On Road No. 69, Main Street, Sec. i, edging and base were 
laid in one operation; gasoline mixer; plenty of water; cement, 
$1.12; sand $1.40; labor, $1.90 per day; stone, $1.12 percu. yd.; 
base 3" thick; 8'' edgings; cost in place, including edging $4! 696 
per cu. yd., or $0,506 per sq. yd., or $0,886 per lin. ft. of road. 

Assumption. — If we assume $0.09 per sq. yd. as an average cost 
for 16' road (exclusive of edging) the manipulation would be 
$0,648 per cu. yd. 

If we assume $0.0655 P^r sq. yd. for street work (Hamburg 
Village) the manipulation would be $0,472 per cu. yd. 

Concrete Edging. 8" thick. 

Hand-mixed; placing same, including erecting of forms, and 
removing same; tamping, placing steel, and all labor necessary. 

Road No. 2-R, Buffalo-Hamburg, $0.0730 per lin. ft. of edging 

0.0821 '' sq. yd. of pavement 
(Road 16' wide) 
Road No. 128, Buffalo-Aurora . . 0.0555 " lin. ft. of 5" edging 

0.0713 *' sq. yd. pavement 
(Road 14' wide) 
Road No. 863, Blasdell Village .. . 0.0826 '' lin. ft. edging 

0.0929 '' sq. yd. pavement 
(Road 16' wide) 
Road No. 87, Main Street, Sec. 2 . 0.0748 '' lin. ft. edging 

0.0842 '' sq. yd. pavement 
(Road 16' wide) 

On Road No. 862, Hamburg Village, concrete curb 6" top, 
10'' bottom, 15" deep; hand-mixed, exposed curbing, all labor, 
including erection and renioval of forms, $0.1294 per lin. ft. 



BRICK PAVEMENTS 649 

Assumption, — ^If we assume $0,082 per sq. yd. of paving as 
cost of edging and $0.09 per sq. yd. cost of base, the total cost 
per sq. yd., 16' road (including edging) would be $0,172 per sq. 
yd., or the manipulation would be $1,238 per cu. yd. 

If we assume $0,073 P^r lii^- ft- of 8" edging 10 J^" deep, the 
manipulation would be $3,379 per cu. yd. of the edging in place. 
(This high cost due to forms, etc., and the small amount of con- 
crete per lin. ft.) 

Sand Cushion. — Spreading sand, rolling, and making bed ready 
for work. 

Road No. 2-R, Buffalo-Hamburg, $0.0102 per sq. yd. 
Road No. 128, Buffalo- Aurora, 0.0082 " " " 
Road No. 863, Blasdell Village, 0.0187 " '' '' 
Road No. 87, Main St., Sec. 2, 0.0151 " '' " 
Road No. 862, Hamburg Village, 0.0160 '' '* " (28' and 30' 

wide) 

On Main Street, Sec. i. Road No. 69; sand, $1 .40; labor, $1 .90; 
cost per sq. yd. 2" thick, $0.0838, including material. 

Assumption. — From the above I would assume $0,013 per sq. yd. 
as cost of preparing sand cushion. 

Brick Pavement. — ^Laying brick, including all labor of handling 
from the piles, removing all culls, and the rolling of the brick. 

Road No. 2-R, Buffalo-Hamburg, $0.0611 per sq. yd. 

Road No. 128, Buffalo- Aurora, 

Road No. 863, Blasdell Village, 

Road No. 87, Main St., Sec. 2, 

Road No. 862, Hamburg Village, 

Road No. 69, Main St., Sec. i. 

Assumption. — I consider Blasdell and Main Street, Sec. i and 
Sec. 2, too high and the engineer claims that the force was cut 
up and wasted time. 

I would assume $0,070 per sq. yd. as cost of laying brick, etc. 

Grouting. — Necessary grouting to [obtain flush joints, scoop 
method, including the placing of the protecting sand covering. 

Road No. 2-R, Buffalo-Hamburg, 
Road No. 128, Buffalo- Aurora, 
Road No. 863, Blasdell Village, 
Road No. 87, Main St., Sec. 2, 
Road No. 69, Main St., Sec. i. 
Road No. 862, Hamburg Village, 

On Main St., Sec. i, Road No. 69; sand, $1.40; cement, $1.12; 
labor, $1.90; actual cost $0.0848 per sq. yd., including materials. 

Assumption. — From the above I would assume $0,028 per sq. 
yd., as the cost of applying grout. 

Expansion Joints. — Removing strips, cleaning joints, and pour- 
ing tar. 



0.0544 




" 


0.0969 '' 




a 


0.0965 " 




a 


0.0700 '' 




" (28' and 30' 


0.0983 '' 




" wide) 



^o 


0219 per sq. yd. 









0211 




' 









.0322 




' 











0321 
0285 
0273 


11 a 


( 
c 


(28' 


and 30' 
wide) 



650 COST DATA AND ESTIMATES 

Road No. 2-R, Buffalo-Hamburg, $0.0067 per lin. ft. of joint 

0.0076 '' sq. yd. pavement 
(Road 16' wide) 
Road No. 128, Buffalo- Aurora, $0.0057 per lin. ft. of joint 

0.0073 '* sq. yd. pavement 
(Road 14' wide) 
Road No. 863, Blasdell Village, $0.0115 per lin. ft. of joint 

0.0129 '' sq. yd. pavement 
(Road 16' wide) 

On Main Street, Sec. i, Road No. 69, the expansion joints cost 
$0.0296 per lin. ft., or $0,033 P^^ sq. yd. (Road 16' wide), in- 
cluding material, labor, etc. 

Assumption. — From the above I would assume $0.0075 P^r 
sq. yd. as the cost of expansion joints. 

Unloading. — Data for unloading not reliable. 

Road No. 2-R Buffalo-Hamburg, $0,014 per sq. yd. 

Road No. 863, Hamburg Village, Contract taken for $1.50 per 

1000 brick; unloaded, haul 
J^ mile, and pile; this would 
be $0.06 per sq. yd. 

Road No. 69, Main St., Sec. i. . . $0,019 per sq. yd. 

Assumption. — I would assume $0,028 per sq. yd. as on and off. 
Hauling. — No reliable data. 

If we allow 600 brick per load, $5 per day for teams, 10 loads per 
day, haul i mile costs $0,034 per sq. yd. 
Summary, Labor Cost of Brick Pavement. 

Manipulation of Concrete 
Pavement 16' wide; edging 8'' X loj^''. 

*Concrete base $0.09 per sq. yd. . . . $0. 648 per cu. yd. 

edge 0.082 " " '' ... 3.378 " '' " 

Concretebase and edging $0. 172 " " *' . . . 1.238 " " " 

Brick Work Labor 

Preparing sand cushion $0.0130 per sq. yd. 

Laying brick 0.0700 

Grouting 0.0280 

Expansion joints 0.0075 

On and off o . 0280 

Haul one mile o . 0340 



Cost of labor $0. 1805 " " " 

Useful Data for Brick Roads. — 

6" X 10 J^" edging per lin. ft. of edging 0.016203 cu. yd. 

8'' X io3^'' " " " ^c u ^ u 0.021605 '' '' 

5" X 16' concrete foundation per lin. ft. 16' road. o. 24691 " " 

2" sand cushion loose per sq. yd o- o55S " " 

I barrel of cement will grout 36 sq. yd. of pavement. 
I barrel of paving pitch will fill 130 lin. ft. of joints i" wide. 
* Recent cost data indicates that ^0.35 per cu. yd. is ample. 



BRICK PAVEMENTS 651 

Amount of Grout Required for Stone Block Paving. — For blocks 
similar to Medina sandstone blocks, running about 26 to the sq. yd., 
Gillette states that 0.6 cu. ft. of joint filler are required per sq. yd. 
of pavement with joints averaging J^" wide. Second quality 
blocks with wider joints require proportionally more. 

STANDARD ESTIMATE, BRICK SURFACING, EXCLUSIVE 

OF FOUNDATION 
Materials. 

Per Sq. Yd. 

Cost of brick, f.o.b. unloading point $ 

" " sand for sand cushion, on job 

" " ^' " grout, on job 

" " cement for grout, on job 

" " paving pitch for expansion joints, on job 

Labor and Teaming. 

Unloading brick and piling along road $0,035 

Hauling brick per mile o. 040 

Preparing sand cushion 0.020 

Laying brick o .070 

Grouting o . 028 

Expansion joints 0.007 

Total $ — 

Add 20 % profit — 

Estimate —..... $ — 

SAMPLE — Standard Estimate, Brick Pavement — 
^NM. C. Perkins 
Brick: $22.50 per 1000 f.o.b. cars at Road siding, 
bricks lay 40 to the sq. yd. 
Labor, $0,175 per hour, 10 hours. 
Sand, 1 . 00 per cu. yd. on cars at siding. 
Stone, 1.25 per cu. yd. on cars at siding. 
Cement, i . 30 per bbl. delivered on work. 

Sand: 

f.o.b. cars $1 .00 

Unloading 0.15 

Haul I mile @ $0 . 30 o . 30 

Cost cu. yd. sand $1 • 45 

Stone: 

f.o.b. cars $1 . 25 

Unloading 0.15 

Haul I mile @ $0 . 30 o . 30 

Cost cu. yd. ston^ $1 . 70 



6s 2 COST DATA AND ESTIMATES 

Concrete: i - 2}^ - 5. 

Use any standard mixing tables, stone 1" and under, dust 
screened out. 

Cement, 1.19 bbl. ... X $1.30 = $1.55 

Sand, 0.46 cu. yd. ... X 1.45 = 0.67 

Stone, 0.91 " "... X 1 . 70 = 1.55 

*Manipulation = o . 50 

$4.27 
20% profit 0.85 

Total $5.12 

The manipulation is based on machine-mixing and is for base 
alone laid 5'' thick. The concrete edging is estimated separately 
and runs from $0.13 to $0.15 per Ijn. ft. 

Material per Square Yard 

Brick f .o.b. cars $0 . 900 

Sand cushion and cover o . 080 

Grout (sand and cement) 0.042 

Material expansion joint o. 008 

$1,030 

Labor per Square Yard 

Unloading and piling $0,035 

Haul I mile o . 040 

Laying and rolling o . 070 

Making sand cushion % 0.020 

Grouting o . 028 

Expansion joints . 0.007 

Culling, replacing, etc 0.005 o. 205 

$1,235 
20% profit o . 247 

Total $1,482 

Therefore, standard 16' road is estimated to cost, per square 
yard (exclusive of edging) : 

Concrete base $0. 711 

Brick 1 . 482 

Total $2 . 193 per sq. yd. 

Say, $2 . 20 per sq. yd. 

*Recent cost data indicates that $0.35 is ample with labor at $o.i7S per 
hour. 



MAINTENANCE COSTS 



6S3 



In the above estimate I have allowed 20% profit on material 
and freight. I do this so as to cover all interest charges, inci- 
dentals, contingencies, etc. I consider this one of the fairest 
wsiys to take care of all general expenses. 



MAINTENANCE AND REPAIR COSTS 

Cold Oiling. — The following data is furnished by Mr. Frank 
Bristow, Supt. of Repairs, Division No. 5, New York State Depart- 
ment of Highways. The work was done in 1910. Labor averaged 
J^.2o per hour; teams, $0.50 per hour. 

Oiling. Actual Cost Data. — No. 6 stock or 65% asphaltic base 
oils applied cold by Studebaker Oiler upon macadam road which 
had been swept by horse sweeper, oil being broomed by hand where 
necessary and then covered by a thin coat of dustless screenings, 
or gravel, spread by hand. 

The labor costs include pumping oil from the car tank, hauling 
same to road, applying same, sweeping road and spreading screen- 
ings; also, demurrage on cars and moving tools and repairs, but 
not cost of the plant. 

Table 64 







Average cost of 
materials 


Average 

Quantities of 

Materials Used 


Average Cost 


>> 
c 

d 


^ 0) 
W) 




Oil per Gal. 
on siding 






SI 




Total Labor 
and Material 
per Sq, Yd, 


Orieans 

Niagara 

Erie 


7 
4 

T2 

3 


2.48 
2.24 
2.00 
4-43 


$0.0435 
0.0425 
0.0437 
0.045s 


$1.82 
1.57 

1.88 
1.83 


0.42 
0.43 
0.34 
0.42 


0.016 
0.016 
0.012 
0.015 


$0,013 
0.014 
0.007 
0.019 


$0,057 
0.057 
0.045 
0.066 


Erie . 





Other information would show that cost per mile to sweep average 
road is $8.33; cost per gallon applying oil $0.0075; cost all labor 
sweeping, hauling, applying oil and cover about $0.25 per gal. used. 



6S4 COST DATA AND ESTIMATES 

Table 64A 
Division 7 N. Y. S. Dept. Highways 

H. G. HOTCHKISS SUPT. MAINTENANCE 

Cost Data for Oiling, Surface Treatment 1915 





No. 


Kind 


Gals. 


No. Tons 


Total Cost 


Total Av. 


Cost per 


Miles 


Sq. Yds. 


Bit. Mat. 


per 


of Cover 


per 


Cost per 


Mile 16' 








Sq. Yd. 


per Mile 


Sq. Yd. 


Sq. Yd. 


Surface 


20.54 


158144 


CO. 


0.25 


62 


0.0344 






23.63 


188208 


CO. 


0.25 


41 


0.0250 






17.75 
19.94 


146734 
172775 


CO. 
CO. 


0.24 
0.191 


37 
43 


0.0237 
0.0189 


0.026 


244.06 


21.47 


200995 


CO. 


0.19 


59 


0.0264 






16.22 


199925 


CO. 


0.28 


74 


0.0287 






22.51 
41.09 


188601 
382330 


L. C 0. 
L. C 0. 


0.20 
0.20 


31 
27 


0.0195 
0.0177 


0.0183 


171.78 


15.44 
13.42 


126657 
126056 


H. C T. 
H. C T. 


0.25 
0.25 


40 
40 


0.0323 
0.0337 


0.0330 


309.77 


17.19 


143846 


L. C T. 


0.2s 


47 


0.0319 


0.0319 


299.45 



Table 64 B 

Division 7 N. Y. S. Dept. Highways 

Cost Data Repainting and Rebuilding Guard Rail 19 14 



No. Lin. Ft. 
Painted One Coat 


Cost 
per Lin. Ft. 


No. Lin. Ft. 
Painted Two Coats 


Cost 
per Lin. Ft. 


15325 
79925 
17486 
42027 


$0.0212 
o.0233_ 
0.0251 
0.0264 


26428 

8433 
12824 
13160 


$0.0425 
0.0360 
0.0352 
0.0442 


Rebuilding Wooden 
Guard Rail 


Rebuilding Concrete 
Guard Rail 


No. Lin. Ft. 


Cost per Ft. 


No. Lin. Ft. 


Cost per Ft. 


160 

554 
360 
272 


0. 219 
0. 189 
0. 200 
0. 141 


100 
335 


$0,896 
0.764 



MAINTENANCE COSTS 655 

COST DATA SURFACE TREATMENT 

It will be noted in the following table that the tendency of surface 
oiling practice is to each year reduce the amount of oil and cover 
used. This is in line with the data set forth in the chapter on 
Maintenance. 

Hot Tar Flush Coats. — The cost of applying hot tar flush coats by 
hand is practically the same as given for applying Bituminous 
Binder penetration method. 

The writer has no reliable data on the cost of machine application. 

Calciiun Chloride. — The cost of applying calcium chloride as 
a temporary dust layer on ten miles of road in Monroe County, 
N. Y., as given by Mr. Frank Bristow, First Assistant Engineer, 
New York State Department of Highways, is as follows: 

The material was applied by an ordinary agricultural drill. The 
force used was, i horse and driver, $0.30 per hour; i helper, 
$0.20 per hour. No preliminary work of sweeping was done; 
the material was spread on the middle 12 feet of macadam, using 
approximately 0.75 lb. to the sq. yd., the average speed being 
0.5 miles, or 3500 sq. yd., per day, at a cost of $0.0015 P^r sq. yd. 

Cost of calcium chloride at plant $13 .00 net ton 

Freight , i . 60 per " 

Unloading from cars, approximately. . . o. 15 '' '^ 

Hauling three miles, '' .... 0.90 '* " 

Total, delivered on road $15 • 65 " " 

Total per sq. yd. delivered ^n road. . . . 0.0059 
Labor of spreading 0.0015 

Total per sq. yd. in place $0. 0074 

Total per mile 12' wide, approximately $52 . 00 



Cost of Applying Calcium Chloride 

Road No. 5507 Scottsville— Canawagus. Season 1915. W. G. 

Harger, Eng. in charge. 

15 tons were applied at the rate of ij^ lb. per sq. yd. on a 16' 
road for $22.00 or at the rate of $1.50 per ton. 

Force used, 1 team hauling agricultural plaster spreader. 2 
laborers helping dniver. Calcium Chloride in metal drums had 
been previously distributed along the road. 

Wages: Team, $5.00 per day; Laborers, $2.00 per day. 

Recapping. — The cost of recapping with any style of macadam 
is practically the same as original construction for that style of 
work except the item of scarifying and reshaping the old road. 

Scarifying. — The cost of scarifying, as given by Mr. E. A. Bonney 
on the Erie County repair work for the season of 1907, is as 
follows: 

{Continued page 658.) 



656 



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658 COST DATA AND ESTIMATES 



COST DATA ON RESHAPING ROAD 

Work was done on Main Street Road, No. 69, Erie County, N. Y., 
between July 15 and Sept. 13, 1907. 

The road had been built as a waterbound macadam. It was 
worn out, particularly in the center. There were few ruts, but the 
road was nearly level; in some stretches the center was lower than 
the sides. It was proposed to reshape the road and to lay a new 
top course treated witlf tarvia. 

The work of reshaping was done by loosening the old surface with 
spiked wheels of roller; this separated the crust into chunks of 
various sizes which were broken up by men with picks. The 
stone was then raked from the sides to the center, brought to the 
required crown, and rolled ready for the new course of stone. 

The cost of the complete operation included the number of men 
picking and the rollerman's salary. 

Labor $0,175 per hour 

Rollerman 0.300 '' " 

The roller was rented at a flat rate of $5.00 per day, and a portion 
of the time it was used on other parts of the work. This cost plus 
the coal and oil is not included. 

The data was compiled daily, and as the work was performed prac- 
tically every working day between the dates named an average of 
the square yard price should be nearly correct. The highest cost on 
any one day was $0.06 per sq. yd., the lowest cost $0,016, and the 
general average $0.03 per sq. yd. 

^Through the courtesy of Mr. Halbert P. Gillette, author of 
"Handbook of Cost Data," we are able to publish the following: 

Cost of Resurfacing old Limestone Macadam. — "In Engineer- 
ing News, June 6, 1901, I gave the following data to show that the 
intermittent method of repairing macadam is the most economic. 
The data were taken from my timebooks and can be relied upon as 
being well within the probable cost of similar work done by contract 
under a good foreman. It will be noted that the cost of operating 
the roller is estimated at $10.00 per day. This includes interest 
and depreciation as well as fuel and engineman's wages. 

"The road was worn unevenly, but as it still had sufficient metal 
left, very little new metal was added. 

"The roller used was a 12-ton Buffalo Pitts, provided with steel 
picks on the rear wheels. It required eighty hours of rolling with 
the picks in to break up the crust of a surface 19,400 sq. yd. in area, 
240 sq. yd. being loosened per hour. The crust was exceedingly 
hard, and, at times, the picks rode the surface without sinking in, 
so that a lighter roller would probably have been far less efficient. 
In fact, a ten-ton roller had been used a few years previous for the 
same purpose at more than double the expense per square yard, 
I am told. The picks simply open up cracks in the crust to a 

1 Gillette's Handbook of Cost Data, Myron C. Clark Publishing Company, 
edition of 1907, page 147. Pages 288 and 289, edition of 1910, in slightly 
different form. 



MAINTENANCE 659 

depth of about four inches, and It is necessary to follow the roller 
with a gang of laborers using hand picks to complete the loosening 
process. The labor of loosening and spreading anew the metal 
was 1.880 man-hours, or a trifle more than 10 sq. yd., per man-hour. 
About 60% of this time was spent in picking and 40% in respreading 
with shovels and potato hooks. 

"After the material had been respread, the short section was 
drenched with a sprinkling cart, water being put on in such abund- 
ance that when the roller came upon the metal the screenings 
which had settled at the bottom in the spreading process were 
floated up into the interstices. The roller and sprinkling cart were 
engaged only 63 hours in this process, 300 sq. yd. being rolled 
per hour; an exceptionally fast rate. The rapidity of rolling was 
due to four factors; i. The great abundance of water used, the 
water being a very short haul. 2. The unyielding foundation (tel- 
ford) beneath. 3. The abundance of screenings and fine dust, the 
road not having been swept for some time. 4. The great weight 
of the roller, which was run at a high rate of speed. I am not pre- 
pared to say that longer rolling would not have secured a harder 
surface, but I doubt very much whether it would. The metal, 
I should add, was hard limestone. Summing up, we have the 
cost of resurfacing the road per square yard to have been as follows : 

Cents per sq. yd. 

Picking with roller at $1 per hour $0 . 40 

Picking by hand labor at $0 . 20 per hour i . 20 

Respreading by hand labor at $0 . 20 per hour o. 80 

Rolling with roller at $1 per hour o . 33 

Sprinkling with cart at $0 . 40 per hour 0.13 

Foreman, 143 hours at $0.30 for 19,400 sq. yd. 0.44 

Total 3 . 30 

"At this rate a macadam road sixteen feet wide can be resurfaced 
for a little more than $300 per mile. The frequency with which 
such resurfacing is necessary will, of course, depend upon several 
factors, chief of which are the amount of traffic and the quality of 
the road metal. I should say that five years would not be far from 
the average for a country road built of hard limestone. Unless the 
road has had an excess of metal used in its construction, new metal 
should be added at the time of resurfacing to replace that worn out. 

"I am unable to see how any system of continuous repair with its 
puttering work here and there can be as economical as work done 
in the manner above described. I would not be understood, how- 
ever, as favoring an entire neglect of the road between repair periods. 
At times of heavy rains and snows, ditches and culverts need atten- 
tion and there should be some one whose duty it is to look after such 
matters. WHiat I do question is the economy of having a man con- 
tinuously at work putting in patches upon the road." 



66o COST DATA AND ESTIMATES 



iNEW YORK STATE PATROL MAINTENANCE, 1910 

The standard Patrol distance is five miles. 

The standard Patrol distance, brick roads, Is twelve miles. 

Patrolman's wages $78 per month, including horse and cart. 
Patrol is operated eight and one-half months in a year. 

The cost of this system of maintenance per mile for 1910 was, 
approximately, $250 exclusive of administration charges. 

Patrolman's wages $125 .00 

Materials 1 25 . 00 



$250.00 



These costs do not include surface treatments. Such a treat- 
ment of a road every two years would amount to about $375 a mile 
per year on waterbound roads. 

Automobile Truck Repair System. — The tendency on minor 
repair maintenance work seems to be toward lengthening the patrol 
distance; confining the duties of the patrolman to cleaning culverts" 
and ditches, trimming shoulders, and reporting the necessity of 
minor repairs. It is believed that these repairs can be handled more 
economically from a central point by the use of an automobile truck 
specially equipped for such work and which can operate within a 
radius of 20 to 30 miles. Special trucks have been devised with 
facilities for heating and applying bituminous materials as well as 
carrying materials. 

Conclusion. — In conclusion the author desires to again call the 
attention of the reader to the fact that while cost data is valuable 
it must be used with discretion and not figured too closely. 

1 Data obtained from Mr. Frank Bristow, Supt. of Repairs, N. Y. S. Dept. 
of Highways. 



MAINTENANCE 



66i 



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CHAPTER XV 

NOTES ON CONSTRUCTION 

No matter how well a road is designed, unless the constructing 
engineer uses good judgment, and the inspection is conscientious 
and intelligent, the results will not be satisfactory. This chapter 
emphasizes the importance of the different stages of the work and 
gives a few suggestions as to the manner of meeting common 
difficulties. 

Staking out for Construction. — The construction survey picks 
up the center line shown on the plans and by means of offset 
stakes driven to a certain elevation marks the position and ele- 



^ staking Qyj^ ^ 






Notes 


\ 


Std. 


Offsets 


Cut or Fill 


Levels 




Orade 


Grade 
Reading 


RodReadinqonSfdkesI 


L. 


R. 


L. 


R. 


B.S. 


F.S. 


Elev. 


H.I. 


Elev. 


L. 


R. 


B.M*5 














526.42 












10 


25 


13 


ros 


F/.0 


4.17 






530.59 


524.2 


6.4 


6.9 


7.4 


f50 


25 


22 


F0.5 


Fl.5 








9T 


524.6 


6.0 


6.5 


7.5 


II 


24 


25 


FOB 


F/5 








99 


525.0 


5.6 


6.1 


7.1 


1-50 


21 


26 


C0.5 


FI.0 








99 


525.4 


5.2 


4.7 


0.2 


n 


22 


25 


COS 


FIB 








99 


525.8 


4.8 


4.3 


6.3 _ 


tSO 


23 


24 


CI.O 


F2.0 








99 


526.2 


4.4 


3.4 


6.4 


93 


24 


24 


6r. 


Gr 








9f 


526.6 


4.0 


4.0 


4.0 


tSO 


25 


23 


Gr. 


Fas 








»» 


527.0 


3.6 


3.6 


4.1 


f4 


?P 


17 


Or. 


COS 




3.20 


527.33 


99 


527.8 


2.8 


2.8 


2Z 


tSO 


'2b 


26 


Gr 


CI.0 


7:41 






554.60 


628.6 


6.2 


6.2 


5.2 


fS 


Zb , 


23 


CO.b 


Fl.b 








99 


529.4 


5.4 


4.9 


6.9 


■fSO 


it 


2S 


hl.O 


FI.0 








19 


530.Z 


4.6 


S.6 


5.6 


_/.<b 


Zi> 


26 


or 


CI.O 








ff 


5-51.0 


3.8 


3.8 


2.8 


tw. 


2b 


'23 


F/5 


CI.0 








99 


631.8 


3.0 


4.5 


2.0 


17 


24 


'24 


Fl.5 


Gr. 








99 


532.6 


2.2 


3.7 


2.2 


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1.4- 


2.4 


6.4 ' 


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Pig. 137. 

vation of the road conveniently for building. Any arrangement 
of stakes that shows the position of the proposed center line and 
the elevation of the proposed grade is satisfactory. These stakes 
may be set on one or both sides of the road at intervals of 50 or 
100 feet. The offsets to the center line may be marked to the 
nearest one-tenth foot, or the stakes may be so set that the offset 
is an even foot, and they may be driven so that the elevation of the 
proposed grade is above or below them an even foot, one-half foot, 
or an odd tenth. A satisfactory method in general use in western 

662 



STAKING OUT 663 

New York is to set the construction stakes on both sides every 
50 feet, with an even foot offset and driven to such elevation that 
they are either an even foot or one-half foot above or below grade. 

Such stakes can be readily explained to the ordinary grading 
foreman so that he has no difficulty in working from them without 
the assistance of an inspector. The 50-foot interval is convenient 
for fine grading, as the lines can be stretched this distance with 
no apparent sag, while if a 100-foot interval is used the sag is ob- 
jectionable. With stakes on both sides of the road the elevation 
of the proposed grade can be readily transferred to the center by 
stretching a line between them and measuring down or up the 
required amount. This is a much simpler and more accurate 
method than transferring by straight-edge where two or three 
lengths of straight-edge must be used from the stake to the center. 

The left stake marked C 4.0' offset 28.0' means that the crown 
grade of the finished road is 4.0 feet below the top of this stake and 



Marked C 4.0'%^. g! ^ g^ 

Offset 26.0' ^^^ , ^1: ^,^/ ^^ 

\< -%s^— 28.0 M; • ^^-^"'jm^ 

.;..;^p...,h. ....... ..•.«..-.. .. • ,,v,..,,^,..- MarkedCI.O 

! Offset 24:0' 

Fig. 138. — Showing suggested method of staking out. 

that the proposed center line of macadam is 28.0' from the face of 
the stake. 

To transfer the proposed grade to the center by the siring method. 
Fasten chalk line to top of left stake; measure up 3.0' above top of 
right stake and draw line taut at this elevation. The string is level 
and 4.0' above crown grade. Pull as tight as possible, allow about 
3^" for sag and measure down 3' n)^" for finished grade. 

Cost of Staking Out. — The speed and cost of staking at 50-foot 
intervals will, of course, vary with the experience of the men and 
the character of the road. A party of four men should pick up 
the proposed center line and set offset stakes on both sides at 
a speed of 1.5 to 2 miles a day; a party of three men should grade 
these stakes at a speed of i.o to 2.0 miles a day, and the cost of 
staking out for construction, including livery and board, would 
be from $20 to $30 per mile. 

It is common for new men to spend an unnecessary amount of 
time in setting the grade stakes. They will often attempt to have 
the elevation of the grade stakes correct to within 0.0 1 foot. For 
all practical purposes, for work of this character, stakes correct to 
within 0.1 foot in elevation and o.i foot in alignment are satisfac- 
tory. Curb stakes for village work, however, should be carefully 
set to within 0.02 foot in elevation and line. 



664 



NOTES ON CONSTRUCTION 



CONSTRUCTION 

Rough Grading. — By rough grading is meant all of the work pre- 
liminary to the finished shaping, and includes moving practically all 
the dirt that is to be handled. It is particularly important to 
supervise this stage of construction, as it is here that the construct- 
ing engineer regulates the placing of the best material in the center 
(under the metalling) and the poorer materials on the sides. 

In order to grade economically, the contractor and inspector 
should each be furnished with lists similar to those given below, 
showing, in a convenient form, the ariiount of excavation station 
by station and within what bounds it is to be placed. 

Cuts. — For cuts over 3 feet deep slope stakes are placed and care 
taken that the slopes are properly carried down. If excavated 



Excavation 
Summary 


Lists 


Std.foSI-a. 


Exc. 


Emb. 


Waste 


Sorrow 


Remarks 


IZ5 


154 


476 


375 






Quaniiiies in cu. yds. 


134 


/40 


236 


240 








I40 


157 


642 


662 


c 


W(55 


Haul from Sf a. 179 to 150 


IS7 


173 


766 


629 


\ 






ns 


179 


251 




251^ 






179 


186 


238 


244 








Petal 1 Quantities - | 






Sta.toSta. 


Exc. 


Emb. 




123 


/25t50 


575 


225 


Quantities in cu. ft. 


I2Z1-5G 


124 


150 


900 




IZ4 


1 24 1 50 


— • 


1450 




/24tS0 


125 


150 


300 




125 


/25t50 


320 


200 




f25tS0 


126 


170 


500 




126 


/26t50 


30 


925 




I26f50 


127 


30 


350 




127 


/27t50 


260 


410 




I27f50 


126 


350 


250 




128 


1281-50 


635 


160 




r23t50 


129 


635 


75 










y 


^ } 



Pig. 139. 

beyond the finished lines it is practically impossible to make a 
Imck-fill that will hold and the resulting irregularities are unsightly. 

Fills. — For fills slope stakes are set in the same manner as^ for 
cuts.i The earth should be deposited in thin layers, six to eight 
inches deep, extending from slope to slope, and each^ layer well 
compacted either with a roller or by driving over it with wagons 
in the process of building Where the old surface has ft steep slope 
it must be plowed to give a good bond with the new fill and prevent 
slide. 

1 Slope stakes can be located directly from the templet Cross Section 
which is a much easier method than the railroad practice of rod and level 
computation. 



FILLS 665 

It is bad practice to build the center of the fill and then shovel 
loose material off of the edge to widen the slopes, as^t];^i^ .k>0|e. 
side-fill is not compacted and -'dnuer the- g,-CVi6n of frost will nearly 
always slough away from the harder central portion. 

To get the full benefit of the teaming in compacting the dirt, 
a deep fill should be started at a point nearest the cut from which 
the material is hauled and each load driven over the loose layer. 
In this way nearly every fill can be better compacted than by 
the use of a roller alone. For long fills where there is considerable 
teaming over each layer a roller is not usually needed. 

^ -^ " -^ -"^^'/^ 

Old ^ . ^ -^^ Layers 

Surface^ ^ ^ X 




Wet clay or heavy loam should never 6e placed in the bottom 
of a fill, as it dries slowly when not in contact with the air and keeps 
the fill "spongy." The writer has seen cases where fills not over 
3 feet deep have remained soft for two months where wet material 
had been used and it was finally necessary to remove it. 

Transferring Grade from Stakes. — A handy level for transferring 
the grade from stakes to the center of the road is shown below. 
If well made it will transfer the grade elevation 50 feet with an error 
of less than 3 inches, which is close enough for this stage of the 
construction : 

String >^f^'ng 



Fig. 140. 

Ditches. — The ditches must always be dug out enough to protect 
the center grading before the fine grading (stone trench) is com- 
pleted, and it is usually cheaper for the contractor, as well as better 
for the road, to dig them out before the fine grading begins. 

Regulation of Material in Fills. — In fills, particularly shallow 
ones, the road can be greatly improved by a judicious selection 
of available materials. Material taken from two nearby cuts, 
or at different depths in the same cut, will often vary in character 
and the most experienced man on the job should indicate which 
materials to use in the center of the fill, under the metalling, and 
which on the sides. The soils in the order of value for fills are 
gravel, coarse sand, loam, and clay. For shallow fills on a good 
foundation clay should not be used under the stone, as mentioned 
on page 151, and a*good material must be overhauled or borrowed. 
It is better to avoid overhaul if possible, as it is an item liable to be 
disputed as to the amount. Where it. is necessary, a good practical 
method of determining the amount of the small quantities of earth 
usually needed is to keep track of the number of wagon loads over- 
hauled from station to station. 



666 NOTES ON CONSTRUCTION 

Sod may be used in the sides of the fill, but should be kept at 
least eleven feet off center. It should NEVER be used as a 
shoulder close to tlie ?tone Or ir, tilt center of the fill under the 
metalling. 

The author wishes to emphasize the importance of this regu- 
lation of material. At present the inspection of rough grading 
is often confined to keeping the sod from the center fill, and the 
center fill is made of the dirt just as it happens along. As a result, 
the sub-grade will vary greatly in character and if a uniform depth 
of stone is used over this '* spotty" fill the results are often not 
satisfactory, while if the depth of stone is varied to meet the 
sub-grade conditions an unnecessary amount of stone is used. In 
cases where there is no choice of earth materials the stone depth 
must be made thick enough to meet the requirements of the grade. 

FINE GRADING FOR STONE TRENCH 

The fine grading includes the shaping and consolidation of the 
stone trench. 

^! ,..' V ''* Shoulder 

i ^\^ ' ' ' '■' 




Pig. 141. — Showing 3 lines of grading pins. 



The construction shoulder must be at least 2.5' wide and well 
consolidated in order to hold the stone solidly during rolling. This 
must be watched continually by the inspector as it is a point often 
slighted. 

Shaping the Grade. — A simple guide for shaping the grade is 
shown in the accompanying sketch and consists of three strings 
(center and sides) stretched between pins driven at least every 50 
feet and preferably every 25 feet. The pins should not be placed 
at intervals of more than 50 feet as this will cause objectionable 
sag in the lines and the grade will be undulating. The grade ele- 
vation is transferred and the lines carefully set at their proper 
elevation by means of a straight-edge, level and rod, or by stretch- 
ing a line between grade stakes on opposite sides of the road as 
previously described. The string level recommended for rough 
grading can not be used, as it is not sufficiently accurate. 

The general level of the finished consolidated grade should be 
correct to within i inch. This leeway of i inch from the figured 
grade makes it possible to get satisfactory results without wast- 
ing time on finical work and does not appreciably affect the total 
amount of excavation, as the errors tend to balance. There 
should, however, be no short, small irregularities of grade notice- 
able to the eye. Continuous inspection on shaping the grade is ^ 
not necessary. l 



SUB-BASE 667 

Consolidating the Grade. — Most soils when slightly moist 
will consolidate readily if thoroughly rolled. Clay, heavy loams, 
or excessively fine sandy loams (quicksand) will not pack when 
wet. Continued rolling is injurious for these soils in this condition, 
as they will "work" under the roller. If they occur only in small 
pockets they can be removed and replaced with good material; 
if in stretches of any length the grade must dry out before placing 
the stone. Under drains are constructed at this time, where nec- 
essary, and the surface ditches are cleaned out and made effective. 
Where a hard shower has softened the surface only of a previously 
consolidated grade of this kind and the contractor wishes to lay 
stone, the surface can be hardened by spreading a thin layer of 
gravel or waste No. 2 stone and rolling it into the earth. This 
will help in preventing the stone teams from cutting up the grade. 

Gravels and finely pulverized clay, or clay loams (deep dust), 
will not consolidate when dry; such material must be thoroughly 
sprinkled to get a compact grade. It is not, however, customary 
to sprinkle coarse gravels, even if slightly loose, as no objectionable 
results follows from placing stone on such a grade; deep clay or 
loam dust is objectionable and must be sprinkled. 

Coarse sand makes an ideal foundation but is hard to keep 
in shape while placing the first layer of stone. In some cases 
sprinkling will harden it sufl&ciently; in others a layer of fine loam 
has been spread over the sand and flushed in with satisfactory 
results. Sometimes where loam is not available a cheap cheese- 
cloth has been spread over the top of shifting sand to prevent the 
stone from punching in too much under the roller. The author 
has never encountered any coarse sand that could not be suc- 
cessfully treated by sprinkling and covering with i inch or 2 
inches of No. 2 stone; the blanket of No. 2 stone prevents the sand 
from squeezing up into the loose bottom stone and spreading the 
fragments. 

While coarse sand makes a good foundation, a fine sand or 
sandy loam approaching quicksand is very treacherous; it is 
difficult to judge the degree of fineness at which a sand becomes 
treacherous, particularly when it is dry. A laboratory method 
is given on page 150, but a good practical method in the field is to 
saturate the material thoroughly with water; a satisfactory sand be- 
comes more compact while an exceedingly fine sand gets "quaky." 

DETERMINATION OF STONE DEPTHS AND 
CONSTRUCTION OF SUB-BASE 

Practically the only engineering problem that the constructing 
engineer has to* solve is that of foundations. It is recognized 
by most designers and estimators that it is impossible from even 
a careful preliminary examination of the soil to specify exactly 
the amounts and depths of foundation stone. To meet this an 
extra quantity of sub-base or bottom stone is allowed the construc- 
tor, to be used as he sees fit. During the progress of the rough 
and fine grading the exact limits of the different kinds of sub-grade 



668 NOTES ON CONSTRUCTION 

soil are determined and the stone depths varied according to his 
judgment. (See page 152.) Men that really understand this 
part of the work are hard to get, as it is only from extended expe- 
rience and intelligent study of their own failures and successes that 
a Sound jutigment is developed. A good constructing engineer 
is much more difficult to find at present than a good technical 
designer. 

Where sub-base is used the sub-grade is dug out to the required 
extra depth and rolled if it is in such shape that it will not "work.'* 
Peat, muck, wet fine sand, or wet clay can not be rolled until the 
sub-base is placed and filled. Where it is possible, such soils 
should be drained and allowed to dry before placing the base, 
but is often not feasible to dry them enough to allow rolling, 
even though underdrainage is put in, which partially hardens 
them and successfully protects the road after the stone has been 
placed. This is particularly true on flats where it is hard to get 
an outlet for a drain or in the fine sands on which an under drain 
has little effect on account of the capillary action of the material. 
Where a soft sub-grade of this kind is encountered, a stony gravel 
makes the best sub-base, as it contains no voids between the larger 
fragments and when roHed the soft underlying material can not 
squeeze up through the course. In case boulder or quarry stone 
base is used on a soft grade, it is necessary to lay them in close 
contact by hand and then fill the voids completely with gravel 
or No. 2 stone before rolling; otherwise the sub-grade material 
would squeeze up between the stones, separating them and par- 
tially destroying the efficiency of the base. 

In the Spring and Fall of the year it is common to find good ; 
material so saturated from long-continued rains that it acts badly 
under the roller and instead of waiting for the grade to dry out, 
when the normal thickness of stone would be sufficient, sub-base 
is often put in either to help the contractor so that he will not be . 
delayed or because the engineer is misled as to the character of ' 
the material. This results in a waste of money. On the other 
hand, clay, when thoroughly dry, is hard and firm, which often 
influences a new man to omit sub-base where it will surely be 
needed. 

The use of sub-base should not depend too much on the action 
of the grade under the roller unless the degree of saturation of the 
material is considered, although it serves as a guide in locating 
doubtful spots. The final determination should depend on test 
pits, which develop the character of the underlying material. 

The sub-base is constructed, as explained, in the chapter on 
Foundations, either of gravel, boulder or quarry stone. The depth 
is gauged by lines. The ratio of loose to rolled depth is given 
on page 591. 

Continuous inspection is not needed on sub-base; the depth of 
grading is checked before the stone is placed and the width, depth, 
and workmanship can be readily determined after the base is 
completed, and by an occasional inspection during the progress 
of the work. 



BOTTOM COURSES 669 

Bottom Stone. — The earth sub-grade must be firm and compact 
before the stone is spread. Bottom stone must NEVER be 
laid on a soft grade. One of the most common slips of inspection 
is to allow this to be done and the result is a ''punky" bottom 
course that is never up to standard. The distributing power of 
this course depends largely on the stone fragments being firmly 
interlocked; if the stone is placed on a soft grade and rolled, the 
earth will squeeze up between the fragments and separate them. 

The depth of the loose stone is gauged by the lines or cubical 
wooden blocks placed on the sub-grade. Blocks are more conven- 
ient than lines except over sub-base of stone fills, where lines must 
be used to get a spread true to shape and grade. The ratio of 
loose to rolled depths is given on page 591. 

The loose stone is rolled until the stones are solidly interlocked 
and there is no movement under the roller. A thin layer of sat- 
isfactory filler (see materials page 240) is spread over the top, 
rolled and broomed in; the process is repeated until the stone is 
thoroughly filled. Continuous inspection on bottom course is not 
necessary. The widths and depths can be readily checked by 
occasional inspection. The two points to be carefully watched 
during construction are: i. That the grade is firm; 2. that the 
loose fragments are thoroughly rolled before the filler is applied. 

It is desirable to complete the bottom course well in advance 
of the top, in which case the contractor can work to advantage 
after rains, and the course will be better compacted by subjecting 
it to some traffic action. 

Where local stone is crushed on the job and the stone used 
ranges in size from i in. to tailings, care must be used in spreading 
that the sizes are well mixed, as pockets of fine or coarse stone 
are objectionable. The simplest method of mixing is to run the 
No. 3 and No. 4 and tailings into one bin at the crusher; if they are 
separated they can be well mixed by loading one end of the wagons 
with the No. 3 and the other end with No. 4 and when dumped on 
the grade they will run together. When difficulty is experienced 
with these methods in obtaining a well-mixed stone spread the 
loose stone can be harrowed. Many specifications call for harrow- 
ing thoroughly where a large range of crushed stone size are allowed 
in one course. If possible, tailings should be used as sub-base. 
When used in the bottom course having a rolled depth of 4 or 5 
inches they should be placed in the lower part of the course, but 
for a 3 -inch depth they should be placed on top and broken with a 
knapping hammer into fragments of less than 3 J^ inches. 

The filler should not be dumped directly on the stone unless 
absolutely necessary. Drawing the loads onto the unfilled stone 
loosens the course, and, also, at each pile of filler there is apt to 
be left an excess which is hard to clean off. 

Table 65 gives the approximate amount of filler required per 
100 feet, and the spacing of i J^-yard loads. The amount varies 
for the different materials used. 

Grading and foundations have been treated at some length, as 
they are the most difficult parts of the construction. 



670 



NOTES ON CONSTRUCTION 



Table 65. Giving the Approximate Amount of Filler Re- 
quired PER 100 Feet of Road for Crushed Stone Maca- 
dam Bottom Courses of Different Widths and Depths, 
Using 0.35 Cubic Yards of Filler per Cubic Yard of 
Rolled Bottom 



II 


Rolled Depth of Bottom Course 


Z" 


4" 


5" 


6 


" 


10' 
12' 


3.2 CU. yds. 
3.8 " '' 


4.3 CU. yds. 

5.1 '' "• 


5.4 CU. yds. 

6.5 " " 


6.6 cu. yds. 
7.6 " '' 


14' 
16' 


4.5 " " 
4.9 " " 
5.2 " " 


6.0 " " 
6.4 " " 
6.9 " " 


7.5 " " 
8.0 " " 

8.6 " " 


9.0; 

9.9 
10.4 




18' 

20' 


5.9 " " 
6.4 " " 


7.9 " " 
8.6 " " 


9.7 " " 
10.8 " " 


11.8 ' 
12.8 ' 




22' 


7.0 '' " 


9.4 " '' 


11.8 '' " 


14.2 ' 





Table 65 A. Giving the Approximate Spacing of 1.5 Cubic 

Yard Loads of Filler for the Widths and Depths 

SHOWN IN Table 65 



Width of 


Rolled Depth oi 


Bottom Course 


Macadam 


y 


4^ 


5'' 


t" 


10' 


46 feet 


34 feet 


27 feet 


23 feet 


12' 


40 " 


30 " 


23 " 


20 " 


14' 


ZZ " 


25 " 


20 " 


17 " 


15' 

16' 
18' 


31 " 
29 " 

25 " 


23 " 
22 '* 
19 " 


19 " 
17 " 
16 " 


15 " 
13 " 
12 " 


20' 
22' 


23 " 
21 " 


18 " 
16 '' 


13 " 
12 " 


II " 

10 *' 



TOP COURSES 

Waterbotind Top. — Waterbound top is constructed in the same 
way as the bottom course except that stone dust is used for a 
filler and the course is puddled as has been described. 

If the stone used is a local stone crushed on the job the output 
of the crusher must be carefully controlled, especially where 
selected boulders are used, as it is very important that the size 
and quality of such stone shall be uniform. 

Imported stone can be inspected on the cars. Aside from this, 
comparatively little inspection is required except at the stage 
when the loose stone has been rolled and before the binder is 
spread. At this time the inspector should examine the rolled 
course very carefully to see that it is true to shape and has no short 
depressions or humps. The smooth riding quality of the road 



BITUMINOUS MACADAM 671 

depends on this inspection and too much care cannot be taken. 
This point is particularly emphasized, as many of the stone roads 
in New York State have been criticized as rough for automobile 
traffic. Any depressions are filled with stone of the same size as 
the body of the course and rolled, after which the course is again 
inspected and corrected until it is made true. The binder is then 
spread, broomed in dry, and puddled. In puddling use plenty of 
water and roll rapidly. If a pipe line and hose are used a pressure 
of 100 to 125 pounds at the pump should be maintained. The 
road can be conveniently puddled in stretches of 100 to 200 feet. 
After the road has dried out and been opened to traffic, if raveling 
occurs it can usually be remedied by light sprinkling and rolling. 
Where the top course is granite, gneiss, or trap, it is often nec- 
essary to use a certain percentage of limestone dust with the normal 
screenings. The limestone is more effective when spread last, 
filling the top voids of the course. 

Bituminous Top. Penetration Method. — The same procedure 
applies to the quality, size, and lajdng of the stone for a bituminous 
as for waterbound top, and does not require continuous inspection. 
Just before pouring the bitumen the course should be carefully 
examined and any pockets of fine stone, dirt, dirty or dusty stone 
removed, as fine stone or dirt prevents the penetration of the binder 
and the bitumen will not adhere properly to the stone unless 
it is clean and dry. The course is not rolled as firmly at this stage 
as for waterbound tops because excessive rolling tightens the stone 
too much and prevents the penetration of the bitumen. There 
should, however, be no creep in front of the roller. The bitumen 
is poured into the voids of this clean ^ dry, partially compacted course, 
usually by means of hand-sprinkling pots or hods. Pots having 
vertical slots are preferable to the fan-spout pots, as they give 
better penetration. 

When hods or pots are used, however, the bitumen should be 
poured across the road instead of in a longitudinal direction as this 
prevents overlap and minimizes the difficulty of preventing humps 
or waves. 

, In placing the bitumen the following precautions must be 
{observed: It must be hot enough to run freely; for each grade 
the temperature of applications is usually specified and it must 
\not be overheated, for if charred it is useless. In applying, by 
(whatever method, care must be taken not to overlap, as waves 
[or humps will develop at these points. These defects do not 
appear for some time- after the road is opened to travel, and an 
inexperienced inspector fails to realize the necessity of care in 
this particular. The stone must be clean and dy, and, in the 
writer's opinion, the air temperature should not be less than 50° F., 
! as bitumen applied in cold weather is so chilled when it strikes the 
cold stone that an excessive amount is retained on the surface. 
As soon as the bitumen is applied a thin layer of No. 2 stone is 
spread over the surface and rolled lightly; continued rolling at this 
point is injurious, as freshly laid bituminous tops tend to shove 
under the roller and form waves. The road can be thoroughly 



672 



NOTES ON CONSTRUCTION 



rolled and shaped to advantage only after the bitumen has had 
some time to harden. Good results have been obtained by rolling 
thoroughly the succeeding day after the binder is applied, unless in 
the meantime rain has saturated the course, in which case it must, 
be allowed to dry before rolling. 

The amount of bitumen spread per square yard is usually con-; 
trolled by spreading a given number of pots or hods in a given' 
length of the road. These units of length can readily be marked 
off by the inspector with a stick or tape. This method will be* 
satisfactory if checked up twice a day by the number of barrels - 
used. When the binder is heated in small kettles it will some- 
times catch fire, but this is usually due to scale which has collected 
in the tank and if cleaned out it generally remedies the trouble. 

Where bituminous materials are heated by steam it is often con- 
venient to know the temperature of steam at different pressures; 
the following table is inserted for this purpose: 



Table 66 



Pressure 
Gauge Lbs. 
per Sq. In. 


Temperature 

of Steam 

op 


Pressure 

Lbs. per 

Sq. In. 


Temperature 
"F of steam 


Pressure 

Lbs. per 

Sq. In. 


Temperature 
°F of steam 


'IS 

20 
40 
60 
80 
100 


213 

228 
267 

293 
312 
328 


100 
120 
140 
160 
180 
200 


32S 
341 
353 
363 
373 
382 


200 
220 
240 
260 
280 
300 


382 
390 
397 
404 
411 
417 



1 Fifteen pounds normal air pressure; to get ordinary steam gauge reading sub- 
tract IS lbs. from the values given in this table. 



HASSAM CONCRETE PAVEMENT 



By E. E. Kidder 

The principal mechanical difficulty in laying a Hassam pavement 
is in getting a proper penetration of the grout. 

This requires stone free from small particles and a grout of the 
proper consistency. 

Stone. — The stone should be sized i J^'' to 3K" uniformly mixed. 
Any pockets of fine stone should be shoveled out or if they occur 
in small areas raked over till the fine goes to the bottom of the 
course. 

The spreading is followed by rolling with a lo-ton road roller. 
Close attention should be given to obtaining as nearly a perfect 
surface as possible as it is practically impossible to add or deduct 
material once the stone is grouted. 

Grout. — The grout should penetrate to the bottom but should 
not be so thin that separation occurs. The size of sand is important. 



CONCRETE ROADS 673 

Coarse sand will not penetrate well. Sand passing a 10 mesh to 
the inch screen and containing much that is finer works well. 

Manipulation. — Each morning the end of the previous day's 
work should be cut down vertically and square across the road, 
shoveled out and replaced with new stone. This insures a vertical 
joint. Continuous Inspection is Necessary on both Stone and Grout. 
The grout will float a few of the top stone out of place but the 5-ton 
tandem roller will smooth them down. The final finish is obtained 
by hand tamping and brooming the surface. The tamping is abso- 
lutely necessary to get the best results and it will be neglected unless 
insisted upon. 

Shoiilders. — It is desirable that the earth shoulders be left i'' 
higher than the finished pavement until the grouting is completed 
to prevent waste. During the rolling of the grout some water will 
flush to the surface and run to the edge; it should be let off by 
digging small trenches through the shoulder. The grading of the 
shoulders should be practically complete before la3dng stone in order 
that the Sand and Cement may be placed on one side of the road 
and the other shoulder may be used as a walk for the workmen and 
traffic. The gang organization is shown by a sketch (page 607, 
Cost Data). 

FIRST CLASS CONCRETE PAVEMENTS 

By F. W. Bristow 

\ The sub-grade should be formed true to alignment, elevation and 
shape and consolidated well in advance of the mixing machine to 
permit the delivery of materials both on the sub-grade and shoulders. 
,' The materials, stone or screened gravel, sand and cement should 
I be distributed uniformly in the proper quantities to construct the 
pavement as planned. (For quality of materials see specifications. 
For amounts required see Cost Data.) The cement should be de- 
livered on the road only as required and covers provided for its 
protection in case of storm. 

Inspection of Manipulation. — A diagram showing a typical 
■ mixing gang organization is given in the chapter on Cost Data. 
Two inspectors are necessary to properly supervise the work. The 
i inspection must he continuous. The inspector ahead of the mixer 
1 sees that the sub-grade is correct; that the edging forms are properly 
, set; that the fine and coarse aggregate conforms to the requirements, 
and that the proper amount of materials are placed in each batch 
. of concrete. 

I He also should keep a daily record of the amount of cement used, 
\ the amount of concrete laid and should figure the amount of cement 
1 per. cu. yd. of concrete as a check on his batch inspection. He 
! should be careful to observe that no empty cement sacks from the 
j previous days run are counted the second time. 

* The inspector back of the mixer first sees that the sub-grade is 

♦ smoothed as the mixing machine moves ahead; that any muddy 
j condition is remedied by removal and that a dry dusty sub-grade is 



674 NOTES ON CONSTRUCTION 

sprinkled to prevent rapid absorption of water from the concrete; 
that the concrete as delivered from the mixer has the proper consist- 
ency and is thoroughly mixed; that the transverse expansion joints 
are properly placed; that the striking of the concrete with the 
screed^ or template is so done as to leave no projecting stone, or 
humps or hollows in the surface. Any surface irregularities must 
be immediately remedied and the mass restruck. The screeding 
is kept up closely to the mixer and is followed by the wood float 
finishers working from a bridge that spans the concrete. 

In case surface brooming is required the inspector determines 
when it shall be done; the best time is just after the initial set 
starts. Long-handled steel brooms are used and the brooming is 
done lightly transversely to the road. 

In hot weather the fresh concrete should be sprinkled to prevent 
sun checking. It is covered within 24 hours with a coat of earth 
i" to 2" thick which is sprinkled and kept damp for 10 days when it j 



Wrought 
Iron 
Shoe^ 



i f^PierR<i /"Planks 
^^^ v fll Spiked Togethea 



\d^—- /^- —"W^-F/a /Subgrc^sre' 

/ //y////'7/////////////yy///y/y//y/// ///yiryy//// 

Sketch of Screed '•'^^^^ ^^^"^^ 

Fig. 142. 

is removed. Traffic must be barricaded from the road for this 
time. 

Before turning traffic on to the completed concrete the earth 
shoulders should be finished along the edge to prevent spauling. 

Amount of Water. — Excess water must be guarded against as 
it weakens the concrete. A good practical rule is the use of about 
53^ to 6 gal. of water per sack of cement, see Chapter pn Materials 
on the Use of Water in Concrete, page 262. 

SUGGESTED SPECIFICATIONS FOR ROLLER FINISH2 

The following is a suggested form of specifications for roller 
and belt finish: "as soon as possible after the concrete has been 
struck off, it shall be rolled with an approved metal roller, having 
a smooth, even surface, approxiniately six (6) feet in length, not 
less than eight (8) inches, nor more than twelve (12) inches in 
diameter, and weighing not more than one hundred (100) pounds. 
On pavements less than twenty (20) feet in width, the roller may 
be operated with a handle, which shall be at least two (2) feet 
longer than the width of the pavement, and all rolling shall be done 
from one side of the slab. On pavements twenty (20) feet and 

1 The screed should be two feet wider than the finished pavement as it 
progresses with a see saw movement rather than a direct full. 

2 Quoted from the "Concrete Highway Magazine," of March, 1918. 



CONCRETE ROADS 



67s 







sun J34u9y' 



676 



NOTES ON CONSTRUCTION 



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TOPEKA MIX 677 

more in width, the roller shall be provided with two (2) bails to 
which ropes shall be attached, and the roller pulled across the 
pavement. The roller shall be operated at such an angle with the 
center line of the pavement that it advances along the pavement 
about two (2) feet for each time across. The roller shall pass from 
one edge of the pavement to the other, care being taken not to 
run the roller over the side forms so that earth or other foreign 
material will adhere to it. After the roller has covered a given 
area in the manner described, the same area shall be similarly 
covered by the roller for not less than three times at intervals of 
fifteen to forty minutes, and as many times additional as may 
be necessary to remove excess water. 

"After the rolling has been completed the pavement shall be 
finished by two applications of a belt made of canvas or rubber 
belting, not less than six (6) inches wide and not less than two (2) 
feet longer than the width of the pavement. The belt shall be 
applied with a combined cross-wise and longitudinal motion. 
For the first application vigorous strokes at least twelve (12) 
inches long shall be used, and the longitudinal movement of the 
belt along the pavement shall be very slight. The second applica- 
tion of the belt shall be immediately after the water glaze or sheen 
disappears, and the stroke of the belt shall be not more than four 
(4) inches, and the longitudinal movement shall be much greater 
than for the first belting." 

Sheet Asphalt, Topeka Mix, Etc. — The important points in any 
form of a mixed Bituminous surface are a proper grading of the 
aggregate and care not to char the binder in mixing. The concrete 
base for asphalt pavements should have a rough finish. 

Two inspectors are required; one at the plant and one where the 
asphalt is being laid. Plant inspection should be continuous. The 
plant inspector is responsible for the proper proportions of the dif- 
ferent sizes of the aggregate and for the proper temperature of the 
mix. To insure the proper proportions he should test the measuring 
scales at short intervals and sift a sample of the dry mineral aggre- 
gate at least once a day. His most important duty is to prevent 
charring of the binder. It is not necessary to take the tempera- 
ture of each batch as with a little experience any objectionable con- 
dition can be detected by the character of the smoke; a dense white 
smoke given off when mixing indicates a dangerously high tempera- 
ture. When this is observed the batch should be tested with a 
thermometer and immediately rejected if over the specified tempera- 
ture limit. (See specifications.) The temperature of the mineral 
aggregate will fluctuate very rapidly in the small plants generally 
used for road work and care should be observed in picking the plant 
inspector that he is a very conscientious man. He should also 
furnish the driver of each load of asphalt with a ticket giving the 
weight of the mix on that load. 

The Inspector on the road records the temperature of the mix 
as received, the weight of each load and indicates to the spreaders 
the number of sq. yd. it should cover. 

(The surface mix weights approx. 100 lb. per sq. yd. per inch of 
consolidated depth.) 



678 



NOTES ON CONSTRUCTION 



He also should take a sample of the mix as delivered once a day 
and ship to the laboratory for check analysis. 

The following sketches show a sample of a plant inspector's and 
road inspector's record book. 

Sept. 29, 1914. Plant Record 



Load Record 



Load 



I 
2 

3 
4 
5 
etc. 



Time 



7-30 
7.45 
7.55 
8.15 
8.25 
8.45 



Temperature 
of Mix. 



320" 

310 

300 

300 

290 

310 



Weight of 
Load 



5000 
5000 
6000 
6000 
5000 
5000 



lbs. 



Bitumen Record 



Time 



7.00 

8.00 

9.00 

10.00 

11.00 

12.00 



Temperature 



310" 
345 
340 
310 

305 
320 



Test Sample No. 7. Sept. 29, 191 5. Road Record 



Tempera- 
ture of 
Mix. 



Load 
No. 



I 
2 

3 

4 

5 etc. 



Time 



8.00 
8.20 
8.30 

8.45 
9.00 



310° F. 

300 

29s 

295 

280 



Weight as 
per Ticket 



No.Yds. 
Covered 



5000 lbs. 
5000 " 
6000 " 
6000 " 
5000 " 



25 
25 
30 
30 



Location on Road 



Sta. 10 + 30 to 10 + 42 
" 10 + 42 " 10 + 54 
" 10 + 54 " 10 + 69 
" 10 + 69 " 10 + 84 
" 10 + 84 " 10 + q6 



Proportions of Mix. — The proportions of mix should be deter- 
mined by the engineer by screen analysis of the different materials 
that the contractor proposes to use. 

As an example assume that a mixture of cement, fine sand, coarse 
sand and buckwheat stone is proposed and it is desired to determine 
the relative amounts of the different materials to use in order to 
get the correct proportion of sizes specified. 

For all ordinary purposes a size analysis can be safely made using 
the following screens: #200, #80, #40, #10, J^'' and J-^''. 

The materials are thoroughly dried and the percentages expressed 
by weight. 



Fine Sand (Feeder Pit) 

Passing # 200 5 % 

^' # 80 retained on # 200 70 % 

" #40 '' "if So 25% 

Good Quality 
Coarse Sand (Bauerman Pit) 

Passing #200 .' i % 

" # 80 retained on #200 2 % 

" #40 '' " #80 29% 

" #10 " " #40 68% 



TOPEKA MIX 



679 



Buckwheat Stone. (Commercial plant.) 

Passing # 200 i % 

'' # 40 retained #200 2 % 

" # 10 " # 40.. 7% 

H" " #10 60% 

m' " M" 30% 

The proportions can now be varied to produce practically any 
required mix. 



Tabulation Showing Method of ^Determining the Number of Pounds of Each 
Material to be Used in a 100 lb. Batch to Produce a Required^Mix. 


Material 


No. 
lbs. 


Bitu- 
men 


#200 


Ho 


#10 


\ 


\ 


Bitumen 

Cement 

Fine Sand 

Coarse Sand . . 
Buckwheat 

Stone 

Totals 


10 

7 
47 
20 

16 
100 


10 
10 


7 
2.5 

9-5 


44.5 
6.0 

50.5 


14.0 

I.O 

15.0 


9.6 
9.6 


5-4 
5-4 



In this way the effect of varying any of the component parts of 
the mix can be readily seen and determined. 

The total size of the batch is of course varied to suit the capacity 
of the plant. ~ 

The laboratory analysis of the daily sample taken on the road 
furnishes a check on the plant inspector. 

Rollers. — The best results can be obtained by the use of two 
tandem rollers; a light roller not over 5 tons for first compression 
to anneal the surface while hot and a heavier 8 to 10 ton roller 
for final compression and cross-rolling. This is more important 
where the asphalt is laid on a macadam base than when laid on 
concrete. 

BRICK ROADS 

To cover the points of construction of brick roads we can not 
do better than to give "Instructions for Inspectors," by William 
C. Perkins, Resident Engineer, New York State Department 
of Highways. Mr. Perkins is well qualified to judge of this class 
of work. 

Grading. — "Read your specifications carefully and follow 
them in every particular. 

"Do not let the contractor dig beyond the back slopes of your 
ditches. Your ditches should be straight, no sudden jogs; back 
slopes all true; no rubbish deposited back of the ditches, and be 
sure that your ditches drain. 



68o NOTES ON CONSTRUCTION 

I 

"Follow your cross-sections as closely as possible. Try to ^ 
aid the contractor to take care of his dirt so that when the road ) 
is cleaned up there will not be a great amount of material to be 
moved. 

''Never make a shovel fill over 6 inches without rolling it. 

''In making a heavy fill with dump wagons begin to dump 
at the end toward your dirt supply. Have each pile of dump 
dirt spread thin and draw the next load over this, which will 
help to pack it. All should then be thoroughly rolled. 

"Examine your sub-grade carefully, particularly when the 
roller is going over same, and if it waves or shakes under the 
roller, sub-base or drain should be put in, or the material dug out 
and the proper material put in. Do not make a fill with any old 
material found along the road. Use judgment in this particular. 

"Clearing and grubbing does not mean the grubbing of sod. 
It means the cutting down of bushes, trees, etc. Remember 
that the life of your pavement is the condition of your sub-grade. 
The same should be inspected by the engineer in charge before 
any stone or concrete is placed. 

"Grade the full width of your macadam or concrete. Never 
deposit stone in the rut. Keep your sub-base free of ruts. 

"If your roller is not working on other work roll your sub-grade. 
You can not roll it too much. 

"Do not shift center line or grades until you have reported the 
necessity for it to headquarters, and if absolutely necessary give 
an estimate of the increase or decrease in quantities that such 
change would make. 

"Shoulders should not contain sod within i8 inches of the 
macadam. 

"Back slope all ditches i on i J^. Be careful that your gutters 
are not too deep. Deep gutters where not necessary for drainage 
purposes make a road dangerous and must be avoided. 

"In trimming shoulders and ditches a good inspector should 
be put on the work, and instructed to see that the contractor 
sets proper stakes. A stake should be set out from the edge of the 
macadam, and also one in the ditch, and should be set at least 
every loo feet. The bottom of the ditch must be a true grade, 
no depression, and the ditch alignment must be good. These 
stakes can be easily set with a 1 6-foot level board. When approach- 
ing a culvert it is not necessary to deepen the gutters until you 
reach within 50 feet of same, when a straight grade can then be 
run to the invert. 

*'In all cases be sure your ditches will carry water, and, I re- 
peat, be sure they are not ragged and the back slopes are well 
graded. In trimming shoulders be sure there is no ridge next to 
the macadam. 

*'In setting your stakes for the shoulder work use the ordinates 
and distances shown on the standard section. 

"Subgrade. Be sure that your subgrade has been properly 
graded so as to obtain 5 inches of concrete. If the contractor 
builds the curb first, a templet should be run over the curbing 
and test made to be sure that you have the correct depth. 



BRICK PAVEMENTS 68i 

"Concrete Edging. — Stakes for concrete edging can be placed 
every 50 feet for line and grading, with the exception at change 
of grades and curves, where they should be placed every 25 feet. 

*'Be sure that your forms are properly set as to line and grade. 

'*With stakes 50 feet apart be careful that there is no sag in the 
line when the forms are set. 

*'If edging is set first it is better that the concrete be hand- 
mixed, as a machine turns out too large a quantity and can not be. 
placed in the proper time. 

"See that your forms are wet before the concrete is placed, 
and if steel forms are used they should be oiled. 

"Have a careful inspector on the mixing of the concrete for 
the edging and watch the mix. 

"Keep track of the number of bags of cement used and see 
that the proper proportion of cement to the lineal foot of edging 
is obtained. 

"Edging 6'' X loj^'' will use i bag in 12.95 feet 

"Edging 8'' X io3^" will use i bag in 9.73 feet 

"Mixture, 1-2^^-5. 

"Make the mixture rather wet and spade the same thoroughly, 
using a hoe straightened and punched full of holes, or some similar 
instrument, so as to get a good face next to the forms. 

"If you find you can not get a good top surface keep the edging 
a couple of inches low, and about every third batch mix a batch 
of fine material and bring the edging up to the proper height, 
thoroughly working the same in. 

"Do not get a plaster effect, but get a good top surface. 

"Round both edges with a rounding tool, making the inner 
^edge of a smaller radius than the outer edge. 

"When the forms are taken down all spots which are honey- 
combed, or rough, should be floated at once with cement. A 
rough edging should not be left on any road. 

"Have the contractor back up the edging as soon as possible. 

"In warm weather the edging should be kept wet for, at least, 
twenty-four hours. Have the contractor use care in delivering 
materials after the edging is built so that the edges of same are 
not broken by wagons, etc. 

"A good edging is often ruined by carelessness on the part of 
the contractor. 

"Concrete Base. — Before laying base be sure that the founda- 
tion is in proper shape and of a proper depth. 

"Lay the concrete rather wet and drag same with a heavy templet. 
Have men back of the templet with tamping irons or blocks, tamp- 
ing the concrete. This is important if you wish to get a smooth 
surface, and you must insist that the concrete be well tamped. 

"Be sure that you keep track of your bags, and, also, that the 
machine is working properly. 

"For a i6-ft. road nJi bags will lay 10 ft. concrete base, mix- 
ture 1-2)^-5. 

"After the day's run examine your base, and if there are any 
spots which are porous, grout same and check up your bags at 
the end of each day. 



682 NOTES ON CONSTRUCTION 

"If the weather is very hot the base should be kept wet for 
twenty-four hours. 

*'Sand Cushion. — Sand for this cushion should be absolutely 
free of stones, and you must insist that the contractor screen same, 
if stones are in the sand delivered. No excuses will be taken for 
stones or pebbles in the cushion. Spread sand for a sufficient 
depth, then roll same with a small roller; then drag, roll again, 
and then drag with templet. 

"This should be sufficient to give a firm cushion. 

"The smoothness of the pavement depends on the proper 
form of the cushion. 

"Cement Sand Cushion. — Use same order of manipulation as for 
sand cushion except that after culling and rolling the brick the 
pavement must be sprinkled thoroughly to wet the cushion and 
set it up before grouting. 

"Brick. — Great care must be used in obtaining proper brick 
surface. 

"Be sure that your strips on the side expansion joints are in 
when the contractor starts to lay brick. 

"Allow no pinning in at the ends under 2^^ inches. 

"Be sure that the expansion joint is not ragged. It must be 
uniform in width, otherwise you will have transverse cracks. 

"All bricks should be laid with lugs in the same direction. 
This is a point that the bricklayers very often do not do. The 
bricks should be laid by experienced bricklayers, not by amateurs. 

"After the brick are laid the contractor will start culling. Then 
you and your inspectors should carefully go over them, marking 
all soft^ bricks to be taken out and rejected; all kilnmarked bricks 
to be turned over, and if not satisfactory to be taken out and used 
for pinning in; all overburned bricks, ^ which are burned to a cinder 
to be rejected. All underburned bricks, which, in your opinion, 
will not make a satisfactory pavement, to be rejected. All bronzed 
bricks (which have the appearance of overburned brick but this 
on one side only) to be turned over, and if satisfactory allowed to 
remain in the pavement. 

"Be sure that you have culled all of the bricks before the pave- 
ment is rolled, for after the pavement is rolled if much culling is 
done you are liable to have a rough pavement. After the pave- 
ment is rolled go over same and mark all broken and spalled 
bricks, to be taken out or turned over. 

"Be careful of all high and low bricks in the pavement, for same 
will wear badly when the road is finished. 

"Be sure that your bricks are laid at right angles to the curb 
and are not wavy as to line. 

"In no case allow any 'Dutchman'^ in your pavement except 
on curves where absolutely necessary. 

iSoft brick are found by sprinkling the pavement lightly; the soft or 
under-burned brick will absorb the moisture, rapidly becoming dull, while 
the good brick still glisten with the water. 

2 Over-burned brick are known by their color, which is much darker than 
the average. 

3 "Dutchman." Brick chipped to wedge shape to fill in between radial 
courses on curves. - 



CULVERTS 683 

"Grouting. — The grouting of the pavement is its life, and the 
greatest care must be used. Insist that all grout be placed on the 
pavement by the use of scoops from a box with unequal legs, or 
better still it should be mixed in a machine g^out mixer with a 
spout delivery. 

" The grout should be mixed in small quantities and of the exact 
proportions. The sand should be sharp, not too coarse nor too 
fine. Care should be taken in using lake sand, as same is probably 
not sharp and too heavy for the grout. As soon as the grout 
reaches the pavement it should, at once, be pushed into the joints 
by means of brooms or squeegees. 

'*It is best to use brooms on the first grouting and a squeegee 
on the second and third groutings. 

" Be sure that the joints are well filled in the first grouting, and 
do not let the grout escape over the edging and be lost. 

"Follow closely with the second grouting, otherwise the two 
groutings will not unite. 

**Be careful that the second grouting does not overlap the first. 
After the second grouting examine the pavement carefully and, if 
necessary, put on a third grout to get flush joints. 

"The pavement should be completely covered with grout and 
all joints should be well filled before you pass on same. 

"Allow enough time for the grout to obtain initial set, and cover 
pavement with a layer of sand to protect same from the weather; 
and pavement should be kept wet for, at least, twenty-four hours. 

"In no case permit traffic on the pavement under ten days; 
longer, if possible. 

** Expansion Joints. — Be careful in removing the expansion joint 
boards that you do not disturb the pinning-in bricks and break 
the bond. We found it advisable to use two wedge-shaped boards 
to make the expansion joints and loosen up the back one as soon 
as grouting was started. 

"In pouring the asphalt filler be sure that the joints are abso- 
lutely clean the full depth. This is very important, or, other- 
wise, you will have cracks in the pavement. The joints are to 
be flushed with asphalt." 

Author's Note: These instructions were written in 191 2. 
Premolded asphalt joints are practically universally used today 
and overcome the dangers mentioned above. 

CULVERTS 

Culverts are usually constructed before the road is graded. 
They should be completed well in advance of the macadam, 
because even though the back-fill is carefully tamped there is 
bound to be some additional settlement under traffic action, and 
if the macadam is laid over a fresh back-fill depressions are sure 
to develop which, if not repaired, make " thank-you-marms " 
in the road. 

Cast-iron Pipe. — Trenches for pipe are dug the required depth, 
making the bottom wide enough to allow the joints to be properly 



684 



NOTES ON CONSTRUCTION 



calked. This requires a trench i8" to 24" wider than the pipe 
diameter, i.e., for a 12" pipe the trench is 30" to 36". Bell holes 
are dug as shown in Fig. 144, so that the pipe will have a uniform 
bearing its entire length. At no point should it rest directly 
on boulders or ledge rocks. If the foundation is soft the pipe should 
be laid on a concrete base. For ordinary soils the only precaution 
the inspector need take is to prevent backfill under the pipe. 



Fig. 144. 

Unless the foreman is alert the trench is often excavated too 
much in some places, which are then back-filled. This is bad 
practice except where boulders are encountered which must be 
removed and the cavities back-filled with good material. 

Pipe. — The pipe is inspected for flaws; it is then placed in the 
trench with the bell end upstream. At each joint the spigot 



Fig. 145. — Steel caulking tool. 

end is placed in the bell and forced against the shoulder, making a 
tight joint. The pipe is then lined correctly and a gasket of 
jute or oakum driven into the joint with an iron calking tool 
having a 2" to 3" offset, as shown in Fig. 145. The balance of the 
joint is then filled with a i to i cement mortar. 

The trench is then back-filled, care being taken not to throw 
the pipe out of line: the back-fill must be well tamped in layers 




Fig. 146. 

not exceeding 6'', using heavy paver's rammers. A good working 
rule is to use two of the best men on the job tamping and the 
laziest man on the force throwing dirt to them. 

Head- Walls for Culverts.— The face of the head-wall should 
extend beyond the end of the pipe, as it is difficult to get a good- 
looking connection if it is flush with the end. 

Figure 146 shows a convenient plug form for this extension. This 
plug is set into the end of the pipe and can be readily removed; 
the resulting head-wall being pleasing in appearance. The head- 
wall form can, also, be readily skewed (set at an angle with the 
pipe) if required. 



CULVERTS 68s 

CONCRETE CULVERTS 

Excavation. — The trench is dug to the required depth; if the 
material will stand vertically no back forms are necessary, and 
the width of the trench is made the width of the out to out di- 
mensions of the culverts. If back forms are needed the trench 
is usually made 2 feet wider. If running water is encountered 
which can not be temporarily dammed, or diverted, the trench is 
made wide enough to flume the stream through on one side of the 
back forms for small culverts, or between the abutments for 
larger span structures. 

Back-fill. — The back-fill is made as for cast-iron pipe except 
that it should not be deposited on the fresh top of a culvert within 
twenty-four hours of laying the concrete. 

Forms. — Forms should be true to shape and constructed of 
planed tongue and groove or carefully sized lumber, for the exposed 
surfaces. Face form lumber should never be less than % in. thick 
and should be well ribbed. They should be water-tight, as other- 
wise the fine material will run out of the face of the concrete and 
leave a rough *' pop-corn" surface. They must be well braced to 
' prevent bulging. Triangular or feather-edged grooved moldings 
are placed in the angles of the forms to shape them satisfactorily. 

Removal of Forms. — The length of time that the forms should 
remain in place is a matter of judgment; it depends upon the 
cement and weather conditions. 

The author's practice is as follows: 

Head-walls or parapet forms are removed within thirty-six 
hours in dry weather or within forty-eight hours in damp, cold 
weather, in order to rub down the surfaces. 

Low side-wall forms for spans of 2' to 3', where the deck is 
constructed later, may be removed in 36 to 48 hours. 

Tnmk forms for small culverts 2' to 3' span may be removed 
in from 3 to 7 days. 

Trunk forms for medium culverts up to 10' span 7 to 14 days. 

Deck forms for spans above 10' may be removed in from 14 
to 28 days. 

Any unusual load, such as a roller, should not be allowed over 
a new culvert of even a small span in less than seven days, unless 
precautions are taken to distribute the pressure by planking the 
back-fill, or otherwise, and on the larger structures a time limit 
of three to four weeks is advisable. 
Amount of Cement, Sand, and Stone required. 

Table 62, page 623 gives these amounts for one yard of concrete. 

The following table gives the amount of stone, sand, and cement 
required for culverts similar to Plate 15, assuming that no embedded 
boulders are used in the sides and bottom. If boulders are used see 
footnote, Table 62. 

MIXING AND PLACING CONCRETE 

The strength of the concrete depends largely upon the thorough- 
ness of the mixing and the water content. 



686 NOTES ON CONSTRUCTION 

The author's practice has been as follows: 

Hand-Mixing. Cement and Sand. 

3 turns dry ... .3d class concrete (foundations and side walls) 

4 " " .... 2d ^' " (decks and parapets) 

Add water and mix mortar. 

Drench stone and turn stone and mortar. 

3 times for 3d class concrete 

4 " " 2d " " * 



Deposit in forms by dropping. Do not cast, as this separates 
the coarse and fine material. Use enough water to give a mixture 
that quakes like liver under the rammer (about 6 gals, per sack 
of cement) . 

Deposit in layers not over 6" deep and ram each layer thor- 
oughly; spade the concrete thoroughly, and work an excess of 
the fine stuff to the face of the forms by prying the larger frag- 
ments back from the form with a narrow spade or broad-tined 
fork. 

Machine Mixing. — Culverts generally contain such a small 
quantity of concrete that machine-mining is rarely used. In case 
a batch-mixer is employed, the inspection is simplified to checking 
the quantities of cement, sand, and stone in each charge. If a 
continuous mixer is used it is well to keep watch of the cement 
hopper, as the cement is liable to run low, feeding only a portion 
of the worm, or a large lump of cement may ride on top of the 
worm and hinder the feed; or the worm may become coated with 
damp cement which reduces the capacity. If the inspector 
watches the cement hopper the contractor will tend to the sand 
and stone hoppers. 

^ Finishing Concrete. — If a smooth, marble-like surface is de- 
sired it can be obtained by rubbing down the surface before it 
has fully set with a cement sand brick moistened with water. If 
a rough sandpaper-like finish is wanted it can be secured by rubbing 
with a wooden float moistened with water. This finish is not 
as apt to hair-check as the smooth finish. 

Freshly laid concrete should be protected from a hot sun by 
covering it with canvas, or blankets, and wetting it down fre- 
quently for four or five days. No plastering of surfaces should 
be allowed after the cement has set. If, however, it has been 
badly hair-checked from heat the defect can usually be remedied 
by rubbing with a carborundum brick. Freshly laid concrete 
must be protected from frost. A satisfactory method is to cover 
with canvas and a thick layer of manure or straw. If the concrete 
has been frost-pitted, on the surface only, bush hammering will 
give a rough stone finish, pleasing in appearance. No culvert work 
should be allowed in continued cold weather, as it is diflScult to 
get a good finish and in road work there is no necessity of doing 
this work in the winter. Concrete inspection must be continuous. 



CULVERTS 687 



CONCLUSION 

For obvious reasons the inspection of construction is generally 
the weak point in Municipal and State Engineering undertakings. 
It is often due to the employment of inferior inspectors, and fre- 
quently to the impossibility of even good inspectors controlling 
certain contractors. The work is rarely bad, but it will not be as 
strong nor as lasting as a first-class job, and if such conditions are 
foreseen, and can not be avoided, it is, perhaps, best to design the 
work stronger than would otherwise be required, as this seems to be 
the only practical method of meeting a recognized evil. 



p 



p 



688 NOTES ON CONSTRUCTION 

Table 67. — Concrete Culverts 







I. 


5' high X 2.0' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Paving 
Square 
Yards 


Ex. Met. 

Square 

Feet 


Cement 
Barrels 


Sand 
Cubic 
Yards 


Crushed 
Stone 
Cubic 








Second 


Third 










Yards 


20 


2.2 


5.6 


6.4 


80 


8.4 


3.6 


7.2 


21 


2.2 


5.8 


6.4 


84 


8.6 


3.7 


7.4 


22 


2.3 


6.1 


6.4 


88 


9.0 


3.9 


7.8 


23 


2.4 


6.3 


6.4 


92 


9-3 


4.1 


8.1 


24 


2.5 


6.5 


6.4 


96 


9.7 


4.2 


^^Z 


25 


2.5 


6.7 


6.4 


100 


9.9 


4.3 


8.5 


26 


2.6 


6.9 


6.4 


104 


10.2 


4.4 


8.8 


27 


2.7 


7.2 


6.4 


108 


10.6 


4.6 


9.2 


28 


2.8 


7-4 


6.4 


112 


10.9 


4.8 


9-5 


29 


2.8 


7.6 


6.4 


116 


II. I 


4.9 


9.6 


30 


2.9 


7.8 


6.4 


120 


11.5 


5.0 


9.9 


31 


3.0 


8.1 


6.4 


124 


11.9 


5-2 


10.3 


32 


3.1 


8.3 


6.4 


128 


12.2 


5.3 


10.6 


33 


3-1 


8.5 


6.4 


132 


12.4 


5.4 


10.8 


34 


3.2 


Z,7 


6.4 


136 


12.7 


5.6 


II.O 


35 


3-3 


8.9 


6.4 


140 


I3-I 


5.7 


11.3 


36 


3-4 


9.2 


6.4 


144 


13.5 


5.9 


11.7 


Z1 


3.4 


9.4 


6.4 


148 


13-7 


6.0 


11.9 


38 


3.5 


9.6 


6.4 


152 


14.0 


6.1 


12. 1 


39 


3.6 


9.8 


6.4 


156 


14.5 


6.3 


12.4 


40 


3.6 


lO.I 


6.4 


160 


14.8 


6.4 


12.7 


41 


3.7 


10.3 


6.4 


164 


I5-I 


6.5 


13.0 


42 


3.8 


lo.s 


6.4 


168 


iS-4 


6.7 


13.3 


43 


3.9 


10.7 


6.4 


172 


15-7 


6.8 


^Z'S 


44 


3-9 


10.9 


6.4 


176 


15-9 


6.9 


13.7 


45 


4.0 


1 1.2 


6.4 


180 


16.4 


7.1 


14.1 


46 


4.1 


11.4 


6.4 


184 


16.7 


7.2 


14.4 


47 


4.2 


11.6 


6.4 


188 


17.0 


7.4 


14.7 


48 


4.2 


11.8 


6.4 


192 


17.2 


7.5 


14.8 


49 


4.3 


12. 1 


6.4 


196 


17.6 


7.7 


15-2 


50 


4.4 


12.3 


6.4 


200 


18.0 


7.8 


15-5 



CULVERTS 689 

Table 67. — Concrete Culverts. — Continued 









2' high 


X 2' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 

Metal 

Square 

Feet 


Paving 
Square 
Yards 


Portland 
Cement 
Barrels 


Sand 

Cubic 

Yards 


Crushed 
Stone 
Cubic 
Yards 


Second 


Third 


20 


2.4 


7.1 


80 


9.8 


lO.I 


4.4 


8.8 


21 


2.4 


7.3 


84 


9.8 


10.4 


4.5 


9.0 


22 


2.5 


74 


88 


9.8 


10.8 


4.7 


9-4 


23 


2.6 


7.9 


92 


9.8 


II. 2 


4.9 


9.7 


24 


2.7 


8.1 


96 


9.8 


II-5 


5.0 


lO.O 


25 


2.7 


8.4 


100 


9.8 


II.8 


5-2 


10.3 


26 


2.8 


8.6 


104 


9.8 


12.2 


5.3 


10.6 


27 


2.9 


8.9 


108 


9.8 


12.6 


5.5 


10.9 


28 


3.0 


9.2 


112 


9.8 


13.0 


5-7 


II-3 


.29 


3-0 


9.4 


116 


9.8 


13.2 


5.8 


11.5 


30 


3.1 


9.7 


120 


9.8 


13.6 


6.0 


11.9 


31 


3.2 


9.9 


124 


9.8 


14.0 


6.1 


12. 1 


32 


3.3 


10.2 


128 


9.8 


14.4 


6.3 


12.5 


33 


3.3 


10.5 


132 


9.8 


14.7 


6.4 


12.8 


34 


3.4 


10.7 


136 


9.8 


15.0 


6.6 


I3-0 


35 


3.5 


II.O 


140 


9.8 


15.4 


6.8 


13.4 


36 


3.6 


II. 2 


144 


9.8 


15.8 


6.9 


13-7 


37 


3.6 


11.5 


148 


9.8 


16.1 


7.1 


14.0 


38 


3.7 


11.8 


152 


9.8 


16.5 


7.2 


14.4 


39 


3.8 


12.0 


X56 


9.8 


16.8 


7.4 


14.7 


40 


3-9 


12.3 


160 


9.8 


17.3 


7.6 


15.0 


41 


3-9 


12.5 


164 


9.8 


17.5 


7.7 


• 15.2 


42 


4.0 


12.8 


168 


9.8 


17.9- 


7.9 


15.6 


43 


4.1 


13.1 


172 


9.8 


18.3 


8.0 


16.0 


44 


4.2 


13.3 


176 


9.8 


•18.6 


8.2 


16.2 


45 


4.2 


13.6 


180 


9.8 


18.9 


8.3 


16.5 


46 


4.3 


13.9 


184 


9.8 


19.4 


8.5 


16.9 


47 


4.4 


14.1 


188 


9.8 


19.7 


8.6 


17.2 


48 


4.4 


14.4 


192 


9.8 


20.0 


8.8 


17.4 


49 


4.5 


14.6 


196 


9.8 


20.4 


8.9 


17.7 


50 


4.6 


14.9 


200 


9.8 


20.8 


9.1 


18.1 



690 NOTES ON CONSTRUCTION 

Table 67. — Concrete Culverts. — Continued 









2' high 


X 3' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expended 
Metal 


Steel 
Pounds 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 






Square 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


2.3 


7.6 


100 


78 


lo.s 


4.6 


9.2 


21 


2.4 


7.9 


105 


81 


II.O 


4.8 


9.6 


22 


2.5 


8.2 


no 


85 


IM 


5-0 


9.9 


23 


2.6 


8.5 


IIS 


88 


II.8 


5-2 


10.3 


24 


2.6 


8.8 


120 


91 


12. 1 


5.3 


10.6 


25 


2.7 


9.1 


125 


95 


12.5 


5-5 


10.9 


26 


2.8 


9.4 


130 


98 


13.0 


5.7 


II.3 


27 


2.9 


9.7 


135 


lOI 


13.4 


5.9 


II.7 


28 


3-0 


9.9 


140 


105 


13-7 


6.0 


12.0 


29 


3.1 


10.2 


145 


108 


14.1 


6.2 


12.3 


30 


3.2 


10.5 


150 


112 


14.6 


6.4 


12.7 


31 


3.3 


10.8 


155 


115 


15-0 


6.6 


I3-I 


32 


3.4 


II. I 


160 


118 


154 


6.8 


13-4 


33 


3.5 


11.4 


165 


122 


15.9 


7.0 


13.8 


34 


3.6 


II. 7 


170 


125 


16.3 


7.2 


14.2 


35 


3-7 


12.0 


175 


128 


16.7 


7.3 


14.6 


36 


2>'^ 


12.2 


180 


132 


17.0 


7.5 


14.8 


37 


3.9 


12.5 


185 


135 


17-5 


1-1 


15.2 


38 


3.9 


12.8 


190 


139 


17.8 


7.8 


15.5 


39 


4.0 


I3-I 


195 


142 


18.2 


8.0 


15.9 


40 


4.1 


13.4 


200 


145 


18.6 


8.2 


16.2 


41 


4.2 


^Z'1 


205 


149 


19.0 


8.4 


16.6 


42 


4.3 


14.0 


210 


152 


19-5 


8.6 


17.0 


43 


4.4 


14.3 


215 


156 


19.9 


8.7 


17-3 


44 


4-5 


14-5 


220 


159 


20.2 


8.9 


17.6 


45 


4.6 ' 


14.8 


225 


162 


20.7 


9.1 


18.0 


46 


4.7 


15.1 


230 


166 


21. 1 


9.2 


18.4 


47 


4.8 


15.4 


235 


169 


21.5 


9-4 


18.7 


48 


4.9 


15.7 


240 


172 


21.9 


9.6 


19.1 


49 


5.0 


16.0 


245 


176 


22.4 


9.8 


19.S 


SO 


5.1 


16.3 


250 


179 


22.8 


lO.O 


19.8 



CULVERTS 
Table 67. — Concrete Culverts. — Continued 



691 







2' high 


X 4' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 
Metal 
Square 


Steel 
Pounds 


Portland 
Cement 
Barrels 


Sand 
Cubic 
Yards 


Crushed 
,Stone 
Cubic 








Second 


Third 


Feet 








Yards 


20 


2.7 


8.4 


120 


78 


II.8 


5-2 


10.3 


21 


2.8 


8.7 


126 


81 


12.3 


5-3 


10.7 


22 


2.9 


9.0 


132 


85 


12.7 


5.6 


II.O 


23 


3.1 


9.3 


138 


88 


13.2 


5.8 


11.5 


24 


3.2 


9.7 


144 


91 


13.8 


6.0 


12.0 


25 


3.3 


lO.O 


150 


95 


14.2 


6.2 


12.3 


26 


3-4 


10.3 


156 


98 


14.6 


6.4 


12.7 


27 


3.5 


10.6 


162 


lOI 


15.0 


6.6 


13.1 


28 


3.6 


10.9 


168 


105 


15.5 


6.8 


13.4 


29 


S'7 


II. 2 


174 


108 


15-9 


6.9 


13.8 


30 


3.8 


II-5 


180 


112 


16.3 


7.1 


14.2 


31 


3-9 


11.9 


186 


115 


16.8 


7.4 


14.6 


32 


4.0 


12.2 


192 


118 


17.3 


7.6 


15.0 


33 


4.2 


12.5 


198 


122 


17.8 


7.8 


15.5 


34 


4.3 


12.8 


204 


125 


18.3 


8.0 


15.9 


35 


4.4 


I3-I 


210 


-128 


18.7 


8.2 


16.2 


36 


4.5 


13-4 


216 


132 


19.1 


8.4 


16.6 


37 


4.6 


13.8 


222 


135 


19.6 


8.6 


17.1 


38 


4.7 


14.1 


228 


139 


20.1 


8.7 


17.4 


39 


4.8. 


14.4 


234 


142 


20.5 


9.0 


17.8 


40 


4.9 


14.7 


240 


145 ' 


20.9 


9.1 


18.2 


41 


5.0 


15.0 


246 


149 


21.4 


9.4 


18.6 


42 


5.2 


^5-3 


252 


152 


21.9 


9.6 


19.1 


43 


5.3 


15.6 


258 


156 


22.3 


9.8 


19.4 


44 


5.4 


16.0 


264 


159 


22.9 


lO.O 


19.9 


45 


5.5 


16.3 


270 


162 


23.3 


10.2 


20.2 


46 


5.6 


16.6 


276 


166 


23.7 


10.4 


20.6 


47 


5-7 


16.9 


282 


169 


24.1 


10.6 


21.0 


48 


5.8 


17.2 


288 


172 


24.6 


10.8 


21.3 


49 

0^ 


5.9 


17.5 


294 


176 


25.0 


10.9 


.21.7 


50 


6.0 


17.8 


300 


179 


25-4 


II. I 


22.1 



692 NOTES ON CONSTRUCTION 

Table 67. — Colcrete Culverts. — Continued 



3' high X 3' wide 


Length 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 
Pounds 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 


Feet* 






Square 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


2.3 


10.4 


100 


82 


134 


5»9 


II.8 


21 


2.4 


10.8 


105 


85 


13.9 


6.2 


12.3 


22 


2.5 


II. 2 


IIO 


88 


14.4 


6.4 


12.7 


23 


2.6 


II.5 


115 


92 


14.9 


6.6 


13.1 


24 


2.6 


II.9 


120 


95 


15.3 


6.8 


13.5 


25 


2.7 


12.2 


125 


99 


15.7 


7.0 


13.8 


26 


2.8 


12.6 


130 


102 


16.2 


7.2 


14.3 


27 


2.9 


13.0 


135 


105 


16.8 


7.4 


14.8 


28 


3.0 


13-3 


140 


109 


17.2 


7.6 


15.1 


29 


3.1 


13.7 


145 


112 


17.7 


7.9 


15.6 


30 


3.2 


14.0 


150 


116 


18.2 


8.1 


16.0 


31 


3-3 


14.4 


155 


119 


18.7 


8.3 


16.4 


32 


3-4 


14.8 


160 


122 


19.2 


' 8.5 


16.9 


33 


3.5 


I5.I 


165 


126 


19.6 


8.7 


17.3 


34 


3.6 


15.5 


- 170 


129 


20.2 


8.9 


17.6 


35 


3-7 


15.8 


175 


133 


20.6 


9.1 


18.1 


36 


3.8 


16.2 


180 


136 


21. 1 


9.4 


18.6 


37 


3.9 


16.6 


185 


139 


21.6 


9.6 


19.0 


38 


3-9 


16.9 


190 


143 


22.0 


9.7 


19-3 


39 


4.0 


17.3 


195 


146 


22.5 


lO.O 


19.8 


40 


4.1 


17.6 


*200 


150 


22.9 


10.2 


20.1 


41 


4.2 


18.0 


205 


153 


23.4 


10.4 . 


20.6 


42 


4.3 


18.4 


210 


156 


24.0 


10.6 


21. 1 


43 


4.4 


18.7 


215 


160 


24.4 


10.8 


21.4 


44 


4.5 


I9.I 


220 


163 


24.9 


II.O 


21.9 


45 


4.6 


19.4 


225 


167 


25.4 


II. 2 


22.3 


46 


4.7 


19.8 


230 


170 


25-9 


II.4 


22.7 


47 


4.8 


20.2 


235 


173 


26.4 


II. 7 


23.2 


48 


4.9 


20.5 


240 


177 


26.8 


II.9 


23.6 


49 


5.0 


20.9 


245 


180 


27.4 


12. 1 


24.0 


50 


5.1 


21.2 


250 


184 


27.8 


12.3 


24.4 



CULVERTS 693 

Table 67. — Concrete Culverts. — Continued 







3' high 


X 4' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 
Metal 
Square 


Steel 
Pounds 


Portland 
Cement 
Barrels 


Sand 
Cubic 
Yards 


Crushed 
Stone 
Cubic 


, 






Second 


Third 


Feet 








Yards 


20 


2.7 


II.3 


120 


82 


14.8 


6.5 


13.0 


21 


2.8 


II.7 


126 


85 


15-3 


6.8 


13.5 


22 


2.9 


12. 1 


132 


88 


15.8 


7.0 


13.9 


23 


3.1 


I2.S 


138 


92 


16.S 


7.3 


14.5 


24 


3.2 


12.9 


144 


95 


17.0 


7.5 


14.9 


25 


Z'S 


13.2 


150 


99 


17.4 


7.7 


15.3 


26 


3.4 


13.6 


156 


102 


18.0 


7.9 


15.8 


27 


3.5 


14.0 


162 


105 


18.5 


8.2 


16.3 


28 


3.6 


14.4 


168 


109 


19.0 


8.4 


16.7 


29 


3-7 


14.8 


174 


112 


19.6 


8.7 


17.2 


30 


3.8 


15.2 


180 


116 


20.1 


8.9 


17.6 


31 


3.9 


15.6 


186 


119 


20.6 


9.1 


18.I 


32 


4.0 


16.0 


192 


122 


21. 1 


9.4 


18.6 


33 


4.2 


16.4 


198 


126 


21.8 


9.6 


19.I 


34 


4.3 


16.8 


204 


129 


22.3 


9.8 


19.6 


35 


4.4 


I7.I 


210 


- 133 


22.8 


lO.I 


20.0 


36 


4.5 


17.5 


216 


136 


23-3 


10.3 


20.4 


37 


4.6 


17.9 


222 


139 


23.8 


10.5 


20.9 


38 


4.7 


18.3 


228 


143 


24.3 


10.8 


21.3 


39 


4.8 


18.7 


234 


146 


24.9 


II.O 


21.8 


40 


4.9 


I9.I 


240 


150 


25.4 


II. 2 


22.3 


41 


S-o 


19-5 


246 


153 


25.9 


II.4 


22.7 


42 


5-1 


19.9 


252 


156 


26.5 


II. 7 


23.2 


43 


5.3 


20.3 


258 


160 


27.1 


12.0 


23.7 


44 


5.4 


20.7 


264 


163 


27.7 


12.2 


24.2 


45 


5.5 


21.0 


270 


167 


28.1 


12.4 


24.6 


46 


5.6 


21,4 


276 


170 


28.6 


12.6 


25.0 


47 


5-7 


21.8 


282 


173 


29.1 


12.9 


25-5 


48 


5.8 


22.2 


288 


177 


29.7 


I3-I 


26.0 


49 


5-9 


22.6 


294 


180 


30.2 


13.3 


26.4 


50 


6.0 


23.0 


300 


184 


30.7 


13.6 


26.9 



694 NOTES ON CONSTRUCTION 

Table 67. — Concrete Culverts. — Continued 









4' high X 4' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 
Metal 
Square 


Steel 
Pounds 


Portland 
Cement 
Barrels 


Sand 
Cubic 
Yards 


Crushed 
Stone 
Cubic 








Second 


Third 


Feet 








Yards 


20 


2.7 


14.5 


120 


87 


18.1 


8.1 


15.9 


21 


2.8 


15.0 


126 


90 


18.7 


S.3 


16.5 


22 


2.9 


15-4 


132 


94 


19.2 


8.6 


17.0 


23 


3-1 


15-9 


138 


97 


20.0 


8.9 


17.6 


24 


3.2 


16.4 


144 


100 


20.6 


9.2 


18.2 


25 


3.3 


16.8 


150 


104 


21. 1 


9.4 


18.7 


26 


3.4 


17.3 


156 


107 


21.8 


9.7 


19.2 


27 


3.5 


17.7 


162 


III 


22.3 


9.9 


19.7 


28 


3.6 


18.2 


168 


114 


22.9 


10.2 


20.2 


29 


3.7 


18.7 


174 


117 


23-5 


10.5 


20.8 


30 


3-8 


19.1 


180 


121 


24.1 


10.7 


21.2 


31 


3.9 


19.6 


186 


124 


24.7 


II.O 


21.8 


32 


4.0 


20.1 


192 


128 


25.3 


11.3 


22.4 


33 


4.2 


20.5 


198 


131 


26.0 


11.6 


22.9 


34 


4-3 


21.0 


204 


134 


26.6 


11.9 


23.5 


35 


4.4 


21.4 


210 


138 


27.1 


12. 1 


24.0 


36 


4.5 


21.9 


216 


141 


27.8 


12.4 


24.5 


37 


4.6 


22.4 


222 


145 


28.4 


12.6 


25.1 


38 


4.7 


22.8 


228 


148 


28.9 


12.9 


25.5 


39 


4.8 


23.3 


^34 


151 


29.6 


13.1 


26.1 


40 


4.9 


23.8 


240 


155 


30.2 


13.4 


26.6 


41 


5.0 


24.2 


246 


158 


30.7 


13.7 


27.1 


42 


5.1 


24.7 


252 


162 


314 


14.0 


27.7 


43 


5.3 


25.2 


258 


165 


32.1 


14.3 


28.3 


44 


5.4 


25.6 


264 


168 


32.6 


14.5 


28.8 


45 


5-5 


26.1 


270 


172 


33.3 


14.8 


29-3 


46 


5.6 


26.5 


276 


175 


33.8 


15.0. 


29.8 


47 


5.7 


27.0 


282 


179 


34.4 


15.3 


30-3 


48 


5.8 


27.5 


288 


182 


35-1 


15.6 


30-9 


49 


5.9 


27.9 


294 


185 


35-6 


15.8 


31-4 


50 


6.0 


28.4 


300 


189 


36.2 


16.1 


31-9 



CULVERTS 

Table 67. — Concrete Culverts. — Continued 



69s 









3' high 


X 5' wide 






Length 
Feet 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 
Pounds 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 






Square 


Barrels 


Yards 


Cubic 




Second 


Third 


Feet 








Yards 


20 


4.0 


12.4 


140 


^3 


17.5 


7-7 


15.2 


21 


4.2 


12.8 


147 


86 


18.I 


7.9 


15.7 


22 


4.4 


-^3-3 


154 


90 


18.9 


8.3 


16.4 


23 


4.6 


^3-7 


161 


93 


19-5 


8.6 


17.0 


24 


4.7 


14. 1 


168 


96 


20.1 


8.8 


17.4 


25 


4.9 


14.5 


175 


100 


20.7 


9.1 


18.0 


26 


5-1 


14.9 


182 


103 


21.4 


9-3 


18.5 


27 


5-3 


154 


189 


106 


22.1 


9.6 


19.2 


28 


5.4 


15.8 


196 


no 


22.6 


9.9 


19.7 


. 29 


5.6 


16.2 


203 


113 


23.3 


10.2 


20.2 


30 


5.8 


16.6 


210 


117 


23.9 


10.5 


20.8 


31 


5.9 


17.0 


217 


120 


24-5 


10.7 


21.2 


32 


6.1 


17.4 


224 


123 


25.1 


II.O 


21.8 


33 


6.3 


17.9 


231 


127 


25.9 


II-3 


22.4 


34 


6.5 


18.3 


238 


130 


26.5 


11.6 


23.0 


35 


6.6 


18.7 


245 


- 134 


27.1 


11.8 


V 
23.5 


36 


6.8 


19.1 


252 


^37 


27.7 


12. 1 


24.0 


37 


7.0 


19-5 


259 


140 


28.4 


12.4 


24.6 


38 


7.2 


19.9 


266 


144 


29.0 


12.7 


25.1 


39 


7.3 


20.4 


273 


147 


29.6 


12.9 


25.7 


40 


7-5 


20.8 


280 


150 


30.3 


13.2 


26.2 


41 


7-7 


21.2 


287 


154 


30-9 


13.5 


26.8 


42 


7.8 


21.6 


294 


157 


31.5 


13.7 


27.3 


43 


8.0 


22.0 


301 


161 


32.1 


14.0 


27.8 


44 


8.2 


22.4 


308 


164 


32.8 


14.3 


28.4 


45 


8.4 


22.9 


315 


167 


33-4 


14.6 


29.0 


46 


8.5 


23-3 


322 


171 


34.1 


14.8 


29.5 


47 


8.7 


23.7 


329 


174 


34.7 


15.1 


30.0 


48 


8.9 


24.1 


336 


177 


35.3 


15-3 


30.6 


49 

f 


9.1 


24.5 


343 


181 


36.0 


15.6 


31.2 


50 


9.2 


24.9 


350 


184 


36.5 


15.9 


31.6 



696 NOTES ON CONSTRUCTION 

Table 67. — Concrete Culverts. — Continued 







4' high 


X 5' wide 








Length 
Feet 


Concrete 
Cubic Yards 


Expand ec 

Metal 

Square 

Feet 


Steel 
Pounds 


Portland 
Cement 
Barrels 


Sand 
Cubic 
Yards 


Crushed 
Stone 
Cubic 
Yards 


Second 


Third 


20 


4.0 


15.8 


140 


88 


21.0 


9.2 


18.4 


21 


4.2 


16.3 


147 


92 


21.7 


9.6 


19.0 




22 


4.4 


16.8 


154 


95 


22.5 


9.9 


19.7 




23 


4.6 


17.2 


161 


99 


23.1 


10.2 


20.2 




24 


4.7 


17.7 


168 


102 


23.7 


10.5 


20.8 




25 


4.9 


18.2 


175 


105 


24.5 


10.8 


21.4 




26 


5.1 


18.7 


182 


109 


25.2 


II. I 


22.1 




27 


5.3 


19.2 


189 


112 


26.0 


ii-S 


22.7 




28 


5.4 


19.7 


196 


116 


26.6 


11.7 


23.3 




29 


5.6 


20.2 


203 


119 


27.4 


12. 1 


23.9- 




30 


5.8 


20.7 


210 


122 


28.1 


12.4 


24.6 




31 


5-9 


21.2 


217 


126 


28.8 


12.7 


25-1 




32 


6.1 


21.7 


224 


129 


29-5 


13.0 


25.8 




Z^ 


6.3 


22.1 


231 


133 


30.2 


13.3 


26.3 




34 


6.5 


22.6 


238 


136 


30.9 


13.6 


27.0 




35 


6.6 


23.1 


245 


139 


31.5 


13.9 


27.6 




36 


6.8 


23.6 


252 


143 


32.3 


14.2 


28.2 




2>7 


7.0 


24.1 


259 


146 


33.0 


14.S 


28.8 




38 


7.2 


24.6 


266 


150 


33.8 


14.9 


29.5 




39 


^7.3 


25.1 


273 


153 


34.4 


15.1 


30.1 




40 


7.5 


25.6 


280 


156 


35-2 


15.5 


30.7 




41 


7.7 


26.1 


287 


160 


35-9 


15.8 


31-3 


i 


42 


7.8 


26.6 


294 


163 


36.6 


16.1 


31.9 




43 


8.0 


27.0 


301 


167 


37-2 


16.4 


32.5 




44 


8.2 


27.5 


308 


170 


38.0 


16.7 


33.1 




45 


8.4 


28.0 


315 


173 


38.7 


17.0 


33.8 




46 


8.5 


28.5 


322 


177 


39.3 


T^I'Z 


34.3 




47 


8.7 


29.0 


329 


180 


40.1 


17.6 


ZS'<^ 




48 


8.9 


29-5 


336 


184 


40.9 


18.0 


35.6 




49 


9.1 


30.0 


343 


187 


41.6 


18.3 


36.3 




50 


9.2 


30-5 


350 


190 


42.2 


18.6 


36.8 





CULVERTS 697 

Table 67. — Concrete Culverts. — Continued 



5' high X 5' wide 


Length 


Concrete 
Cubic Yards 


Expanded 
Metal 


Steel 
^Pounds 


Portland 
Cement 


Sand 
Cubic 


Crushed 
Stone 
Cubic 


Feet 






Square 


Barrels 


Yards 




Second 


Third 


Feet 








Yards 


20 


4.0 


19.5 


140 


^l» 


24.7 


II.O 


21.8 


21 


4.2 


20.0 


147 


96* 


25.5 


II-3 


22.5 


22 


4.4 


20.6 


154 


100 


26.3 


11.7 


23.2 


23 


4.6 


21.2 


161 


103 


27.2 


12. 1 


24.2 


24 


4-7 


21.7 


168 


106 


27.8 


12.4 


24.8 


25 


4.9 


22.3 


175 


no 


28.7 


12.7 


25.4 


26 


5-1 


22.9 


182 


113 


29-5 


13.I 


26.2 


27 


5-3 


23.4 


189 


117 


30-3 


13-4 


26.8 


28 


5-4 


24.0 


196 


120 


31.0 


13.8 


27.6 


29 


5.6 


24.6 


203 


123 


31-9 


14.1 


28.2 


30 


5.8 


25.1 


210 


127 


32.6 


14.5 


29.0 


31 


5-9 


25-7 


217 


130 


33-4 


14.8 


29.6 


32 


6.1 


26.2 


224 


134 


34.1 


I5-I 


30.2 


33 


6.3 


26.8 


231 


^37 


35.0 


15.5 


31.0 


34 


6.5 


27.4 


238 


140 


35.8 


15.9 


31.8 


35 


6.6 


27.9 


245 


144 


36.4 


16.2 


32.4 


36 


6.8 


28.S 


252 


147 


37.3 


16.5 


33.0 


37 


7.0 


29.1 


259 


150 


38.2 


16.9 


33-8 


38 


7.2 


29.6 


266 


154 


38.9 


17.2 


34.4 


39 


7.3 


30.2 


273 


157 


39-6 


17.6 


35.1 


40 


7-5 


30.8 


280 


161 


40.5 


17.9 


35-8 


41 


7-7 


31-3 


287 


164 


41.2 


18.3 


36.5 


42 


7.8 


31-9 


294 


167 


42.0 


18.6 


37.2 


43 


8.0 


32.5 


301 


171 


42.8 


19.0 


37.9 


44 


8.2 


33-0 


308 


174 


43-6 


19.3 


38.6 


45 


8.4 


33.6 


315 


178 


44.4 


19.7 


39.3 


46 


8.5 


34.2 


322 


181 


45.2 


20.0 


40.0 


47 


8.7 


34.7 


329 


184 


45.9 


20.3 


40.6 


48 


8.9 


35.2 


336 


188 


46.7 


26.6 


41.2 


49 


9.1 


35-9 


343 


191 


47.6 


21.0 


42.0 


50 


9.2 


36.4 


350 


195 


48.3 


21.4 


42.8 



PART III 

SPECIFICATIONS 

The following clauses quoted from various sources are examples of 
current practice. They are not ideal but serve to show the points to be 
considered. 

A specification should be complete, concise and clear as to the materials, 
manipulation and basis of measurement and payment. In preparing a 
specification it is convenient to have a general outline of points to be covered. 
Such an outline has been prepared by the U. S. Office of Public Roads to 
serve as a uniform basis for specifications for Federal Aid and is reproduced 
below. It is in the author's opinion a very good reminder of necessary 
requirements. 

The usual size of page used for highway specifications is approximately 
83'^" X ii''; this is an unwieldy size for field use; a size of 6" X 9" is 
much handier and is about the smallest dimension feasible on account of 
space required on the proposal bidding blanks. Where much work is being 
done the Specifications proper can be printed in pocket form 4^i"X6^^" 
and the Proposal, Contract and Bond separately on the usual 8j^"Xii" 
size. This makes a convenient combination for both the field men and for 
Office filing of Contract records. 

Repetitions should be avoided which is helped by segregating the require- 
ments for materials in one part of the specification. Blanks to be filled out 
by hand are undesirable and should be reduced to a minimum. Loose leaf 
specifications are poor practice. Printed bidding sheets containing the 
estimated quantities of work reduce possible complications in connection 
with comparing bids. 

No attempt is made in this book to discuss methods of bidding or the legal 
forms of contract as they must conform to local statutes. 



6g8 



OUTLINE 699 



UNITED STATES 
DEPARTMENT OF AGRICULTURE 

OFFICE OF THE SECRETARY 

STANDARDS 

GOVERNING THE FORM AND ARRANGEMENT OF 

SPECIFICATIONS, AND ESTIMATES 
FOR FEDERAL AID PROJECTS 

AS PROVIDED FOR IN THE RULES AND REGULATIONS OF THL 

SECRETARY OF AGRICULTURE FOR CARRYING OUT 

THE FEDERAL AID ROAD ACT 

(EXCEPT SECTION 8 THEREOF) 



ISSUED APRIL 28, 1917 



700 SPECIFICATIONS 



TITLE-PAGE OR COVER FOR SPECIFI- 
CATIONS, ETC. 



(Note. — The name of the State should appear at top of the title-page in 
bold-faced caps.) 



^ 



OUTLINE 701 



NOTICE TO CONTRACTORS 

Time and place of receiving and opening proposals. 

Brief description of proposed work. 

Place where plans and specifications may be examined or secured, and 
from whom information may be obtained. 

Rights reserved to reject any or all proposals. 

Any additional information desired. 

Note. — The above information should be shown in the advertisement for 
proposals, and on the "Notice to contractors," which may be sent out to 
prospective bidders. It may be attached to the proposal if desired, should 
the proposal be a separate form, or may be attached to or bound with the 
specifications, immediately following the title-page, if the specifications, pro- 
posal, and contract are one volume. 



702 SPECIFICATIONS 

SPECIFICATIONS 
Definition of Terms 

Definition of State, State highway department or commission, engineer, 
contractor, etc. 

INSTRUCTIONS TO BIDDERS 

Interpretation of approximate estimate. 

Statement regarding right of engineer to increase or decrease quantities 
shown in proposal. 
Bidders required to examine the plans, specifications, special provisions, 
etc., and also the site of the proposed work. 

Bidders' attention called to necessity of being familiar with Federal, State, 
and local laws affecting the work. 

Explanation of use of, or contents of, proposal form. 
Instructions for filling in proposal form. 
Requirements regarding signatures on proposals. 
Prohibition of alteration, erasures, etc., on proposal forms. 
Bidders' guaranty to accompany proposals. 

Reference to form of guaranty required — Certified check, to whom payable, 
and amount indicated in proposal or percentage of contract required; 
or, proposal bond, form, amount indicated in proposal, and how 
executed. 
Instructions for submitting or delivering proposals. 

Delivery by mail and delivery in person. 
Statement that proposals may or may not be withdrawn. 

In case withdrawal is allowed, the bidder should be obliged to file his written 
request not later than the day previous to the opening of the proposals. 
Opening of proposals. 

Time and place and invitation to bidders to be present. 
Disqualification of bidders. 
No right to submit more than one proposal; collusion; unbalanced pro* 
posals; failure to carry out previous contracts; and lack of experience 
and capital. 
Any additional clauses desired. 

AWARD AND EXECUTION OF CONTRACT 

Right reserved to reject any and all proposals and to waive technicalities. 
Award of contract. 

By whom, place, to whom, and when made. 
Return of proposal guaranty. 

How and when returned. 
Contract bond required. 

Reference to form furnished by State and to the amount shown in proposal 
or percentage of amount of contract required. 
Execution of contract. 

Time and place. 
Failure to execute contract. 

Restrictions relative to subletting or assigning contracts. 
Statement relative to use of patented processes, materials, or methods. 

GENERAL PROVISIONS 

Scope of work to be done. 

General statement relative to performing work and furnishing labor, 
equipment, etc., except as provided in the *' Special provisions," in 
accordance with the plans, specifications, and contract. 

Necessary State and local permits and licenses to be secured by contractor. 

No deviation from plans, specifications, etc., by contractor. 

Interpretation of plans, etc. 



I 



OUTLINE 703 

Figured dimensions to govern. 
Special work. 

Clause calling attention to special provisions for work or special require- 
ments, not covered by the standard specifications, designating in this 
clause whether the special provisions will he found in the specifications, 
or will be attached to or bound with the proposal. 
Alteration of work. 

Clause regarding right of engineer to alter plans or character of work within 
reasonable limits. 
Additional work. 

Provision referring to additional work due to increase of quantities which 
is to be paid for at contract unit prices. 
Extra work or force account. 

Clause pertaining to work for which no price is named in the proposal 
and which is to be paid for at a price to be agreed upon or on a per- 
centage basis, at prices to be agreed upon for labor, rentals, materials, 
etc. It should be specifically shown to which items the percentage 
applies. 
Unauthorized work. 

No payment made therefor. 
Prosecution or progress of the work. 
Limitation of operations. 
Character of v orkmen and equipment. 
Cooperation of contractor required. 

Clause requiring contractor to have copy of plans, specifications, etc., and 
authorized representative to receive and obey orders of engineer on 
the work at all times. 
Laws to be observed. 
Sanitary provisions. 

Observance of rules of boards of health. 
Public convenience and safety. 

Traffic regulations, nonobstruction of sidewalks, fire hydrants, etc., use of 
barricades, danger, warning and detour signs, precautions in the 
use of explosives. 
Preservation and restoration of public utilities, property, trees, monu- 
ments, etc. 

To be preserved and restored and made good if damaged or injured. 
Contractor's responsibility for damage to persons and property. 
Contractor's responsibility for damage to work. 

Contractor's responsibility for sections or portions of roadway opened to 
traffic prior to final approval or acceptance. 

Contractor required to restore surfaces opened by permit and basis of 
payment therefor, also provision for failure to restore surface openings. 
Tests of samples of materials. 

Statement of where and by whom tests will be made. 
Quality of materials. 

Statement that materials shall maintain qualities equal to the requirements 
of the specifications, or to approved samples. 
Storage of materials. 
Use of materials found on work. 

Statement relative to use of any stone, gravel, sand, etc., found in excavation. 
Disposal of materials, structures, etc., found on work and not used in the 
construction. 

Lines, grades, and measurements. 

To be given by engineer, and stakes and markings to be preserved by con- 
tractor. 
Crown or cross-section of roadway. 

To be as shown on typical cross-section and only changed where drainage or 
other conditions make it necessary. 
Authority and duties of assistants, inspectors, etc., and the limitations of 
such authority and duty. 

Engineer as referee in case of disputes. 
Inspection of materials and work. 
Defective materials and work. 

Clause as to disposition thereof. 
Failure to remove or renew defective materials or work. 
Final cleaning up. 



704 SPECIFICATIONS 

Clause covering removal of temporary structures and excess material and 
condition in which the roadway shall be left upon completion. 
Suspension of work. 

Authority for, reasons — fault of contractor, bad weather, etc. 
Method of computing the time allowance for completing the work. 
Failure to complete work on time. 

Liquidated damages to be collected. 
Annulment of contract. 

Conditions under which contract may be annulled and procedure thereof. 
Measurement of quantities. 
Scope of payments. 

Statement that payments made for all work done shall be full compensation 
for such work, including all claims of any character, and such pay- 
ments do not constitute acceptance of the work. 
Partial payments. 

Method of payment. 
Approval and final payment or acceptance and final payment. 
No waiver of legal rights. 

Statement regarding right of State to show true character of estimates 
should error be discovered, etc. 
Any additional clauses desired. 

CONSTRUCTION DETAILS 
Excavation and Embankment 

Description of work included under excavation, such as clearing and 
grubbing, excavation of roadway, driveways, intersections, ditches, etc., 
and the making of embankments. 
Clearing and grubbing. 
Specific requirements. 
Removal of structures, obstructions, etc. 

Specific requirements. 
Roadway excavation. 

Specific requirements. 
Excavation for structures. 

Specific requirements, including back filling. 
Embankment. 

Specific requirements. 
Disposal of surplus material. 

Specific requirements. 
Borrow excavation. 

Specific requirements. 
Overhaul of excavation. 
Specific requirements. 
Sub-grade. 

Specific requirements, including preparation, removal, and replacing of ; 

defective material, protection, and acceptance. | 

Shoulders. i 

Specific requirements. 
Method of determining excavation quantities. 

A statement of how quantities shall be measured. 
Basis of payment. 

Statement relative to compensation for excavation and its various sub' 
divisions, and whether compensation is made collectively or separately. 
Note. — When several similar types of constructions are set forth in the « j 
same set of specifications, such as several kinds of pipe culverts or pave- 
ments, each should be covered separately in accordance with the outlines 
indicated in the following. 

SUB-BASE 

Any broken stone, gravel, or other material used to replace unsuitable 
sub-grade material or to support the base course. 
Description. '- - - 
Materials. 

Construction methods. 
Basis of payment. 



OUTLINE 70s 



BASE COURSES OR FOUNDATIONS FOR PAVEMENTS 
Base Course 

Insert name 
Description. 
Materials. 

Stone, sand, screenings, etc. 
Construction methods. 

Placing, rolling, etc. 
Basis of payment. 

Repeat the same outline for each kind of base course. 

SURFACE COURSES OR PAVEMENTS 

. Surface Course (or Pavement) 



Insert name 

Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each kind of surfacing. 

CONCRETE 

General description, classification, and statement of forms of construction 
in which each class of concrete is to be used. 
Materials. 

Specify composition and materials for each class. 
Construction methods. 
Basis of payment. 

REINFORCEMENT 

Description. 

Describe each kind in order with the methods for placing. 
Basis of payment. 

MASONRY 

. Masonry 



Insert name 
Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each of the other kinds of masonry. 

DRAINAGE STRUCTURES 

Concrete and Masonry Culverts, End Walls, Retaining Walls, Catch Basins, 
Drop Inlets, Etc. 

Statement that all concrete and masonry culverts, end walls for pipe 
culverts, retaining walls, catch basins, drop inlets, etc., shall be built of 
the class of concrete or kind of masonry indicated and according to the 
plans and specifications therefor. 

Basis of payment. 

PIPE CULVERT 



Insert name 
Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each kind of pipe culvert. 



7o6 SPECIFICATIONS 



UNDERDRAINS 

. Underdrains 



Insert name 
Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each kind of underdrain. 

GUTTERS 

Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each kind of gutter. 

CURBING 

Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each kind of curb. 

GUARDRAIL OR FENCING 

Guardrail 

Insert name 
Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each kind of railing or fencing. 



Description. 
Materials. 

Construction methods. 
Basis of payment. 



Description. 
Materials. 

Construction methods. 
Basis of payment. 



Description. 
Materials. 

Construction methods. 
Basis of payment. 



MONUMENTS 



RIPRAP 



CRIBBING 



PILING 



Description. 
Materials. 
Construction methods. 
Basis of payment. 

STRUCTURAL STEEL AND IRON 

Description. 
Materials. 
Fabrication. 
Construction methods. 
Basis of payment. 



OUTLINE 707 

SURFACE TREATMENTS 

Description. 

Materials. 

Methods of application. 

Sweeping, applying, and covering. 
Basis of payment. 

MISCELLANEOUS ITEMS 
Items 

Insert name. 
Description. 
Materials. 

Construction methods. 
Basis of payment. 

Repeat the same outline for each item desired, 

MATERIAL DETAILS 

Note. — Should it be desired to group the specifications for all materials, 
they should be inserted at this place and appropriate references made thereto 
under the various subdivisions in "Construction details." The materials 
should be grouped in classes and placed in the following order: 
Cementing materials. 

Portland cement, lime, etc. 
Water. 
Fine aggregate. 

Filler dust, sand, grit, etc., for all purposes. 
Coarse aggregate. 

Stone, gravel, slag, etc., for all purposes. 
Telford and quarry stone, etc. 
Masonry stone, etc. 
Paving brick and blocks. 
Bituminous materials. 
Nonbituminous binders. 
Culvert pipes, drain tiles, etc. 

Cast iron, corrugated metal, concrete, vitrified clay, etc. 
Metal reinforcement. 

Bars, mesh, expanded metal, etc. 
Structural steel. 

Structural shapes, fabricated steel, etc. 
Miscellaneous iron and steel. 

Castings, special wrought work, etc. 
Treated timbers. 
Untreated timbers. 
Paints, oils, etc. 
Monuments. 
Miscellaneous materials. 

Fencing wire, cables, pipe raiU etc. 

SPECLA.L PROVISIONS 

Supplementing the specifications for the construction of • 

Give the identification of proposed work, such as road namCt number, job 

number, etc. 

Under this heading should be placed such provisions or requirements as 

pertain to the particular contract proposed, and are not standard or common 

to all work for which the general specifications may have been prepared, 

such as: 

Materials, etc., furnished by the State. 

All materials, equipment, or other facilities for prosecuting the work, 
furnished by the State to the contractor, should be here listed, with 
conditions governing delivery, use, and return. 
Statement relative to disposal of specific materials or structures found on 
the work and not to be used in the construction thereof. 

Note. — Any "Special provisions" should be placed in this relative 
position, forming a part of the specificatons. If the proposal is separated 



7o8 



SPECIFICATIONS 



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when bids are invited, then the special provisions 
may be bound with the specifications or with the 
proposal; but in either case a proper clause should 
be inserted in the proposal calling the attention of 
the bidder to the fact that there are certain 
"Special provisions" which form a part of the 
specifications. 

PROPOSAL 

Spaces for name and address of bidder. 

Detailed description of location of roadway, 
length and width of surfacing or pavement, refer- 
ring to the plans, drawings, specifications, etc., by 
their titles and markings for identification. 

Note. — If this proposal form is bound with 
the specifications and contract, it should be 
placed directly preceding the contract. If used 
as a separate form, the proposal may be attached 
to the contract, or a list of quantities with spaces 
for unit prices and amounts conforming to the 
outline indicated in the proposal may be shown in 
the contract as a part thereof, to be filled in at the 
time of its execution. 

If the proposal bond form is used in place of the 
certified check, it should be attached to or fur- 
nished with the proposal form. 

Address (as, "To the State Highway Depart- 
ment"). 

Declaration of the bidder that the only persons 
or parties interested in the proposal as principals 
are those named therein; that the proposal is 
made without collusion with any other person, 
firm, or corporation; that he has carefully ex- 
amined the specifications, including special pro- 
visions, if any, and that he has made a personal 
examination of the site of the work ; that he is to 
furnish all the necessary machinery, tools, ap- 
paratus, and other means of construction, and do 
all the work and furnish all the materials specified 
in the manner and time prescribed; that he 
understands that the quantities are approximate 
only and subject to increase or decrease, and 
the declaration of his willingness to perform 
any increased or decreased quantities of work 
at unit prices bid. 

Itemized proposal showing th'fe approximate 
quantities with spaces for unit prices bid, as: 

Item I : cu. yd. Excavation at 

{$ ) per cu. yd. 

Note. — In case the above form is used, it may 
be used either with or without the quantities. 
If used without the quantities, the quantities 
should be listed under the "Special provisions." 
or 

Note. — Spaces should be left for filling in the 
unit prices both in words and figures, as indicated. 
The items of work should be numbered in the 
order and with the same units of measure shown 
in the specifications. The units of measure used 
should be as follows: 

The cubic yard for all volumes except the gallon 
for bitu minous materials when not weighed and the 
barrel for cement. 

The square yard for all surface measurements 
except the square foot for wire mesh or expanded 
metal. 



OUTLINE 709 

The foot for linear measurement. 

The ton of 2000 pounds for iveights except the pound for steel and casting. 

A unit price each for any item desired. 

Proposal to perform "force account or extra work." 

Proposal to execute contract agreement and to begin and complete work 
on time. 

State dates or number of days for beginning and completion. 

Proposal stating the amount of contract bond. 

Proposal for guaranty of work until final completion and acceptance. 

Statement of inclosure of proposal guaranty, naming amount, and condi- 
tions of forfeiture. 

Note whether certified check or bond. 

Spaces for signatures, titles, and individual addresses. 



PROPOSAL BOND 

In case a proposal bond is used in lieu of a certified check, the form therefor 
should be attached to or furnished with the proposal form. 



CONTRACT 

The form of contract should be as short as consistent with legal require- 
ments. 

The "Notice to contractors," "Specifications," "Proposal," and "Plans" 
should be referred to and made a part of this agreement, and such reference 
should identify the specifications, plans, drawing, etc., by their specific 
markings. 

The Federal Government is not to appear as party to this agreement. 



CONTRACT BOND 



INDEX 

Itemized index to be placed at the end of the specifications instead of at this 
point if the foregoing documents are issued as separate pamphlets. 



ESTIMATES 

Estimates shall be made up in accordance with the order and units of 
measure indicated in the proposal forrn. 



710 SPECIFICATIONS 

EXAMPLES OF GENERAL CLAUSES 

The following general clauses are quoted from the U. [S. Forest Road 
Specifications. 

SPECIFICATIONS 

DEFINITION OF TERMS 

In interpreting these specifications, the following definitions shall 
prevail : 

1. Secretary. — The Secretary of Agriculture of the United States. 

2. Chief Engineer. — Chief Engineer of the Bureau of Public Roads, 
United States Department of Agriculture. 

3. District Engineer. — District Engineer of the Bureau of Public Roads, 
in whose district the improvement is located. 

4. Engineer. — Chief Engineer of the Bureau of Public Roads; District 
Engineer of the Bureau of Public Roads, in whose district the improvement 
is located; or a representative of the foregoing duly authorized to supervise 
the work. 

5. Inspector. — An authorized assistant of the engineer, assigned to inspect 
any feature of the materials or workmanship entering into the improvement. 

6. Forest Official. — A duly authorized representative of the Forest 
Service, United States Department of Agriculture. 

7. Contractor. — The person, firm, partnership, or corporation, con- 
stituting one of the principals to the contract, undertaking to perform the 
work herein specified, or any lawful agent of such person, firm, partnership 
or corporation. 

8. Plans. — The official approved plans, profiles, cross-sections, and other 
drawings, or exact reproductions thereof, which show the location, character, 
dimensi9ns and details of the work to be done, and which are to be con- 
sidered in the contract as coordinate with these specifications. 

9. Specifications. — The directions, provisions and requirements contained 
herein, together with all written agreements made or to be made, pertaining 
to the method and manner of performing the work, or to the quantities and 
qualitites of materials to be furnished under the contract. 

10. Contract. — The agreement between the Contractor and the Secretary 
of Agriculture covering the work to be performed, and including the plans 
and specifications. 

11. Laboratory. — The laboratories of the Bureau of Public Roads or other 
laboratories designated by the Chief Engineer. 

INSTRUCTIONS TO BIDDERS 

Interpretation of Approximate Estimate. — Bidders are cautioned that 
the estimate of quantities attached hereto will serve, so far as this project 
is concerned, only for the purpose of comparing bids. The basis of payment 
on the contract will be the actual quantites of work performed in accordance 
with the plans and specifications, and if, upon the completion of the im- 
provement the actual quantities should show either increase or decrease 
from the quantities given in the approximate estimate, the unit bid prices 
mentioned in the proposal will still prevail, except as otherwise provided 
herein. 

Examination of Plans, Specifications and Site. — Bidders are required 
before submitting bids to examine carefully the site of the proposed work, 
as well as the proposal, plans, specifications, and contract form for the 
improvement contemplated. Professions of ignorance regarding the 
requirements for the work will in no way serve to modify the provisions 
of the contract. 

Laws Affecting Public Work. — The attention of bidders is called to the 
necessity for being familiar with the various Federal, State and local laws, 
affecting the length of working days, employers' liabilities, Sunday work, 
etc., etc. 

Proposal Forms. — In filling out proposal forms bidders shall be governed 
by the following provisions: 

I. "Proposals must be made on the blank form provided herewith. The 



GENERAL CLAUSES 71 1 

blank spaces in the proposal form, except as otherwise noted, must all be 
filled in correctly where indicated for each and every item for which a 
quantity is given, and no change shall be made either in the phraseology 
of or the items mentioned in the proposal form. 

2. Proposals must be signed in ink by the bidder with 'the signature in 
full. When a firm is a bidder, the agent who signs the firm name to the 
proposal shall state, in addition, the names and addresses of the individuals 
composing the firm. When a corporation is a bidder, the person signing 
for it shall state under the laws of what state the corporation was chartered 
and the name, title, and address of the officer having authority under the 
by-laws to sign contracts.^ The proposal shall also bear the seal of the 
corporation, attested by its secretary. Anyone signing the proposal as 
agent must file with it legal evidence of his authority to do so. Post- 
ofi&ce address, county and state, must be given after the signature. 

3. Prop9sals that contain any omission, erasure, alteration of form, 
addition, item not called for in the engineer's estimate, conditional or 
alternate bids, or that show irregularities of any kind, may be rejected as 
informal. 

4. Each proposal shall specify a unit bid price, written with ink in both 
words and figures, for each of the separate items as called for, and shall also 
show the products of the respective unit prices and quantities of work, 
written in figures with ink, in the column provided for that purpose. The 
gross bid, or sum of the various products, shall be shown, written in ink, 
on the line provided for such gross bid. ^ ^ .- 

5. Any proposal which does not contain prices set opposite each of the 
several items for which there is an estimated quantity in the engineer's 
estimate, or any proposal which shall in any manner fail to conform to the 
conditions of the published notice inviting proposals, may be deemed 
informal and rejected. 

6. Each proposal must be accompanied by a money deposit in an amount 
at least equal to five (5) per centum of the total amount of the proposal, 
in the form of cash, a draft, or a certified check, issued by a national 
or state bank, in good credit and payable at sight to the Secretary of Agri- 
culture of the United States. Where a certified check is used, it shall bear 
the same signature as the signature which appears on the proposal which 
such check accompanies. 

7. Each proposal shall be placed, together with the money deposit, in a 
sealed envelope so marked as to indicate its contents without being opened. 
This envelope shall then be placed in another which shall be sealed, and 
addressed as indicated in the notice to contractors. Proposals may be 
delivered either in person or by mail. 

8. A bidder_ may withdraw his proposal, without prejudice to himself, 
provided a written request is filed at the address indicated above not later 
than the day before the bids are to be opened. 

9. Proposals will be publicly opened and read at the time and place 
mentioned in the notice to contractors, and bidders are invited to be present 
at the opening. Proposals received after the time set for the opening will be 
returned to the bidder unopened. 

DisqualificatioQ of Bidders. — The following causes will be considered 
sufficient to disqualify any bidder, and no proposals from disqualified bidders 
will be considered in the award of the contract: 

1. Interest by the same persons in more than one proposal for one contract. 

2. Collusion among or between bidders. 

3. Unbalanced proposals; that is, proposals in which the price bid for 
one or more items does not bear the proper proportion to the total amount 
bid to do the whole of the work. 

4. Lack of responsibility on the part of bidders. For example, it is 
probable that no bidder would be considered responsible who had failed to 
carry out any contract in which the U. S. Department of Agriculture had 
been directly or indirectly concerned. 

5. Lack of experience or capital on the part of bidders. Evidence^ of 
experience, ability, and financial standing, as well as a statement regarding 
plant and machinery available may be required of any or all bidders. 

AWARD AND EXECUTION OF CONTRACT 

Consideration of Bids. — After the proposals are opened and read, the bid 
prices will be compared by the District Engineer, and the results of such 



712 SPECIFICATIONS 

comparison will be immediately made public. Until the final award of the 
contract, however, the right will be reserved to reject any and all proposals 
and to waive technical errors. 

Award of Contract. — The award of the contract, if it be awarded, will be 
to the lowest responsible bidder whose proposal shall comply with all re- 
quirements necessary to render it formal. For the purposes of award the 
correct summation of the products of the approximate quantities, herein 
stated, by the unit bid prices will be considered the amount of the bid. 
In no case will an award be made until all necessary investigations are made 
into the responsibility of the bidder to whom it is proposed to award the 
contract. 

Return of Proposal Guaranty. — As soon as the bid prices have been com- 
pared, the District Engineer may, at his discretion, return the guaranty 
deposits accompanying such of the proposals as in his judgment would not 
be considered in making the award. All other proposal guaranties will be 
held until the contract has been awarded, after which they will be returned 
to the respective bidders whose proposals they accompanied, with the 
exception of the bidder to whom award has been made. After a satisfactory 
bond has been furnished and the contract has been approved and executed 
by the Secretary, the proposal guaranty which accompanied the successful 
bidder's proposal will be returned. 

Contract Bond Required. — The bidder to whom the contract is awarded 
will be required to furnish bond to the amount of so % of the total contract 
price. The bond shall be furnished by a reputable bonding company, and 
shall be satisfactory to the Secretary and on the form provided herewith. 

Execution of Contract. — The contract shall be signed by the contractor 
and satisfactory bond furnished within ten days after he has received notice 
of award. In case of failure on the part of the contractor, to enter into 
•contract and furnish bond as above required, the guaranty accompanying 
his proposal will be forfeited to the United States Treasury. Award may 
then be made to the next lowest responsible bidder, the work be readvertised 
or constructed by day labor as the Secretary may decide. 

Subletting or Assigning Contracts. — Award will be made with the under- 
standing that the work awarded will be performed by the contractor to 
whom the award is made, with the assistance of workmen under his imme- 
diate superintendence, and the contract shall not be sublet either in whole 
or in part except with the written consent of the District Engineer. 

The Use of Patented Processes, etc. — The bid prices shall include all 
charges for the use of patented processes, materials or methods, and for 
all other similar incidental charges not expressly provided for in the 
specifications. 

GENERAL PROVISIONS 

Scope of the Work to be Done. — The contractor will be required under 
these specifications to perform the following work: 

1. To grade the roadway and to bring the surface to the lines, grades and 
typical cross-section shown on the plans and to do the work in accordance 
with the plans and specifications. 

2. To do all clearing and grubbing, ditching, grading, shaping, surfacing, 
and compacting; to make all excavations and embankments; to construct 
all paving, masonry, stone and timber work; to build all waterways, drains, 
ditches, bridges, and culverts; and to clear away all rubbish which may 
obstruct the roadway, ditches or waterways, whether such obstructions 
result from his operations or otherwise. In short, the contractor will be 
required to furnish all materials, implements and labor necessary, and to 
build and put in perfect condition for use the entire roadway with all apper- 
taining structures, and shall leave the roadway and adjoining property in 
neat condition and free from rubbish or other waste materials. 

3. To start the improvement at the part of the road designated by the 
engineer, and to conduct and complete the work in accordance with the 
plans and specifications as interpreted by the District Engineer. The unit 
prices mentioned in the proposal shall cover the cost of all materials and 
labor, except as otherwise herein provided. 

Permits and Licenses. — Such permits, licenses, insurance policies, etc., 
as Federal, State or local laws necessitate in conducting the work, shall be 
provided by the contractor at his own expense. 

Interpretation of Plans and Specifications. — The contractor shall not 
deviate from the plans and specifications in any particular without the 



GENERAL CLAUSES 713 

written authority of the District Engineer. In case of discrepancy between 
the plans and specifications, the plans shall govern, and in case of discrep- 
ancies on the plans between figured dimensions and scale, the figures shall 
govern. 

Alterations. — The District Engineer shall have the right to make such 
reasonable alterations in the plans and specifications as in his judgment are 
necessary and desirable, and such alterations will not invalidate the contract. 
Reasonable alterations will be construed to mean alterations in the quantity 
location or extent of the work covered by the various items of the bid, but 
will not be construed to cover any alterations in the general character of 
the contract. 

All orders making alterations in the plans and specifications shall be given 
by the District Engineer to the contractor in writing. Alteration work 
done by the contractor without such written orders, except in cases of 
emergency, and acknowledged as such by the District Engineer, will be 
at the contractor's own expense and will not be paid for under his contract 
for this work. 

The final adjustment covering increases, decreases or eliminations caused 
by alterations will be made on the basis of the unit price bid for the item or 
items concerned and no allowance will be made on account of any claim 
for loss of profit due to the alteration. 

Extra Work. — Alterations or changes in the plans and specifications and 
new or unforeseen items of work shall be classed as extra work when they 
can not be covered by any of the various items or combination of items for 
which there is a bid price. 

The contractor shall furnish such labor, teams, equipment, supplies and 
materials as are necessary and perform such extra work as may be ordered 
in writing by the District Engineer whenever necessary for the proper 
completion or construction of the whole work herein contemplated; and he 
shall make no claim for extra work unless it shall have been done in obedience 
to such written order. 

The contractor shall receive for such extra work the actual cost of all 
supplies and materials, including freight, furnished by him, as shown by his 
paid vouchers, and a reasonable rental charge previously agreed to in writing 
between the engineer and the contractor for the use of special equipment or 
machinery, such as steam rollers, steam shovels, concrete mixers, etc., 
required for the economical performance of the work; for such labor and 
teams as are necessary he shall receive the current prices in the locality, 
which shall have been previously agreed to in writing by the engineer and 
by the contractor, plus 15% of the cost of such labor and teams which shall 
be considered as full compensation for general supervision and the furnishing 
of small tools and ordinary equipment used on the contract, such as plows, 
Fresnos, wagons-, graders, etc. 

Unauthorized Work. — No payment will be made for work not required 
by the plans and specifications or authorized in writing by the District 
Engineer. 

Progress of the Work. — The contractor shall begin work within ten days 
after receiving notice that the contract has been ^gned by the Secretary 
of Agriculture unless consent to begin at a later date is given in writing by 
the said Secretary, and shall so prosecute the work that the work done 
shall at all times bear approximately the same proportion to the total of 
the work required to be done undeft- the contact that the time elapsed since 
the date upon which the work should have been begun bears to the total time 
allowed by the contract in which to do the whole of the work. Failure to 
comply with this requirement may result in the annulment of the contract 
as hereinafter provided. 

Limitation of Operations. — The contractor shall so conduct his operations 
as to have under construction no greater length or amount of work than he 
can prosecute vigorously, and when in the judgment of the engineer such 
operations are being so spread out as to be detrimental to such vigorous 
prosecution, thereby endangering completion of the improvement within 
the contract time, he shall so advise the contractor in writing. 

Character of Workmen and Equipment. — All workmen and equipment 
provided by the contractor shall be the best available for the kind of work 
being performed. Any person employed by the contractor, whom the 
engineer may deem incompetent or unfit to perform the work or who conducts 
himself in a disorderly manner, shall, upon the written instructions of the 
engineer, be discharged, and such person shall not be again employed on 



714 



SPECIFICATIONS 



the work. Failure by the contractor to provide adequate equipment or 
workmen may result in annulment of the contract as hereinafter provided. 

Cooperation of Contractor Required. — The contract9r shall keep a copy 
of the plans and specifications on the work at all times. He shall also 
remain on the work or provide an authorized representative to receive and 
carry out the instructions of the engineer. He shall provide all reasonable 
facilities to enable the engineer and inspectors to inspect the workman- 
ship and materials entering into the work, and shall cooperate in the matter 
of setting and preserving stakes, benchmarks, etc., for controlling the work. 
Laws to be Observed. — In prosecuting the work, the contractor shall 
exercise care to see that all laws are observed, both by himself and his em- 
ployees. He shall also observe the rules and regulations of the United 
States Forest Service and the rules of the Board of Health, and shall take 
all reasonable steps to insure proper sanitation in connection with all of 
his activities. 

Public Convenience and Safety. — In conducting the work the contractor 
shall interfere as little as possible with public traffic. He shall establish 
barricades and danger and detour signs wherever required by law or necessary 
for the safety or convenience of the public. He shall exercise especial pre- 
cautions in the storage and use of explosives to warn away the public as 
well as to safeguard his employees. 

Preservation of Property. — The contractor shall preserve from damage all 
property -along the line of the work, the removal or destruction of which is 
not called for by the plans. This applies to public utilities, trees, monu- 
ments, fences, etc., and wherever such property is damaged due to the 
activities of the contractor, it shall be immediately restored to its original 
condition by the contractor and at his own expense. 

Responsibility in Case of Damage to Persons or Property. — The respon- 
sibility for all damages to persons or property arising out of or on account 
of work done under this contract, shall rest upon the contractor, and he 
shall save the United States harmless from all claims made on account of 
such damages. 

Responsibility for Damage to Work. — Any damage to the work before it is 
finally accepted, whether such damage is due to ordinary or extraordinary 
causes, shall be at once repaired by the contractor; except where a section 
or portion of road is opened to public traffic, with the approval of. the engi- 
neer, before final acceptance, the contractor will not be expected to make 
good the ordinary wear due to traffic, provided no inherent defects in the 
work are disclosed; but this exception will not serve to release the con- 
tractor from responsibility for damage caused by storms, or otherwise, 
except as noted, to sections of road that have been opened to traffic. 

Testing Materials. — Tests of materials to be used in the work shall be 
made in the laboratory designated in the "Definition of Terms" whenever 
such tests are required by the specifications or by the engineer. The con- 
tractor shall afford such facilities as the engineer may require for collecting 
and forwarding samples of materials to be tested as above required, and 
unless otherwise directed in writing by the engineer, the contractor shall not 
use in the work the materials represented by the said samples until he has 
received written notice*rom the engineer that he may do so. 

Materials may be rejected by the engineer whenever, in his judgment, 
they fail to meet the requirements of the specifications, and when so rejected 
they shall be immediately removed from the work and disposed of as here- 
inafter specified. 

Storage of Materials. — All materials intended for use in the work shall 
be so stored by the contractor as to prevent damage from exposure to the 
elements, admixture of foreign material, or from any other cause. The 
engineer will refuse to accept, or to sample for testing, any materials that 
are improperly stored. 

Use of Materials Found on Work. — In the absence of special provision 
to the contrary, any stone, gravel, sand, etc., that may occur in excavations 
opened in grading the road, and may not be needed to make the fills shown 
on the plans, any timber, except as herein otherwise provided, that would 
necessarily be removed in making the improvement, or any existing struc- 
tures that are to be replaced, may be used by the contractor, provided, 
and to the extent, that these materials are suitable for and required in the 
work. Materials found on the work, especially timber and existing struc- 
tures, and necessarily removed, but not used by the contractor as provided 
above, shall be put into shape to be handled economically and neatly piled 
along the right-of-way, as herein provided or as the engineer may direct. 



GENERAL CLAUSES 715 

Lines, Grades and Measurements. — The contractor will be governed by 
such lines, grades and measurements as may be given by the engineer in 
laying out the work and by the engineer's determination of the quantities 
of work performed. Stakes and markings set or made by the engineer 
to mark out the work, shall be scrupulously preserved by the contractor. 
In case the activities of the contractor or his employees result in the destruc- 
tion of such stakes or markings, an amount equal to the cost of replacing 
same will be deducted from subsequent estimates due the contractor when- 
ever in the opinion of the engineer such destruction is due to the neglect or 
carelessness of the contractor or his employees. 

Crown or Cross-section of Roadway. — The typical cross-section contained 
in the plans shall be implicitly followed as regards the crown or cross-section 
of the roadway except, that where considerations of drainage or other special 
conditions make it necessary or desirable to change the shape of the surface, 
or otherwise alter the shape of the cross-section, the engineer may alter this 
feature of the work to fit the conditions. Such an alteration, however, will 
not be considered as extra work. 

Authority and Duties of Inspectors. — The District Engineer may appoint 
inspectors to inspect all materials used and all work done. Such inspection 
may extend to all or any part of the work and to the preparation or manu- 
facture of the materials to be used. The inspectors will not be authorized 
to revoke, alter, enlarge, or relax the provisions of these specifications. 
An inspector is placed on the work to keep the engineer informed as to the 
progress of the work and the manner in which it is being done, also to call 
the attention of the contractor to any infringements upon plans or specifi- 
cations. He will not be authorized to approve or accept any portion of 
the work or to issue instructions contrary to the plans and specifications. 
The inspector will have authority to reject defective material and to suspend 
any work that is being improperly done, subject to the final decision of 
the engineer. 

The inspector will exercise such additional authority, only as may from 
time to time be especially delegated to him by the engineer. 

Inspection of Materials and Work. — The engineer and his inspectors shall 

have free access to all parts of the work and to all materials intended for 

use in the work, and be given authority by the contractor to inspect the 

manufacture of such materials in the factories. Materials will be inspected 

1 and passed upon as promptly as practicable after they are delivered on the 

work, and none shall be used in the work until after approved by the engineer. 

The work will be inspected as it progresses, but failure to reject or condemn 

defective work at the time it is done will in no way prevent its rejection 

whenever it is discovered before the road is finally accepted, approved, and 

paid for. 

' Defective materials or work shall be removed from the site of the work 

: and disposed of immediately after they are rejected. The disposition to 

, be made of defective materials shall in all cases be such that the engineer 

; can always satisfy himself that each parcel or lot of such material has been 

I disposed of as claimed by the contractor. 

Upon the failure of the contractor to remove and properly dispose of 

rejected material or work immediately after receiving formal notice, the 

: engineer shall employ labor and remove such material or work, and charge 

the cost of same to the contractor and deduct it from his next estimate. 

Final Cleaning Up. — When the work is completed the right-of-way, 

' borrow pits, and all ground occupied by the contractor in connection with 

I the work shall be cleared of all rubbish, excess materials, temporary struc- 

' tures and equipment, and all parts of the work shall be left in a neat and 

presentable condition. 

Suspension of Work. — The engineer shall have authority to suspend the 
' work on account of (i) Default of the contractor; (2) Unfavorable weather 
I conditions; and (3) Any other condition which, in the judgment of the 
\ engineer, makes it_ impracticable to secure first-class results. The con- 
, tractor shall immediately respect the written order of the engineer to suspend 
I work wholly or on any particular section of the road. If it becomes necessary 
j to stop the work for a protracted period the contractor shall open proper 
< drainage ditches; erect temporary structures where necessary, prepare the 
j road so there will be a minimum of interference with traffic, and take every 
' precaution to prevent ^ any damage or unreasonable deterioration of the 
J work during the time it is closed down. If upon reopening the work any 
I damage or deterioration has occurred due to negligence on the contractor's 



7i6 



SPECIFICATIONS 



part then he shall correct all such conditions at his own expense. In case 
of failure on the part of the contractor to carry out the provision of this 
section, the engineer shall do the necessary work and deduct the cost of 
the same from any moneys due or to become due the contractor, deducting 
it from the next estimate. 

Time of Completion. — The engineer shall determine the weather working 
days and based thereon he shall compute the date of completion. Weather 
working days shall be considered as days or parts of days when, in the 
judgment of the engineer, it is practicable for the contractor to prosecute 
his work, Sundays, and legal holidays being excepted. 

Should the contractor fail to complete the work within the time allowance 
mentioned in the notice to contractors, and as determined herein, the 
engineer will upon the arrival of the date of completion so notify the con- 
tractor and thereafter keep a record of overtime and deduct from any 
moneys due or coming due to the contractor, as determined by the engineer's 
estimates, an amount equal to the cost of maintaining the necessary force 
of engineers and inspectors on the work during the additional time necessary 
because of the contractor's delay, and this amount shall be considered as 
reasonable liquidated damages due the United States by the contractor for 
his failure to have finished the fwork within the time agreed. 

Annulment of Contract. — The contract of which these specifications form 
a part may be annulled by the Secretary of Agriculture for any one of the 
following reasons: 

I. Substantial evidence that the progress being made by the contractor is 
insufficient to complete the work within the specified time. 

2. Failure on the part of the contractor to observe the requirements of these 
specifications. 

3. Failure on the part of the contractor promptly to make good any 
defects in materials or workmanship that may be pointed out to him by 
the engineer. 

Before the contract is annulled, the contractor and his bondsmen will first 
be notified in writing by the District Engineer of the conditions which make 
annulment of the contract imminent. Twenty days after this notice is 
mailed to the address given in the proposal, if in the judgment of the District 
Engineer no effective effort has been made by the contractor or his bonds- 
men to correct the condition complained of, the Secretary may declare the 
contract annulled, and notify the contractor and his bondsmen accordingly. 

Upon receipt of a notice from the Secretary of Agriculture that the con- 
tract has been annulled, the contractor shall immediately discontinue all 
operations. The Secretary of Agriculture may then proceed with the work, 
in any lawful manner that he may elect, until it is finally completed. 

When the work which was covered by the contract is thus finally com- 
pleted, the total cost of the same will be computed. If this total cost is 
less than the contract price, any money due the contractor will be paid to 
him. ^ If the total cost is greater than the contract price, the difference shall 
be paid either by the contractor or his bondsmen. ^ 

Measurement of Quantities. — The determination of the quantities of 
work performed will be made by the engineer and based on measurements 
taken by him or his assistants. In computing volumes the method of 
average end areas will be used for excavation and embankment. Other 
quantities will be computed in the units used in the proposal form, according 
to well recognized engineering principle, and no local rules or customs will 
be considered. 

^ Payments. — Payments for each kind of work except as otherwise pro- 
vided herein will be made on the basis specified for that particular item, 
and at the rate mentioned in. the proposal. Payment of the amount com- 
puted on this basis and rate shall be payment in full for the work done 
including all claims of every character. No payments, however, shall 
constitute an acceptance of the work. 

Partial payments will be made monthly, provided the work is progressing 
to the satisfaction of the engineer. The total amount of such payments 
at any time before final completion shall not exceed 8$ % of the value of the 
work done, as estimated by the engineer; and in estimating the value of 
the work done no materials that have been delivered but not used in com- 
pleted work shall be included. 

Whenever the work provided for by the contract shall have been com- 
pletely performed on the part of the contractor, and all parts of the work 
have been approved by the District Engineer, a final estimate showing 



MATERIALS 717 

the value of the work done will be prepared by the engineer as soon as the 
necessary measurements may be made. The amount of this estimate, 
less any sums that may have been deducted in accordance with the provisions 
of the contract, and less all previous payments, will be paid to the contractor 
within thirty days after the final estimate has been approved by the Chief 
Engineer. 

^ No Waiver of Legal Rights. — The United States Government reserves the 
right, should an error be discovered in the estimate, or conclusive proofs 
of dishonesty on the part of the contractor, discovered in the work, after 
the final payment has been made, to claim and recover by process of law, 
such sums as- may be sufficient to correct the error or make good the defects 
in the work resulting from the contractor's dishonesty. 

SAMPLE CLAUSES COVERING MATERIALS AND MANIPULATION 

The following sample clauses covering materials and manipulation are 
quoted from various sources. 

MATERIALS 

(New York State Specifications, 1914) 

Materials of Construction 

All materials proposed to be used in construction shall have due examina- 
tion and pass all required tests before acceptance. Those which are to be 
tested by the Bureau of Tests at Albany shall have samples taken and 
submitted in accordance with the commission's instructions to its em- 
ployees. Samples are to be taken of all sand, gravel, cement, concrete, 
bituminous rnaterial, stone, and all other pavement ingredients, of which 
the engineer in charge has not been notified that satisfactory samples have 
already been taken. None of this material is to be used until the written 
notification of acceptance is received by the engineer in charge of the con- 
tract, and then only so long as its quality remains equal to that of the 
accepted sample. 

Portland Cement 

o.i. All the cement used in the work shall be true Portland cement of 
well-known brands which have been in successful use on large engineering 
works in America for not less than two years and which are manufactured 
at works which have been in successful operation for at least one year. 

0.2. Tests will be made as follows: first, for fineness; second, for con- 
stancy of volume J third, for time of setting; fourth, for tensile strength; 
fifth, for composition by chemical tests; sixth, for specific gravity. 

The average result of the separate samples shall be the test for tensile 
strength of any lot. The samples of each lot shall be required to show 
uniform results in tests. Marked deviations from such results may be 
considered cause for rejection, even though test requirements may be 
otherwise fulfilled. 

The results of the tests may be expected in 12 days afer shipment of 
samples. 

Cement not satisfactory in the 7-day tests will be held awaiting the 
result of the 28-day tests before acceptance or rejection. 

0.3. The cement shall meet the following requirements: 

It shall be ground to such fineness that not less than 92 % by weight shall 
pass throifgh a No. 100 standard sieve of 10,000 meshes per square inch, 
and not less than 75 % by weight shall pass through a No. 200 standard sieve 
of 40,000 meshes per square inch. 

0.4. Pats of neat cement about 3 inches by 4 inches in size, 3^^ inch thick 
at the center, and tapering to a thin edge, shall be kept in moist air for a 
period of 24 hours. 

Normal Tests 

Air Test: One of these pats is then kept in air at normal temperature 
for 28 days. 

Water Test: Another pat is kept in water maintained as near 70 degrees 
Fahrenheit as practical for 28 days. 

Accelerated Test: A pat is exposed in any convenient way in an atmos- 
phere of steam, above boiling water, in a loosely closed vessel for 5 hours. 

These pats are observed at intervals and, to satisfactorily pass the re- 
quirements, shall remain firm and hard and show no signs of distortion, 
checking, cracking or disintegration. 



7i8 



SPECIFICATIONS 



0.5. Cement shall not develop its initial set in less than 30 minutes, 
and shall develop a hard set in not less than 60 minutes nor more than 600 
minutes, the determination being made with the Vicat needle apparatus 
from pastes of normal consistency, as follows: 

The paste is molded upon a glass in a conical hard rubber mold 4 centi- 
meters high; this cake is to set in moist air and a Vicat needle with a wire 
I millimeter in diameter and loaded to 300 grammes shall be placed upon 
it. When the needle ceases to pass a point 5 millimeters above the upper 
surface of the glass plate the initial set has taken place. 

0.6. Briquettes of neat cement mixed i minute, in an air temperature 
between 6s and 70 degrees Fahrenheit and using water of about the same tem- 
perature, and put into the molds with fingers and trowel and kept in moist air 
at this temperature for i day of 24 hours, shall show an average tensile 
strength of one hundred and seventy-five (175) pounds per square inch. 

Briquettes of neat cement mixed and molded as above and kept under 
above temperature for i day in moist air and 6 days in water shall show 
an average tensile strength of at least five hundred (500) pounds per square 
inch. 

Briquettes of neat cement mixed and molded as above and kept under 
above temperature for i day in moist air and 27 days in water shall show an 
average tensile strength of six hundred (600) pounds per square inch. 

Briquettes of 3 parts by weight of standard Ottawa sand and i part by 
weight of cement, mixed in the same manner as above and kept 7. days 
under the same conditions, shall show an average tensile strength of at least 
two hundred pounds (200) per square inch. 

Briquettes of sand and cement mixed and molded as above and kept 
under above conditions for 28 days shall show an average tensile strength of 
at least two hundred and seventy-five (275) pounds per square inch. 

In the above tests for tensile strength the briquettes must not show 
any retrogression in strength within the periods specified. 

0.7. The Commission of Highways may cause chemical tests, or analyses, 
of cement to be made, and may reject any cement which shows any adultera- 
tion, or excess of ingredients, which in its judgment would be detrimental 
to the work. 

The cement shall not contain more than 1.75 % of anhydrous sulphuric 
acid (SO3) nor rnore than 4% of magnesia (MgO). 

0.8. The specific gravity of the cement after ignition to a low red heat 
shall not be less than 3' 10; and the cement shall not show a loss in weight 
on ignition of more than 4 %. 

0.9. The standard sand used in the tests shall be natural sand from 
Ottawa, 111., screened to pass a No. 20 standard sieve of 400 meshes per 
square inch and be retained on a No. 30 standard sieve of 900 meshes per 
square inch. 

Water for Concrete 

Water for concrete must be clean and pure, free from silt or animal or 
vegetable wastes; it must not be oily or show either a strong acid or alkaline 
reaction when tested with litmus paper. (It ought to be fit to drink. A 
practical test is to require the contractor to drink it instead of beer. This 
last clause is suggested by the Prohibition element.) 

Fine Aggregate for Concrete 

o.io. Fine aggregate shall consist of sand free from organic matter; 
that which shows a coating on the grains shall not be used until satisfactorily 
washed. Sand shall be classified as No. i, No. 2 and No. 3, and Grout Sand. 

No. I Sand 

0.1 1. No. I sand shall be of the following gradation: 100 % shall pass a 
34-inch screen, not more than 20 % shall pass a No. 50 sieve; and not more 
than 6 % shall pass a No. 100 sieve. In special cases where more than 20 % 
of a sand passes a No. 50 sieve and the sand is well graded to give alow 
percentage of voids, written permission for use of the sand may be given by 
the first deputy commissioner. Sand may be rejected for this class if 
it contains more_ than 5 % of loam and silt. 

0.12. Mortar in the proportion of i part of cement to 3 parts of the sand 



MATERIALS 719 

to be tested shall develop a compressive strength at least equal to the 
strength of a similar mortar of the same age composed of the same cement 
and standard Ottawa sand. 

No. 2 Sand 

0.13. No. 2 sand shall fulfill all of the requirements for No. i sand except 
that restrictions on the percentage that will pass a No. 50 -and No. 100 
sieve shall be governed by the compressive strength of the mortar. The 
compressive strength of the mortar shall be at least equal to that obtained 
with the standard Ottawa sand. 

No. 3 Sand '^ 

0.14. Sand may be rejected for this class if it contains more than 8 % 
of loam and silt. Mortar in the proportion of i part of cement to 3 parts 
of the sand when tested shall develop a compressive strength of at least 80 % 
of the strength of a similar mortar of the same age composed of the same 
cement and standard Ottawa sand. 

Screenings 

0.15. Screenings shall not be used as fine aggregate except to the extent 
and under the restrictions given below. The division engineer shall submit 
samples to the Bureau of Tests; they must pass the required tests; their 
use must be approved in writing by the First Deputy Commissioner. 

0.16. Screenings may be substituted for a portion of the No. i, 2 and 3 
sand under the following conditions: 

The screenings shall be free from dust coating and other dirt. One 
hundred per cent, shall pass a 3'i iiich screen and not more than 6 % shall 
pass a No. 100 sieve. The compressive strength of a mortar in which the 
screenings and sand are in the proportions intended for use, shall be at least 
equal to the standard strength obtained with sand of the given class. 

Grout Sand 

0.17, Grout sand shall be a sand of which 100 % passes a No. 20 sieve, and 
not over 30 % a No. 100 sieve. - Sand may be rejected for this class if it 
contains more than 5 % of loam and silt. The grains shall be free from 
coating. 

Mortar in the proportion of i part of cement to 3 parts of the sand shall 
develop a compressive strength of at least 40 % of the strength of a similar 
mortar of the same age composed of the same cement and standard Ottawa 
sand. 

Cushion Sand 

0.18. Cushion sand shall be a sand of which 100 % passes a No. 6 sieve 
and 90 % passes a No. 20 sieve; an excessively fine sand will not be accepted 
in this class. Sand may be rejected for this class if it contains more than 
10 % of loam and silt. 

Coarse Aggregate for Concrete 

Stone 

©.19. Crushed stone for concrete shall be of hard, durable stone, tested 
by the Bureau of Tests and satisfactory to the engineer. Stone for concrete 
shall be of an approved kind and quality of rock and shall be free, before 
being crushed, from soil, mud and dust. Crushed stone for first-class con- 
crete shall be in fragments that will pass through a i3^-inch circular hole 
"and that will not pass through a 3^-inch square hole. Crushed stone for 
second-class or third-class concrete shall be in fragments that will pass 
through a 2^-inch circular hole and that will not pass through a 3<4-inch 
square hole. 



720 SPECIFICATIONS 

Gravel 

0.20. Gravel shall not be used in concrete except when it has been sub- 
mitted by the Division Engineer to the Bureau of Tests, has been approved 
by the Bureau of Tests, and its use has been approved by the First Deputy 
Commissioner in writing — and then only under the restrictions given below. 

0.21. Gravel for use in concrete pavement and first-class concrete shall 
be composed of hard, durable stone absolutely clean and free from coating. 
No gravel will be accepted that contains any disintegrated or soft stone or 
shale. Gravel containing any flat stone shall not be permitted. Gravel 
for use in second and third class concrete shall be composed of a sound, 
durable stone. It shall be clean and free from coating. It shall not contain 
more than lo % of soft stone or shale. Gravel containing a larger percentage 
of flat stone shall not be permitted. 

0.2 2. Gravel for first-class concrete shall be in particles that will pass 
through a i^^-inch circular hole and that will not pass through a '^'i-mch 
square hole. Gravel for second and third-class concrete shall be in particles 
that will pass through a 23'i-inch circular hole and that will not pass through 
a >^-inch square hole. 

0.23. Gravel mixed with mud, clay, dirt or quicksand shall be washed 
to the satisfaction of the engineer. Run of bank gravel shall not be per- 
mitted. All gravel shall be properly screened and the coarse and fine 
aggregate regularly proportioned thereafter. 

0.24. All coarse aggregate used for concrete shall be uniformly graded 
from the minimum to the maximum sizes of stone or gravel specified above 
for the several types of concrete, thus producing an aggregate in which the 
voids will be a minimum. 

Stone, Gravel, etc., for Pavements 

0.25. The sizes of all stone, gravel, etc., used under these specifications 
shall be determined by the size of screen aperture through which the stone 
will pass when revolved in a rotary screen. They shall be designated as 
follows: 

Diameter of Aperture 
Min. Max. 

^'^i-inch square Screenings 

J-l-inch square ^^-inch circular No. i 

^|-inch circular iK-inch circular No. 2 

i3^-inch circular 2f4-inch circular No. 3 

2^:4-inch circular 3^-inch circular No. 4 

0.26. Gravel shall consist of clean, spund, tough hard stone. Gravel 
shall be separated into five grades or sizes by means of a rotary screen 
having openings as specified above for broken stone. All the general speci- 
fications given below relating to broken stone shall apply to gravel, except- 
ing that gravel may contain not more than 5 % of loam, but must otherwise 
be free from dirt or foreign matter and shall be washed if so directed by the 
engineer. 

0.27. Broken slag shall be approved acid slag, clean, sound, tough, hard, 
sharp angled and weigh not less than 1800 pounds per cubic yard. If 
specified for use, it shall conform to all the general requirements for broken 
stone as specified below. 

0.28. Broken stone shall be clean and sharp angled, shall pass the standard 
tests for abrasion and toughness as adopted by the American Society for 
Testing Materials, and shall be approved by the Bureau of Tests and 
acceptable to the engineer before being used. 

0.29. Field stones, boulders, or fence stones which are crushed for macadam 
purposes shall be 6 or more inches in diameter, if consisting of rounded 
cobbles. If of the flat variety, the minimum thickness shall be 2 inches, 
which latter requirement will also apply to laminated quarry stone. 

0.30. If after trial it is found that partially developed quarries, ledges or 
other sources of supply do not furnish a uniform product, or if, for any 
reason, the product from any source, at any time, proves to be unsatisfactory 
to the engineer, said engineer may require the contractor to furnish stone 
from other sources of supply, and the contractor shall have no claim for 
increased payment on account of such requirement. 



MATERIALS 72 1 

0.31. The contractor shall furnish one or more stone crushing plants of 
type, composition, and capacity satisfactory to the engineer. The rotary . 
screens shall be provided with openings of size and shape given under 
"Stone Sizes," unless otherwise ordered by the engineer. They must be of 
sufficient length and have the proper pitch and speed of revolution to ac- 
complish complete separation of the sizes noted. 

All crushing plants installed on the work shall be fitted up with a tailing 
chute so that no stone will reach the bins other than that which passes 
through the proper screen. 

0.32. All stone must be of the required size when placed in the roadway, 
and no breaking up of stone by hammers or otherwise will be permitted 
after the stone has been placed in the work. 

0.33. In no case shall any constituent of macadam pavement be dumped 
into place in mass; the final placing shall be by shovel or by thin spreading 
such that no appreciable fall occurs. 

Filler or Binder.— ^The filler for the bottom course shall be clean, coarse 
sand or stone screenings supplemented by product of the crusher not other- 
wise used in top or bottom courses. The filler and wearing surface for the 
top course shall be of top course stone screenings and when bituminous 
binder is- used screenings must be dry, free from dust, and not larger than 
will pass a ^|-inch screen. 

BITUMINOUS MATERIALS 

Methods of Testing Bituminous Materials in the 
Laboratory of the Commission 

Preparing Laboratory Samples. — Each laboratory sample Is usually 
composed of several sarnples that have been taken to represent pne lot of 
material. The material in the separate samples is examined, and, if uniform 
in appearance, equal amounts are taken frorn each and thoroughly blended ' 
to form a sample of about one-half pint on which the complete analysis is run. 

In case of mineral bitumen, the sample received is thrown on a large 
piece of paper, pieces which are evidently foreign to the material are rejected, 
and the whole "quartered down" to a sample of about 300 grams. This is 
ground in a mortar and the analysis run on this part of the original sample. 

Water Present. — The presence of water in an oil, asphalt, or tar is deter- 
mined by putting about 40 grams of the material into a deep, seamless 
3-ounce tin box, a thermometer being suspended in the material. This 
is then heated to about 230°F. without stirring. If water is present, even 
in very small quantities, the material will froth when heated to about 2I2°F. 
The per cent, of water present is determined by heating 20 grams of the 
material in a 2-ounce seamless tin box in an oven maintained at a tempera- 
ture of 2i2°F, for an hour. The per cent, of water in mineral bitumen is 
determined in a similar manner. The loss in weight, while not absolutely 
correct, is considered as moisture. 

Homogeneity. — The homogeneity of the mixture is shown by its general 
appearance at a temperature of 77°F. when in a melted condition and when 
examined under the microscope. 

Gravity. — The gravity is determined by taking a small test tube about 
% of an inch by 3}i inches, which is accurately weighed (weight A). The 
tube is then filled with distilled water at 77°F. and weighed (weight B). 
To get the gravity of the oil, asphalt, or tar the tube is filled with the material, 
cooled to a temperature of 77°F., cut ofiE level with the top, and weighed 

Q A 

(weight C). The gravity is determined as follows: .p _ . = gravity. 

Penetration. — The penetration test is made by putting the material to 
be tested in a 3-ounce deep, seamless tin box. Melting the material at the 
lowest possible temperature, cooling in air and then placing the material 
in a bath, for one hour, maintained at the temperature at which the test 
is to be made._ The penetration is the distance expressed in hundredths of a 
centimeter which a standard needle under a stated load, and at a stated tem- 
perature, will penetrate into the material. The factors usually employed 
are a No. 2 sewing needle, loaded with 100 grams, applied for five seconds 
at a temperature of 77°F. 

Residue Having a Penetration of 10 Millimeters. — This test is made as 
follows: so grams of the oil are placed in a 3-ounce deep, seamless tin box, 
the box placed in a sand bath and heated over a Bunsen Burner. A ther- 



72 2 SPECIFICATIONS 

mometer is suspended in the oil, the bulb not touching the bottom of the box. 
The temperature of the oil is kept at from 48o°F. to SOO^F. and the oil is 
stirred from time to time with the thermometer to prevent overheating 
in any part. Depending upon the nature of the oil, as usually indicated 
by Its flash, consistency at 77°F. and gravity, the operator can tell about 
what per cent, it will be necessary to evaporate before cooling and taking a 
penetration as described under the test for penetration. It is sometimes 
necessary to make several trials before the desired result is obtained. When 
the required penetration is reached, the residue left from evaporation is 
weighed and its per cent, of the original sample taken is computed. 

Ductility. — The ductility of an asphalt cement or bitumen is determined 
by the distance in centimeters that a briquette of the material will draw 
out before breaking. The briquette of the asphalt cement is molded in a 
Dow briquette mold having a central cross-section i centimeter square a 
2-square centimeter cross-section at mouth of clips, and a distance of 3 
centimeters between clips. The molding of the briquette is done as follows: 
The mold is placed on a brass plate. To prevent the asphalt cement from 
adhering to this plate and the inner sides of the two pieces of the rnold, they 
shall be well amalgamated. The asphalt cement to be tested is poured 
into the mold while m a molten state, a slight excess being added" to allow 
for shrinkage on cooling. After the asphalt cement is nearly cooled, the 
briquette is smoothed off level by means of a hot spatula. When it is 
thoroughly cooled to the temperature at which it is desired to make the 
test, the clamp and the two side-pieces are removed, leaving the briquette 
of asphalt cement held at each end by the ends of the mold which serve 
as clips. The test is made by pulling the two clips apart at a uniform 
rate of S centimeters per minute by means of hooks inserted in the eyes, 
until rupture occurs. ^ The briquette is kept in water at 77°F. for at least 
30 minutes before testing, and the test is performed while the briquette is 
so immersed in the water at the above temperature, and at no time is the 
^temperature (of the water allowed to vary more than half a degree from 
the standard temperature. 

Toughness. — The bitumen is heated until liquid; it is then poured into an 
amalgamated brass mold of such shape as to give a cylinder of the bitumen 
i^i inches in height by i^^ inches in diameter. After cooling, the mold is 
removed and the cylinder of bitumen is placed in a mixture of finely crushed 
ice and water, giving a temperature of zero degrees centigrade. After re- 
maining in the freezing mixture for about three hours the cylinders are broken 
in a Page impact machine (the standard machine of the American Society 
for Testing Materials for determining the toughness of macadam stone). 
When the cylinder to be broken is placed in the impact machine a piece of 
linen cloth about one inch square is placed on the end on which the plunger 
rests. ^ This prevents the plunger from sticking to the bitumen and makes 
it easier to clean the machine. In making the test, the first drop of the 
hammer is from a height of five centimeters, and for each succeeding blow 
the height of the drop is increased five centimeters. The height from which 
the hammer falls when rupture occurs is given as the toughness of the 
material. 

Melting Point of Bitumen. — The melting or softening point of bitumen is 
determined by filling a ring ^ inch in diameter by ^'i inch in depth, with 
the bitumen to be tested. After cooling, the bitumen is cut off level with 
the top of the ring. The ring containing the bitumen is placed in water at 
41 °F. for 20 minutes before making the test. In performing the test the 
ring is put in a support so placed that the bottom of the ring is i inch above 
the bottom of an 800 cc. beaker. On the center of the bitumen in the ring, 
is placed a ^^-inch steel ball, a thermometer being placed with its bulb on a 
level with the ring containing the bitumen. The beaker is nearly filled with 
water at a temperature of 4i°F. and the temperature raised at the rate of 8°F. 
to io°F. per minute. The temperature recorded by the thermometer at 
the time the ball touches the bottom of the beaker is taken as the melting 
point of the bitumen. 

Evaporation. — Fifty grams of the material are weighed into a flat-bottomed 
dish 2^6 in. in diameter by 1% in. in depth. This is placed in an oven 
maintained at a uniform temperature of 32S°F. for a period of five hours. 
At the end of this period the loss in weight or per cent, of loss is found by 
reweighing. 

Flash. — About 40 grams of the material to be tested are placed in a 3- 
ounce deep, seamless tin box. The box containing the material is placed 



i 



MATERIALS 723 

on a sand bath over a Bunsen Burner, the bulb of a thermometer being 
placed in the material, but so adjusted as not to touch the bottom of the box. 
The flame of the Bunsen burner is so adjusted that the temperature of the 
material being tested is raised at the rate of lO^F. to IS°F. per minute. As 
soon as vapors are seen coming off, the small flame from a capillary tube is 
passed over the center of the liquid and about 34 inch above it, and repeated 
for about every 5°F. rise in temperature until the slight explosion indicates 
the flash-point is reached. The temperature at this point is recorded as 
the open flash-point of the material being tested. 

Total Bitumen. — The solubility in C S2 is found by weighing approximately 
I gram of the material into an Erlenmeyer flask, adding 50 cc. of C 52 and 
allowing the solvent to act 12 hours at laboratory temperature, care being 
taken to break up all lumps before filtering. The filtration is made through 
a C. S. & S. 9-centimeter filter paper No. 589. The papers are first dried, 
and weighed immediately before using. The filtration is made in a valve 
funnel, a watch glass being placed on the funnel to prevent evaporation of 
the solvent. After washing until washings come clean, the filter and residue 
are placed in an oven at 2i2°F. for 30 minutes, cooled in a desiccator and 
weighed. The difference in weight gives the amount of material insoluble 
in C 52 from which the per cent, of soluble bitumen is computed. ^ 

The total bitumen in mineral bitumen is determined by weighing about 
25 grams of the dried material into a dried and weighed C. S. & S. extraction 
cartridge and extracting in a continuous extraction apparatus, using C 52 for 
a solvent; drying and weighing after extraction is completed. The loss gives 
the amount of bitumen soluble in C S2. 

Carbon Tetrachloride Solubility. — This test is made in the same manner 
as determining the bitumen soluble C 52, except that C C /4 is used as solvent. 

Naphtha Solubility. The amount of material soluble in 76° naphtha 
(boiling point 140^. to i90°F.) is found by the same method that is used 
in getting the amount soluble in C S2, except that naphtha is used for a 
solvent in place of C 52. The character of the filtrate is determined by 
placing about 10 cc. of the filtrate in the tin covers of the 2-ounce boxes 
used in making the heating tests and allowing the filtrate to evaporate. 
The residue is noted to be sticky or oily by rubbing between the fingers. 

Water Soluble Materials.7- Water soluble materials in tar are determined 
by weighing about 2 grams into a casserole, adding 50 cc. of distilled water, 
and boiling for i hour. The solution is then filtered into a weighted porcelain 
evaporating dish, using hot distilled water for a wash and evaporated to 
dryness on a steam bath. The weight at the evaporating dish and contents 
after drying to a constant weight at 2i2°F., less the weight of the dish itself, 
gives the amount of water soluble materials in the tar, from which the per 
cent, may be calculated. 

Free Carbon. — Thelfree carbon in tar is determined by extraction at room 
temperature with C S2. In extraction C 52 is used in the same manner as 
making the determination for the amount of bitumen soluble in C S2 in 
asphalts. Determination as to whether extraction is complete is made by 
placing some of the carbon on white porcelain, moistening it with C S2, and 
if the porcelain is stained the extraction is not complete, and the carbon 
requires more washing. 

Paraflfine. — Fifty grams of the material are placed in a half-pint retort, 
E. & A. No. 4521, fitted with a tee condenser. To the 20-inch iron delivery 
tube of the retort is attached a lo-inch glass tube, and between the cover and 
the retort is placed a paper gasket cut from heavy wrapping-paper. The 
material is rapidly distilled to a dry coke from which no further distillate 
can be obtained, not over 25 minutes being allowed from the time of placing 
flame under retort until distillation ceases. About 5 grams of the distillate 
are taken if the materials contain 2 per cent, or less of parafl&ne and about 
3 grams if the material contains over 2 per cent, of paraffine. This amount 
of distillate is dissolved in 25 cc. of Squibbs Absolute Ether in a 2-ounce 
glass flask, after which 25 cc. of Squibbs Absolute Alcohol are added. A 
one-to-one wash of 25 cc. each of similar ether and alcohol is made up, and 
the solution of oil and the wash are then frozen separately for 40 minutes in 
a salt and ice mixture, giving a temperature of o^F. The precipitate is 
filtered quickly by means of a suction pump by using a No. 575 C. S. & S. 
9-centimeter hardened filter-paper; the paper being placed in a funnel packed 
in a freezing mixture of salt and ice. The paraffine caught on the filter- 
paper is washed with the cool one-to-one wash until the paraffine is white. 
The paraffine is then scraped into a weighted crystallizing dish and main- 



724 SPECIFICATIONS 

tained at a temperature of 2i2''F. until a constant weight is obtained, after 
which it is weighed and the percentage of paraffine in the original material 
is computed by dividing the weight of the paraffine obtained by the number 
of grams of distillate taken for freezing, and multiply this result by the per- 
centage distilled from the original sample (i.e., by lOO per cent, less weight 
of coke expressed in percentage). The paraffine so determined to have a 
melting point of at least I20°F. 

The melting-point of paraffine is determined by covering the bulb of a 
thermometer with the paraffine; suspending the thermometer in a beaker 
of water at 65''F., and heating the water at the rate of 8° to io**F. per 
minute. The temperature recorded by the thermometer at the time the 
paraffine melts from the bulb is taken as the melting-point of the paraffine. 

Distillation of Tar. — The distillation test of tar is made by measuring 
100 cubic centimeters of the tar into a 250 cc. Engler distilling flask with 
delivery tube at the middle of the neck. The thermometer is so placed that 
the mercury bulb is opposite the outlet of the flask._ The thermometer used 
to have a nitrogen chamber to insure accurate reading at high temperatures. 
The flame is so regulated that approximately i cc. of distillate is caught per 
minute. The distillation is made continuous. 

The following fractions should be reported: 

Start of distillation to iio^C. 
iio°C. '* i70*C. 
i70°C. " 235°C. 
235°C. " 27o''C. 
270°C. '* 300°C, 
Residue (pitch) 

Fixed Carbon and Mineral Matter. — The fixed carbon is determined by 
weighing approximately i gram of the material into a weighed platinum 
crucible with a tightly fitting cover. The crucible, with its cover in place, 
is then placed about 4 inches over a freely burning Bunsen burner so as to 
be completely enveloped in the flame and exposed to the full heat of the 
burner for about 3 minutes or until the top of the crucible cover is burned 
free from the carbon; the under side of the cover being covered with the 
carbon. The flame is then withdrawn, the crucible cooled and weighed. 
The weight after burning, less the weight of the crucible, gives the amount 
of fixed carbon plus the mineral matter. The fixed carbon is then burned 
off in the open crucible until a constant weight is obtained; the crucible 
cooled and weighed. This weight is the crucible plus the mineral matter. 
The mineral matter subtracted from the combined weight of fixed carbon 
and mineral matter gives the fixed carbon. 

Items 64 to 74 Inclusive — Bituminous Materials 

64.1. Under items 64 to 74 inclusive the Contractor shall furnish and 
deliver on the work at such points as the Engineer may direct, bituminous 
material of the kind shown on the proposal sheet as to be furnished under 
its respective item. 

64.2. Bituminous material furnished shall be of approved quality and 
shall meet the requirements specified below for the kind of material furnished, 
and for any contract, the material furnished shall be of one brand and shall 
show a uniform test unless special permission is given to furnish other brands 
of material. 

64.3. The quantity to be paid for under this item shall be the number of 
gallons delivered on the work, unless the material is to be incorporated in 
the work by the same Contractor, and under the same contract. 

If the material is to be incorporated in the work by the same Contractor, 
and under the same contract, the quantity to be paid for under this item 
shall be the number of gallons incorporated in the work under directions of 
the Engineer. 

Bituminous material that has been rendered unfit for use by overheating 
or by long-continued heating, shall not be paid for. For purposes of meas- 
urement, a gallon shall be a volume of 231 cubic inches and measurement 
shall be based on the volume of the bituminous material of a temperature 
of 60 degfrees Fahrenheit. 

The price bid when the material is not to be incorporated in the work 
under this contract, shall include the furnishing of the material along the 
road as directed by the Engineer. Any material wasted through careless 
handling will not be paid for. 



MATERIALS 725 

The price bid shall include the furnishing of the bituminous material 
alongside the road at places designated by the Engineer. ^ Where the material 
delivered is to be incorporated into the work under this contract, the cost 
of manipulating and incorporating this material shall be included in the 
price bid for the top course of the pavement being constructed. 

Item 64 — Specification for Bituminous Material A 

Mixing Method (Type i) (Open Mix) 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in a homoge- 
neous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of not less 
than 0.97- 

(4) The penetration shall be between 8 and 12 millimeters when tested for 
S seconds at 77 degrees Fahrenheit with a No. 2 needle, weighted with 100 
grams. 

(5) Fifty grams of it upon being maintained at a uniform temperature of 
325 degrees Fahrenheit for 5 hours in a cylindrical vessel 53^^ centimeters in 
diameter by 3}^^ centimeters high shall not lose more than 4 per centum in 
weight. The penetration (5 seconds, 77 degrees Fahrenheit, No. 2 needle, 
100 grams weight) of this residue shall be at least 50 per centum of the original 
penetration. 

(6) Its solubility at air temperature in chemically pure carbon disulphide 
for the following named materials, or materials similar thereto, shall be at 
least 99.5 per centum for pure bitumen products, 96 per centum for Bermudez 
products, 81 per centum for Cuban products and 66 per centum for Trinidad 
products. 

(7) The solubility of the bitumen at air temperature, in 76 degrees Beaum^ 
paraffine petroleum naphtha distilling between 140 degrees and 190 degrees 
Fahrenheit, shall be between 68 and 88 per centum. 

(8) The bitumen shall show between 8 and 17 per centum fixed carbon. 

(9) It shall show an open flash point not less than 375 degrees Fahrenheit. 

(10) It shall not contain more than 4.7 per centum paraffine scale. 

(11) It shall show a toughness at 32 degrees Fahrenheit not less than 10 
centimeters. Toughness is determined by breaking a cylinder of the mate- 
rial i^i inches in diameter by i^^ inches in height in a Page impact machine. 
(American Society of Testing Materials, August 15, 1908). The first drop 
of the hammer is from a height of 5 centimeters and each succeeding blow 
is increased by s centimeters. 

(12) Jt shall have a ductility at 77 degrees Fahrenheit of not less than 
25 centimeters (Dow mould) .^ 

(13) All bituminous material A. will be sampled by an Engineer of the 
Department of Highways and samples sent to the Bureau of Tests, Albany, 
N. Y. 

Item 65 — Specification for Bituminous Material A 

Mixing Method (Type No. 2) (Topeka Mix) 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in a homoge- 
neous solution. ^ ^ -— 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of not less 
than 0.97. 

(4) The penetration shall be between 6 and 8 millimeters when tested 
for 5 seconds at 77 degrees Fahrenheit with a No. 2 needle, weighted with 
100 grams. 

(5) Fifty grams of it being upon maintained at a uniform temperature of 
325 degrees Fahrenheit for 5 hours in a cylindrical vessel, 53^ centimeters 
in diameter by 3^-2 centimeters high shall not lose more than 4 per centum 
in weight. The penetration (5 seconds, 77 degrees Fahrenheit, No. 2 needle, 
100 grams weight) of this residue shall be at least 50 per centum of the original 
penetration. 

(6) Its solubility at air temperature in chemically pure carbon disulphide 



726 SPECIFICATIONS 

for the following named materials, or materials similar thereto, shall be at 
least 99.5 per centum for pure bitumen products, 96 per centum for Bermu- 
dez products, 81 per centum for Cuban products and 66 per centum for 
Trinidad products. 

(7) The solubility of the bitumen at air temperature, in 76 degrees Beaum^ 
paraffine petroleum naphtha distilling between 140 degrees and 190 degrees 
Fahrenheit shall be between 68 and 88 per centum. 

(8) The bitumen shall show between 8 and 17 per centum fixed carbon. 

(9) It shall show an open flash point not less than 375 degrees Fahrenheit. 

(10) It shall not contain more than 4.7 per centum paraffine scale. 

(11) It shall show a toughness at 32 degrees Fahrenheit not less than 5 
centimeters. Toughness is determined by breaking a cylinder of the mate- 
rial 1^4 inches in diameter by i^i inches in height in a Page impact machine. 
(American Society of Testing Materials, August 15, 1908.) The first drop 
of the hammer is fr9m a height of 5 centimeters and each succeeding blow is 
increased by 5 centimeters. _ _ 

(12) It shall have a ductility at 77 degrees Fahrenheit of not less than 25 
centimeters (Dow mould). 

(13) All bituminous material A. will be sampled by an Engineer of the 
Department of Highways and samples sent to the Bureau of Tests, Albany, 
N. Y. 

Item 66 — Specification for Bituminous Material A 

Penetration Method 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in a homo- 
geneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of not less 
than 0.97. 

(4) The penetration shall be between 14 and 19 millimeters when tested 
for 5 seconds at 77 degrees Fahrenheit with a No. 2 needle, weighted with 
100 grams. 

(5) Fifty grams of it upon being maintained at a uniform temperature 
of 325 degrees Fahrenheit for 5 hours in a cylindrical vessel 5^^ centimeters 
in diameter by 3>^ centimeters high shall not lose more than 5 per centum 
in weight. The penetration (5 seconds, 77 degrees Fahrenheit, No. 2 needle, 
100 grams weight) of this residue shall be at least 50 per centum of the origi- 
nal penetration. 

(6) Its solubility at air temperature in chemically pure carbon disulphide 
for the following named materials, or materials similar thereto, shall be at 
least 99-5 per centum for pure bitumen products, 96 per centum for Bermudez 
products, 81 per centum for Cuban products and 66 per centum for Trinidad 
products. 

(7) The solubility of the bitumen at air temperature, in 76 degrees Beaum6 
paraffine petroleum naphtha distilling between 140 degrees and 190 degrees 
Fahrenheit shall be between 70 and 88 per centum. 

(8) The bitumen shall show between 8 and 16 per centum fixed carbon.^ 

(9) It shall show an open flash point not less than 375 degrees Fahrenheit. 

(10) It shall not contain more than 4.7 per centum paraffine scale. 

(11) It shall show a toughness at 32 degrees Fahrenheit not less than 15 
centimeters. Toughness is determined by breaking a cylinder of the mate- 
rial i^^ inches in diameter by i^^ inches in height, in a Page impact machine. 
(American Society of Testing Materials, August 15, 1908.) The first drop 
of the hammer is from a height of 5 centimeters and each succeeding blow is 
increased by 5 centimeters. 

(12) It shall have a ductility at 77 degrees Fahrenheit of not less than 40 
centimeters (Dow mould). 

(13) All bituminous material A. will be sampled by an Engineer of the 
Department of Highways, and samples sent to the Bureau of Tests Albany, 
N. Y. 

Item 67 — Specification for Bituminous Material H. O. (Surface application) 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 



MATERIALS 727 

(2) The various hydrocarbons composing it shall be present in a homo- 
geneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of not less 
than 0.96. 

(4) When evaporated in the open air at a temperature not exceeding 500 
degrees Fahrenheit until the residue remaining has a penetration (5 seconds, 
77 degrees Fahrenheit, No. 2 needle, 100 grams weight) of 10 millimeters 
the amount of such residue shall not be less than 85 per centum nor more 
than 95 per centum of the original oil. At a temperature of 77 degrees 
Fahrenheit such residue shall have a ductility of at least 25 centimeters 
(Dow mould). 

(5) Fifty grams of it upon being maintained at a uniform temperature 
of 32s degrees Fahrenheit for five hours, in a cylindrical vessel 5^ centi- 
meters in diameter by 3}^ centimeters high, shall not lose more than 10 per 
centum in weight. 

(6) It shall be soluble in chemically pure carbon disulphide at air tem- 
perature to the extent of at least 99.5 per centum. 

(7) It shall be soluble at air temperature in 76 degrees Beaum6 paraffine 
petroleum naphtha distilling between 140 degrees and 190 degrees Fahren- 
heit to the extent of not less than 75 per centum and not more than 90 per 
centum. 

(8) It shall show between 6 and 14 per centum of fixed carbon. 

(9) It shall show an open flash point of not less than 325 degrees Fahren- 
heit. 

(10) It shall not contain more than 4.7 per centum paraffine scale. 

(11) It shall show a toughness at 32 degrees Fahrenheit not less than 20 * 
centimeters. Toughness is determined by breaking a cylinder of the mate- 
rial i^^ inches in diameter by i^^ inches in height in a Page impact machine. 
(American Society of Testing Materials, August 15, 1908.) The first drop 
pf the hammer is from a height of 5 centimeters and each succeeding blow 
is increased by 5 centimeters. 

(12) All bituminous material H. O. will be sampled by an Engineer of the 
Department of Highways, and samples sent to the Bureau of Tests, Albany, 
N. Y. 

Item 68 — Specification for Bituminous Material C. O. (Surface application) 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 

(2) The various hydrocarbons composing it shall be present in a homo- 
geneous solution. 

(3) It shall have a specific gravity at 77 degrees Fahrenheit of not less 
than 0.93. 

(4) When evaporated in the open air at a temperature not exceedmg 500 
degrees Fahrenheit until the residue remaining has a penetration (5 seconds, 
77 degrees Fahrenheit, No. 2 needle, 100 grams weight) of 10 millimeters 
the amount of residue shall not be less than 50 per centum nor more than 
6s per centum of the original oil. At a temperature of 77 degrees Fahren- 
heit such residue shall have a ductility of at least 25 centimeters (Dow 
mould). 

(5) Fifty grams of it upon being maintained at a uniform temperature 
of 325 degrees Fahrenheit for five hours, in a cylindrical vessel sH centi- 
meters in diameter by 3}^ centimeters high, shall not lose more than 30 per 
centum in weight. 

(6) It shall be soluble in chemically pure carbon disulphide at air tem- 
perature to the extent of at least 99-5 per centum. 

(7) It shall be soluble at air temperatnre in 76 degrees Beaum6 paraffine 
petroleum naphtha distilling between 140 and 190 degrees Fahrenheit to the 
extent of not less than 80 per centum and not more than 95 per centum. 

(8) It shall not show more than 10 per centum fixed carbon. 

(9) It shall show an open flash point of not less than 125 degrees 
Fahrenheit. 

(10) It shall not contain more than 4.0 per centum paraffine scale. 

(11) All bituminous material C. O. will be sampled by an Engineer of the 
Department of Highways, and samples sent to the Bureau of Tests, Albany, 
N. Y. 



728 SPPXIFICATIONS 



Item 69 — Specification for Bituminous Material T 

High Carbon — Binder for Bituminous Macadam 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 

(2) It shall be uniform in character, appearance, and viscosity. 

(3) It shall have a specific gravity of not less than 1.20 at 25 degrees 
centigrade. 

(4) It shall contain not more than 25 per centum nor less than 12 per 
centum of free carbon. 

(5) When distilled by the method of the American Society for Testing 
Materials, it shall contain no body that distils at a lower temperature than 
170 degrees Centigrade; not over 3 per centum shall distil below 235 degrees 
Centigrade; not over 12 per centum shall distil below 270 degrees Centigrade. 
and not over 16 per centum shall distil below 300 degrees Centigrade. The 
specific gravity of the entire distillate shall not be less than 1.03 at 25 degrees 
Centigrade. The residue from the foregoing distillation shall have a melting 
point not greater than 75 degrees Centigrade ball and ring method. 

(6) It shall have a melting point of not less than 27 degrees C, and not 
more than 34 degrees C, by ball and ring method. 

(7) All bituminous material T. will be sampled by an Engineer of the 
Department of Highways and samples sent to the Bureau of Tests, Albany, 
N. Y. 

Item 70 — Specification for Bituminous Material T 

High Carbon — Hot Application, Surface Application 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 

(2) It shall be uniform in character, appearance and viscosity. 

(3) It shall have a specific gravity not less than 1.19 at 25 degrees 
Centigrade. 

(4) It shall contain not more than 22 per centum nor less than 10 per 
centum of free carbon. 

(5) When distilled by the method of the American Society for Testing 
Materials, it shall contain no body that distils at a lower temperature 
than 170 degrees Centigrade, not over 10 per centurn shall distil below 235 
degrees Centigrade; not over 16 per centum shall distil below 270 degrees 
Centigrade and not over 20 per centum shall distil below 300 degrees Centi- 
grade. The specific gravity of the entire distillate shall not be less than 1.03 
at 2 5 degrees Centigrade. The residue from the foregoing distillation shall 
have a melting point not greater than 75 degrees Centigrade ball and ring 
method. 

(6) It shall have a float test (New York Testing Laboratory method) at 
100 degrees Centigrade between eighteen and twenty-eight seconds. 

(7) All bituminous material T. will be sampled by an Engineer of the 
Department of Highways, and samples sent to the Bureau of Tests, Albany, 
N. Y. 

Item 71 — Specification for Bituminous Material T (Surface Treatment) 
High Carbon — Cold Application 

This bituminous material shall have the following characteristics: 

(i) It shall have a specific gravity of 1.14 to 1.18 at 25 degrees Centigrade. 

(2) It shall contain not more than 12 per centum nor less than 4 per 
centum of free carbon. 

(3) When distilled by the method of the American Society for Testing 
Materials, not over 5 per centum shall distil below 170 degrees Centigrade; 
not over 18 per centum shall distil below 235 degrees Centigrade; not over 
25 per centum shall distil below 270 degrees (Centigrade, arid not over 32 per 
centum shall distil below 300 degrees Centigrade. The specific gravity of 
the entire distillate shall not be less than i.oi at 25 degrees Centigrade. The 
residue from the foregoing distillation shall have a melting point not greater 
than 70 degrees Centigrade ball and ring method. 

(4) The viscosity when tested by the standard Engler viscosimeter shall 
not be more than 125 seconds at 60 degrees Centigrade for the first 100 cubic 
centimeters. 



MATERIALS 729 

(S) All bituminous material T. will be sampled by an Engineer of the 
Department of Highways, and samples sent to the Bureau of Tests, Albany, 
N. Y. 

Item 72 — Specification for Bituminous Material T (Bituminous Macadam) 
Low Carbon — Binder 

This bituminous material shall have the following characteristics: 
(i) It shall be free from water. 

(2) It shall be uniform in character, appearance and viscosity. 

(3) It shall have a specific gravity not less than 1.16 at 25 degrees 
Centigrade. 

(4) It shall contain not more than 5 per centum free carbon. 

(5) When distilled by the method of the American Society for Testing 
Materials, it shall contain no body that distils at a lower temperature than 
170 degrees Centigrade; not over 5 per centum shall distil below 235 degrees 
Centigrade; not over 15 per centum shall distil below 270 degrees Centigrade; 
not over 20 per centum shall distil below 300 degrees Centigrade. The resi- 
due from the foregoing distillation shall have a melting point not greater 
than 75 degrees Centigrade ball and ring method. 

(6) It shall have a melting point of not less than 27 degrees C, and not 
more than 34 de|:rees C, by ball and ring method. 

(7) All bituminous material T. will be sampled by an Engineer of the 
Department of Highways, and samplesrsent to the Bureau of Tests, Albany, 
N. Y. 

Item 73 — Specification for Bituminous Material T (Surface Treatment) 
Low Carbon — Hot Application 

This bituminous material shall have the following characteristics : 
(i) It shall be free front water. 

(2) It shall be uniform in character, appearance and viscosity. 

(3) It shall have a specific gravity of not less than 1.14 at 25 degrees 
Centigrade. 

(4) It shall contain not more than 4 per centum of free carbon. 

(5) When distilled by the method of the American Society for Testing 
Materials, not over i per centum shall distil below 170 degrees Centigrade; 
not over 12 per centum shall distil below 235 degrees Centigrade; not over 
20 per centum shall distil below 270 degrees (Centigrade, and not over 25 
I>er centum shall distil below 300 degrees Centigrade. The residue from the 
foregoing distillation shall have a melting point not greater than 75 degrees 
Centigrade ball and ring method. 

(6) It shall have a float test (New York Testing Laboratory method) at 
100 degrees Centigrade between fifteen and twenty-five seconds. 

(7) AH bituminous material T. will be sampled by an Engineer of the 
Department of Highways, and samples sent to the Bureau of Tests, Albany , 
N. Y. 

Item 74 — Specification for Bituminous Material T (Surface Treatment) 
Low Carbon — Cold Application 

This bituminous material shall have the following characteristics : 

(i) It shall have a specific gravity of i.io to 1.13 at 25 degrees Centigrade. 

(2) It shall contain not more than 2 per centum of free carbon. 

(3) When distilled by the method of the American Society for Testing 
Materials, not over 5 per centum shall distil below 170 degrees Centigrade; 
not over 20 per centum shall distil below 235 degrees Centigrade; not over 
28 per centum shall distil below 270 degrees Centigrade, and not over 35 
per centum shall distil below 300 degrees Centigrade. The residue from the 
foregoing distillation shall have a melting point not greater than 70 degrees 
Centigrade ball and ring method. • 

(4) The viscosity when tested by the standard Engler viscosimeter shall 
not be more than 125 seconds at 60 degrees Centigrade for the first 100 cubic 
centimeters. 

(5) All bituminous material T. will be sampled by an Engineer of the 



730 SPECIFICATIONS 

Department of Highways, and samples sent to the Bureau of Tests, Albany, 
N. Y. 

Bituminous Material -for Mastic fillers of Block Pavements (see page 789). 

BRICK 

Paving brick shall be reasonably perfect in shape— shall be free from 
marked warping or distortion, and shall be uniform in size, so as to fit closely 
together and to make a smooth pavement. All brick shall be homogeneous 
in texture and free from laminations and seams. All brick shall be evenly 
burned and thoroughly vitrified. 

Soft, brittle, cracked, or spalled brick, or brick kiln-marked to a height or 
depth of over %4 part of an inch will be rejected. 

If brick have rounded corners, the radius shall not be greater than He 
part of an inch. 

Brick must have not less than two nor more than four vertical lugs or 
projections not more than K inch wide, on one side of each brick, the total 
area of all lugs being not more than 3 square inches, so that when laid there 
shall be a separation between the bricks of at least 3^^ inch and not more than 
J^ inch. The imprint, or name of the brick, or maker, if used, shall be by 
means of recessed and not by raised letters. The two ends of the brick shall 
have a semi-circular groove, with a radius of not less than 3^ of an inch and 
not more than ^i of an inch. Grooves shall be so located that when the 
brick is laid together the grooves shall match perfectly; grooves shall be 
horizontal when brick is laid in pavement. 

All brick shall not be less than 3>:i" X 3^" X 83^" nor more than 3K"iX 
4" X 9" in size. 

All brick shall be subject to tests for abrasion and impact, for absorption, 
according to the standard methods prescribed by the National Brick Manu- 
facturers* Association, as follows: 

THE RATTLER 

The machine shall be of good mechanical construction, self-contained, and 
shall conform to the following details of material and dimensions, and shall 
consist of barrel, frame and driving mechanism as herein described. 

THE BARREL 

The barrel of the machine shall be made up of the heads, headliners and 
staves. 

The heads shall be cast with trunnions in one piece. The trunnion bear- 
ings shall not be less than two and one-half (2>^) inches in diameter or less 
than six (6) inches in length. 

The heads shall not be less than three-fourths (%) Inch thick nor more 
than seven-eighths (J-i) inch. In outline they shall be a regular fourteen- 
sided (14) polygon inscribed in a circle twenty-eight and three-eighths (28%) 
inches in diameter. The heads shall be provided with flanges not less than 
three-fourths (f^) inch thick and extending outward two- and one-half {2}^) 
inches from the inside face of head to afford a means of fastening the staves. 
The flanges shall be slotted on the outer edge, so as to provide for two (2) 
three-fourths (^i) inch bolts at each end of each stave, said slots to be thir- 
teen-sixteenths (^^e) inch wide and two and three-fourths (2%) inches 
center to center. Under each section of the flanges there shall be a brace 
three-eighths {%) inch thick and extending down the outside of the head 
not less than two (2) inches. Each slot shall be provided with recess for 
bolt head, which shall act to prevent the turning of the same. There shall 
be for each head a cast-iron headliner one (i) inch in thickness and con- 
forming to the outline of the head, but inscribed in a circle twenty-eight 
and one-eighth (283^) inches in diameter. This liner or wear plate shall 
be fastened to the head by seven (7) five-eighths (^i) inch cap screws, 
through the head from the outside. These wear plates, whenever they 
become worn down one-half (3^^) inch below their initial surface level, at 
any point of their surface, must be replaced with new.^ The metal of which 
these wear plates are to be composed shall be what is known as hard ma- 
chinery iron, and must contain not less than one (i) per cent, of combined 
carbon. The faces of the polygon must be smooth and give uniform bear- 
ing for the staves. To secure the desired uniform bearing the faces of the 
head may be ground or machined. 



MATERIALS 



731 










K- ^"^^.S 




'^< Jl^ 



Pig. 147. 



732 • SPECIFICATIONS 

THE STAVES 

The staves shall be made of six (6) inch medium steel structural channels 
twenty-seven and one-fourth (27K) inches long and weighing fifteen and 
five-tenths (15.5) pounds per Hneal foot. 

The channels shall be drilled with holes thirteen-sixteenths i^Hs) inch 
in diameter, two (2) in each end, for bolts to fasten same to head, the center 
line of the holes being one (i) inch from either end and one and three- 
eighths (iH) inches either way from the longitudinal center line. 

The space between the staves will be determined by the accuracy of 
the heads, but must not exceed five-sixteenths (Me) inch. The interior or 
flat side of each channel must be protected by a lining or wear plate three- 
eighths (%) inch thick by five and one-half (sj^i) inches wide by nineteen 
and three-fourths (ig^i) inches long. The wear plate shall consist of 
medium steel plate, and shall be riveted to the channel by three (3) one-half 
(^0 inch rivets, one of which shall be on the center line both ways and the 
other two on the longitudinal center line and spaced seven (7) inches from 
the center each way. The rivet holes shall be countersunk on the face of 
the wear plate and the rivets shall be driven hot and chipped off flush 
with the surface of the wear plate. These wear plates shall be inspected from 
time to time, and if found loose shall be at once reriveted, but no wear plate 
shall be replaced by a new one except as the whole set is changed. No 
set of wear plates shall be used for more than one hundred and fifty (150) 
tests under any circumstances. The record must show the date when each 
set of wear plates goes into service and the number of tests made upon 
each set. 

The staves when bolted to the heads shall form a barrel twenty (20) 
inches long, inside measurement, between wear plates. The wear plates 
of the staves must be so placed as to drop between the wear plates of the 
heads. These staves shall be bolted tightly to the heads by four (4) three- 
fourths (^i) inch bolts, and each bolt shall be provided with lock nuts, and 
shall be inspected at not less frequent intervals than every fifth (sth) test 
and all nuts kept tight. A record shall be made after each such inspection, 
showing in what condition the bolts were found. 

THE FRAME AND DRIVING MECHANISM 

The barrel should be mounted on a cast-iron frame of sufficient strength 
and rigidity to support same without undue vibration. It should rest on a 
rigid foundation and be fastened to same by bolts at not less than four 
(4) points. 

It should be driven by gearing whose ratio of driver to driven should 
not be less than one (i) to four (4). The counter shaft upon which the 
driving pinion is mounted should not be less than one and fifteen-sixteenths 
(i^Me) inches in diameter, with bearings not less than six (6) inches in 
length and belt driven, and the pulley should not be less than eighteen (18) 
inches in diameter and six and one-half (63'^) inches in face. A belt of six 
(6) inch double-strength leather, properly adjusted, so as to avoid un- 
necessary slipping, should be used. 

(As a part of this publication will be found a complete working drawing of a 
machine which will meet the above specifications and requirements.) 

THE ABRASIVE CHARGE 

(a) The abrasive charge shall consist of two sizes of cast-iron spheres. 
The larger size shall be three and se vent y-five-hundredths (3.75) inches in 
diameter when new and shall weigh when new approximately seven and 
five-tenths (7.5) pounds (3.40 kilos) each. Ten shall be used. 

These shall be weighed separately after each ten (10) tests, and if the 
weight of any large shot falls to seven (7) pounds (3.1 75 kilos) it shall be 
discarded and a new one substituted; provided, however, that all of the 
large shot shall not be discarded and substituted by new ones at any single 
time, and that so far as possible the large shots shall compose a graduated 
series in various stages of wear. 

The smaller size spheres shall be when new one and eight hundred seventy- 
five -thousandths (1,87s) inches in diameter and shall weigh not to exceed 



MATERIALS 733 

ninety-five-hundredths (0.95) pounds (0.430 kilos) each. Of these spheres 
so many shall be used as will bring the collective weight of the large and 
small spheres most nearly to three hundred (300) pounds, provided that 
no small sphere shall be retained in use after it has been worn down so that 
it will pass a circular hole one and seventy-five-hundredths (i.7S) inches in 
diameter, drilled in a cast-iron plate one-fourth (}4:) inch in thickness or 
weigh less than seventy-five-hundredths (0.75) pounds (or 0.34 kilos). 
Further, the small spheres shall be tested by passing them over such an 
iron plate drilled with such holes, or shall be weighed after every ten (10) 
tests, and any which pass through or fall below specified weight, shall be 
replaced by new spheres, and provided, further, that all of the small spheres 
shall not be rejected and replaced by new ones at any one time, and that 
so far as possible the small spheres shall compose a graduated series in 
various stages of wear. At any time that any sphere is found to be broken 
or defective it shall at once be replaced. 

(b) The iron composing these spheres shall have a chemical composition 
within the following limits: 

Combined carbon — Not less than 2.50 %. 
Graphitic carbon — Not more than o.io %. 
Silicon— Not more than i %. 
Manganese — Not more than 0.50 %. 
Phosphorus — Not more than 0.25 %. 
Sulphur — Not more than 0.08 %. 

For each new batch of spheres used the chemical analysis must be furnished 
by the maker, or be obtained by the user, before introduction into the 
charge, and unless the analysis meets the above specifications, the batch 
of spheres shall be rejected. 

THE BRICK CHARGE 

The number of brick per charge shall be ten (10) for all bricks of the so- 
called "block size" whose dimensions fall between from eight (8) to nine 
(9) inches in length, three (3) and three and three-fourths (3^) inches in 
breadth and three and three-fourths (3^) and four and one-fourth (4}^^) 
inches in thickness. No block should be selected for test that would be 
rejected by any othe» requirements for the specifications. 

The brick shall be clean and dried for at least three (3) hours in a tem- 
perature of one hundred (100) degrees Fahr. before testing. 

SPEED AND DURATION OF REVOLUTION 

^ The rattler shall be rotated at a uniform rate of not less than twenty- 
nine and one-half (293^) nor more than thirty and one-half (30^^) revolutions 
per minute, and eighteen hundred (1800) revolutions shall constitute the 
standard test. 

A counting machine shall be attached to the rattler for counting the 
revolutions. A margin of not to exceed ten (10) revolutions will be allowed 
for stopping. Only one (i) start and stop per test is regular and acceptable. 

THE RESULTS 

The loss shall be calculated in percentage of the original weight of the 
dried brick composing the charge. In weighing the rattled brick any 
piece weighing less than one (i) pound shall be rejected. 

RECORDS 

(a) The operator shall keep an official book, in which the alternate pages 
are perforated for removal. The record shall be kept in duplicate, by 
use of a carbon paper between the first and second sheets, and when all en- 
tries are made and calculations are completed the original record shall be 
removed and the carbon duplicate preserved in the book. All calculations 
must be made in the space left for that purpose in the record blank, and the 
actual figures must appear. The record must bear its serial number and be 



734 



SPECIFICATIONS 



^filled out completely for each test, and all data as to dates of inspection and 
weighing of shot and replacement of worn-out parts must be carefully entered, 
so that the records remaining in the book, constitute a continuous one. In 
event of further copies of a record being needed, they may be furnished on 
separate sheets, but in no case shall the original carbon copy be removed from 
the record book. 



RCPORT or 
standard Rattler Test of Pavlns Bricka 

Identification Data Sorial No. ( 

Name of the firm furnishing sample 

Name of the firm manufactuiing sample 

Street or job which sample represents 

Brands or marks on the brick 

Quantity furnished Drying treatment 

Date received Date tested 

Length Breadth Thickness 

Standardization Data 
Number of charges tested since last inspection 



Weigh! otChMge 


Cooditkm cf LoekMN oa Smtm 


Ce«dii(MoiteaI» 


10 Urge spheres 
Small spheres 

Total 







Number of charges tested since stave linings were renewed 
Repairs (Note any repairs affecting the condition of the barrel) 
Running Data 



Time ReidiBg* 




RiuuMS Mom. Smp.. Etc 




Hour* 


Miaatet 


Stcaod* 






Beginning of test » » <« 
Final Reading * ^^ ^ „ 











^Veighta and Calcui€rtlon» 




Number of broken bricks and remarks on same 

I certify chat the foregoing test was made under the specifications 



of 



and is a true record. 



8inutufeo( 



location of Laboratory 

Fig. 148. 



(b) The blank form upon which the record of all official brick tests is 
to be kept and reported is shown in Fig. 148. 

Any brick which loses twenty-four (24) per cent, or more in the rattler, or in- 
creases more than 3^^ % in weight or less than 3^ of i % in the absorption 
test, will be rejected. 



MATERIALS 735 

HILLSIDE BRICK 

On grades of five (5 %) per cent, or over the engineer may, if he deems 
advisable for the traffic, order the contractor to use special form of brick 
suitable for steep grades. 

Expansion Joint Paving Pitch. — This cushion shall be composed of heavy- 
pitch or asphaltum composition, having a melting point of not less than 
120° F. nor more than i40°F., filling the allotted space. 

PREMOLDED EXPANSION JOINT 

The expansion joints shall be composed of a high grade asphalt, that shall 
pass the following tests: 

Specific gravity at 77°F.. 0.98 to 1.05. 
Melting point, ball and ring method, 220" to 250°F. 
Loss on heating for 5 hours at 32 5°F., not over i %. 
Bitumen soluble in carbon disulphide, at least 98.5 %. 
Bitumen soluble in carbon tetrachloride, at least 99.8 %. 
Bitumen soluble in 76° Beaum6 naphtha, 50 to 75 %. 
Penetration at 32° F. 200 grams, i min., at least 12. 
Penetration at 77° F. 100 grams, 5 sec. between 15 and 35. 
Penetration at 115° F. 50 grams, 5 sec. not more than 45. 

BLOCK STONE PAVEMENT 

(City of Rochester, N. Y., Specifications, 1911) 

Paving blocks shall consist of the best quality of Medina sandstone 
free from quarry checks or cracks, and shall be quarried from fine-grain 
live rock, showing a straight and even fracture. The material shall be of 
uniform quality and texture, free from seams or lines of clay or other sub- 
stances which, in the opinion of the City Engineer, will be injurious to its 
use as paving material. 

Blocks shall measure not less than three (3) nor more than six (6) inches 
thick, and not less than six (6) nor more than six and one-half (6^) inches 
deep, and from seven (7) to twelve (12) inches in length. Stones to have 
parallel sides and ends, and right-angle joints. All roughness in joints of 
stone to be broken off, ^o that when set in place they shall have tight joints 
for a distance of at least two and one-half (2 3'^) inches from the top down. 
The top to have a smooth^ even surface, with no projection or depression 
exceeding one-quarter (H) inch. 

When approved by the City Engineer, paving blocks of the following 
dimensions may be used. 

Three to five inches in width; five inches in depth, with an allowable 
variation of one-quarter inch, more or less, in said depth, and seven to 
twelve inches in length. 

Paving blocks as here referred to shall be understood to mean blocks 
of Medina sandstone, prepared in the usual manner for dressed block pav- 
ing by nicking and breaking the stone from larger blocks, as is done at the 
quarries where such blocks are usually prepared, and not made by redressing 
or selecting from common stone paving material. 

The stones will be carefully inspected after they are brought on the 
line of the work, and the blocks which, in quality and dimensions, do not 
conform strictly to these specifications, will be rejected and must be imme- 
diately removed from the line of the work. The contractor will be reguired 
to furnish such laborers as may be necessary to aid the inspector in the 
examination and the culling of the blocks. 

The stones brought upon the ground having been carefully and thoroughly 
inspected, as provided for herein, and all rejected stones removed from 
the line of the work, the contractor will then be required to pile such stone 
as may have been approved, neatly, on the front of the sidewalk, and not 
within three (3) feet of any fire hydrant, and in such manner as will preserve 
sufficient passageway, on the line of the sidewalks, and also permit of free 
access from the roadway to each entrance on the line of the street. 



736 



SPECIFICATIONS 



SECOND QUALITY BLOCKS 

(the following not in any specifications) 

Second quality block, known as pavers, are practically the same material 
as the first quality block, the only difference being a greater range of size 
and a less careful top and joint finish. They cost $0.50 per square yard 
less. These pavers can be furnished under a specification allowing the 
following range of size and joint width: 

(City of Cleveland Specifications) 

*' Common paving stones shall consist of the best quality of Medina 
sandstone, and shall be not less than three (3) nor more than five (5) inches 
thick, and not less than seven (7) nor more than eight (8) inches deep, 
and from eight (8) to thirteen (13) inches long. The stones to have parallel 
sides and ends, with right-angle joints, all roughness and points of stone 
to be broken off so that when set in place they shall have tight joints for a 
distance of at least three inches from the top; the area of the bottom of 
any stone to be not less than three-quarters i^i) of the area of the top, 
the top of all stones to have a smooth even surface." 

CAST-IRON PIPE 

Cast-iron pipe shall be light weight and may be second quality, but it 
shall be free from all defects impairing its strength. The iron must be of 
good quality, uniform in thickness and of full strength, and the pipe shall 
be coated with coal pitch varnish mixed with linseed oil to form a firm, 
tough coating. The joint shall be formed by calking into the hub a gasket 
of jute or oakum and then filling with mortar formed of equal parts of 
Portland Cement and clean sharp sand. 

MESH REINFORCEMENT 

Mesh reinforcenient shall be placed where called for on the plans or 
ordered by the engineer. It shall be of medium steel. 

If expanded metal is used it shall conform to the above requirements, 
and the weight per square foot shall be as shown on the standard structure 
sheet, and any reinforcement shall be of a character that it will distribute 
the loads evenly. 

DEFORMED BARS 

Deformed bars shall be placed where called for on the plans or ordered 
by the engineer. They shall be of medium steel and shall have a deformed 
cross-section, that is, the various cross-sections must be of different shape 
or their centers must not lie in the same axis. 

CAST IRON 

Cast iron shall be of full standard pattern for shapes or forms used, 
according to drawings or detailed specifications. All cast iron shall be of 
good gray iron, free from blows, sand holes, or other defects, and shall have 
a tensile strength of not less than 17,000 pounds per square inch of section. 

WROUGHT IRON 

Wrought iron shall be tough, fibrous, and uniform in quality and shall 
be manufactured by approved methods. Steel scrap shall not be used in 
its manufacture. Finished material shall be clean, smooth, straight, true 
to shape, of workmanlike finish and free from defects. 

Test pieces cut from finished material shall show an ultimate tensile 
strength of not less than 48,000 pounds per square inch, an elastic limit of 
not less than 25,000 pounds per square inch, and an elongation of not less 
than 20 % in 8 inches. 



MATERIALS 737 

Wrought-iron test pieces cut from finished material when cold, or when 
heated to a bright, cherry-red, shall endure bending i8o degrees around a 
circle whose diameter is equal to twice the thickness of the test piece, with- 
out signs of cracking. Test pieces when nicked and broken shall show a 
fracture not less than 90 % fibrous, free from coarse, crystalline spots. 

Wrought iron when welded shall not show signs of red shortness. 

STEEL 

1. Steel, except as otherwise provided by these specifications, shall 
be made by the acid or basic open-hearth process and shall be uniform in 
character; finished material shall be clean, smooth, straight, true to shape, 
of workmanlike finish, and free frem defects. 

2. Fractures must show a uniform fine grain of a blue, steel-gray color 
, entirely free from a fiery luster or a blackish cast. 

3. No work shall be put upon any steel at or neaf the blue temperature 

■ or between the temperature of boiling water and of the ignition of hard- 
i wood sawdust. 

; 4. No sharp or unfilleted corners will be allowed in any piece of metal. 

' 5. Annealing. — Crimped stiff eners and buckled plates need not be an- 
nealed. All other steel that has been bent cold or partially^ heated and all 
forgings must be wholly annealed; exception may be made in unimportant 
cases and then only upon written permission from the Commission. 

6. Tests of steel that is to be annealed shall be made after annealing, or 
strips cut from such steel shall be annealed at the same time, before testing. 

7. Tests of Medium Steel. — Test pieces cut from finished material shall 
show an ultimate strength of not less than sixty thousand (60,000) pounds 

: per square inch and not more than sixty-eight thousand (68,000) pounds 
per square inch, an elastic limit of not less than thirty-five thousand (35,000) 
\ pounds per square inch, an elongation of not less than twenty-two (22) 
' per cent, in eight (8) inches, and a reduction of area at the fracture of not less 
' than forty (40) per cent. 

8. Medium steel shall not contain more than five one-hundredths (5-100) 
, of I % of sulphur. 

9. Acid steel shall not contain more than eight one-hundredths (8-100) 
I of I %, and basic steel shall not contain more than four one-hundredths 
' (4-100) of I % of phosphorus. 

( 10. Medium steel shall endure bending cold or after quenching from a 
i red heat in water at 8o°F., 180° around a circle whose diameter is equal to 
■- the thickness of the test piece, without signs of cracljing. 

II. Tests for Soft Steel. — Test pieces cut from finished material shall 

. show an ultimate strength of not less than fifty thousand (50,000) pounds 

per square inch and not more than fifty-eight thousand (58,000) pounds per 

square inch, an elastic limit of not less than thirty thousand (30,000) pounds 

., per square inch, an elongation of not less than 28 % in eight inches, and a 

1 reduction in area at the fracture of not less than fifty (50) per cent. 

■ 12. Soft steel shall not contain more than four one-hundredths (4-100) 
•j of I % of sulphur. 

■ 13. Acid steel shall not contain more than six one-hundredths (6-100) 
'of I %, and basic steel shall not contain more than four one-hundredths 
, (4-100) of I % of phosphorus. 

14. Soft steel shall- endure bending flat upon itself without signs of crack- 
J ing, when cold, or after quenching, from a red heat, in water at eighty 
\ (o) degrees F. 
j VITRIFIED PIPE 

Vitrified pipe shall be double strength salt-glazed_ vitrified stoneware 
, sewer pipe of the first quality (for ^dimensions and weights see page 560). 
I The item will include the furnishing delivering, handling, laying, and cement- 
' ing of joints; also the operations of excavating the trench, bracing, sheeting, 
, or otherwise supporting the sides, grading and preparing the bottom, back- 
I filling and compacting to the original surface, and the removal of all surplus 
I material. 



PIPE CULVERTS (U. S. FOREST ROAD SPECIFICATIONS) 

Pipe culverts shall be constructed wherever indicated on the plans or 
directed by the engineer. Typical plans for the guidance of the contractor 
will be, furnished for each particular kind of pipe culvert required. The 



738 



SPECIFICATIONS 



ends of all pipe culverts shall be protected by concrete or masonry end walls 
unless otherwise ordered by the engineer. 

Concrete Pipe. — Concrete pipe must be dense, smooth and free from any 
imperfection that would impair the strength. The concrete shall be 
mixed in the proportion of one (i) part Portland cement, two (2) parts sand, 
and one and one-half (iK) parts clean pea gravel (all of which shall pass 
a screen having three-fourths (^i) inch circular openings and be retained on 
a screen having one-quarter (J^) inch circular openings. It shall be 
thoroughly mixed with water and tamped into properly shaped forms. All 
materials shall conform to the requirements for Concrete and Reinforcement 
herein specified. 

The thickness of pipe shall not be less than that shown in the following 
table of dimensions: 

Thickness 

2 inches 

2K 

3 

3K 

4 

4K 

5 

All pipe shall be reinforced with triangular mesh or other type of reinforce- 
ment approved by the engineer, and shall conform to the following table of 
sizes and weights: 



Inside Diameter 


12 


inchib 


18 






24 






30 






36 






42 






48 







Diameter of Pipe 


Triangfilar 


Reinforcement — four-inch n 


12 inches 


Minimum 


weight 


, 0.20 lb. per sq. f1 


18 •• 


'• 






0.30 " " " " 


24 " • 


'* 






0.35 " " " ;' 


30 " 


" 




** 


0.40 " " 


36 " 


'* 




" 


0.50 " '* " " 


42 ^' 


" 




" 


0.60 " " " " 


48 " 


— " 




" 


0.60 " " " " 



Joints of the reinforced concrete pipe shall be of the lock type, bell and 
spigot or other approved type, with positive connection between sections of 
pipe. 

Cast-iron Pipe. — Cast-iron pipe shall be made with bell and spigot joints, 
and shall conform to the following table of minimum weights and thickness: 



Inside Diameter 


Thickness 


Weight per Foot 


Inches 


Inches 


Pounds 


12 


0.54 


72. 5 


14 


0.57 


89.6 


16 


0.60 


108.3 


18 


0.64 


129.2 


20 


0.67 


150.0 


24 


0.76 


204.2 


30 


0.88 


291.7 


36 


0.99 


391.7 



The weight shall not be less than the standard weight by more than five 
(5) per cent. The pipe shall be straight and the inner and outer surfaces 
shall be true concentric cylinders. All pipe shall be made of cast iron of 
good quality and of such character that the metal of the pipe will be strong, 
tough and of fine grain, and soft enough satisfactorily to admit of drilling 
and cutting. ^ The metal shall be made without any mixture of cinder-iron 
or other inferior metal. The surfaces of the pipe shall be smooth, free from 
scales, lumps, blisters, and holes, and defects of every nature which unfit the 
pipe for the use for which it is intended. 

The pipe shall be coated inside and out with coal-tar pitch varnish. The 
varnish shall be made of coal tar to which sufficient oil has been added to 
make a smooth coating, tough and tenacious when cold, but with no tendency 
to crack or scale. 



MATERIALS 739 

Corrugated Metal Pipe. — Corrugated metal pipe for culverts shall be 
properly fabricated from corrugated galvanized sheets of steel or iron. Each 
culvert shall be made from the same quality of metal throughout and the 
sheets of metal before galvanizing shall be not less than 16 gauge, U. S. 
Standard, for pipe having a diameter of 20 inches or less, and shall be not 
less than 14 gauge, U. S. Standard, for pipe between 20 and 36 inches iii 
diameter. The corrugation shall be not less than 2}^ inches, or more than 
3 inches from crest to crest and shall have a depth of not less than one-half, 
or more than five-eighths inch. 

The galvanizing snail consist of not less than two ounces of prime spelter 
per square foot of metal uniformly distributed over both surfaces of the 
sheet. It shall be applied in such manner that the spelter will not peel off 
during fabrication or in transporting and laying the pipe. The amount of 
spelter per square foot will be determined by the lead acetate method upon 
a sample taken from the culvert. Pipe having bare or uncoated spots will 
be rejected. 

All joints shall be even and close and the jointed pipe shall be straight, 
circular in section, true and rigid. 

In the longitudinal joints, rivets shall^ be driven in the valley of each cor- 
rugation and in the transverse joints rivets shall be uniformly spaced not 
more than six inches apart. The rivets shall be driven in such a manner as 
to draw the sheets tightly together, and to completely fill the rivet holes. 
The rivets shall have neat, workmanlike, semi-spherical or flat heads, and 
shall be at least one inch from the edges of the sheets. 

All rivets shall be of the same quality of metal as the sheets in which they 
are used. They shall be thoroughly galvanized and shall be not less than 
five-sixteenths of an inch in diameter. The heads of the rivets shall have 
a diameter not less than one and five-tenths times the diameter of the rivet 
plus one-eighth of an inch, and all flat heads shall have a thickness not less 
than six-tenths that of the diameter of the rivet. 

All pipe shall be furnished in the lengths ordered, except that pipe for 
culverts more than 24 feet in length may be furnished in sections not less 
1 than 12 feet in length. The connections shall consist of bands not less than 
8 inches in width, made from the same material as the pipe, properly fitted 
I with malleable cast-iron lugs, provided with galvanized bolts not less than 
three-eighths of an inch in diameter. The connections shall be so fabricated 
that a secure and firm connection of the sections of pipe may be readily 
made in the field. ^ 

The diameter of the pipe shall be understood to mean the clear inside 
diameter. 
'[ All pipe shall be so shipped and handled that when placed in position the 
galvanizing will be intact and free from bruises. 

Construction Methods. — Pipe culverts of all kinds shall be laid true to 
the lines and grades furnished by the engineer. A trench shall be excavated 
I to the required depth and of sufficient width to permit proper backfilling. 
The bottom of the trench shall be shaped to conform to the bottom of the 
pipe and shall afford a uniformly firm bed throughout its length. Recesses 
shall be excavated to receive all bells at pipe joints. Where rock is encoun- 
tered the trench shall be excavated 4 inches below the bottom of the pipe 
and this excess depth shall be refilled with thoroughly tamped suitable 
material. Any soft or yielding material shall be removed and replaced with 
i suitable material which shall be thoroughly tamped in place. 
' No pipe culverts, except as above provided, shall be placed upon embank- 
' ment or filled ground unless so ordered by the engineer, in which case a uni- 
^ formly firm bed shall be made by the use of selected materials thoroughly 
i tamped in layers as above specified for the bottom of the trench. 
'I ^ The pipe shall be carefully laid, bells upgrade, spigot ends fully entered 
\ into the adjacent bell, and true to lines and grades given. Cast iron and 
5 reinforced concrete pipe shall be laid with cemented joints. Before succeed- 
i ing sections of pipe are laid, the lower portion of the bell of the preceding 
I pipe shall be cleaned and plastered on the inside with cement mortar of 
• sufficient thickness to bring the inner surfaces of the abutting pipes flush and 
even. After the pipe is laid, the remainder of the joint shall be filled with 
similar material and sufficient additional material shall be used to form a 
bead around the joint. The inside of the joint shall be wiped and finished 
' smooth. After initial set, the cement on the outside shall be protected from 
the air and sun with an earth covering. The mortar for cementing the pipe 
! joints shall be composed of one part of Portland cement, meeting the re- 



740 SPECIFICATIONS 

quirements of cement for "Concrete,'' and two parts of approved, clean sand 
mixed with sufficient water to form a plastic mortar. 

When corrugated metal pipe sections are to be joined on the work the ends 
shall be butted together and the sections joined with the band coupler 
securely bolted in place. 

The filling around the pipe shall be made in layers with approved material 
free from rock and each layer shall be tamped thoroughly around and over 
the pipe to the elevation of the original ground surface. The material sup- 
porting the lower half circumference of the pipe shall be uniformly and se- 
curely tamped to give proper support without displacing the pipe. 

Payment. — All pipe culverts will be paid for by the linear foot in place at 
the respective prices bid for the different kinds of pipe. These prices shall 
be payment in full for all pipe, joint material, etc., and for all labor employed 
in excavation, backfilling, laying the pipe and filling the joints, but will not 
include payment for masonry or concrete end walls. 

POROUS TILE (NEW YORK STATE SPECIFICATIONS) 

Where called for on the plans, or ordered by the engineer, porous tile 
shall be laid true to line and grade, and firmly bedded in clean cinders, 
gravel, or crushed stone. The tile must be whole and free from cracks and 
other defects, and must be satisfactory to the engineer. 

J 
TIMBER j 

(Washington State Specifications) ! 

Quality of Timber and Plank. — All timber and plank in culverts, trestle- 
work, bridge abutments, and pile bridges shall be of good quality, of such 
kinds as the highway commissioner may direct, free from shakes, wanes, 
black and unsound knots, and all descriptions of decay, and shall be measured 
by the thousand feet, board measure; the price shall be understood to cover 
the expense of all labor (including all necessary digging and filling at the 
ends of bridges where grading is done before bridges are put in) and materials, 
pins, or treenails required in the performance of the work. 

All timber structures shall be built in conformity with plans to be furnished 
by the engineer. 

Piles and Pile-driving. — Piles, whether used in foundations, trestle- 
work, or pile bridges, shall be of good, sound quality of such timber as the 
Highway Commissioner may accept, not less than ten inches in diameter 
at the smaller end and of such lengths as the engineer may require. They 
shall be measured by the lineal foot after they are driven and cut off to 
receive the superstructure, and the price per lineal foot shall be understood 
to cover the expense of driving, cutting off, removing the bark from the 
part above the ground, and all other labor and material required in the 
performance of the work; but that portion of each pile cut off shall be esti- 
mated and paid for by the lineal foot as "piling cut off." Piles shall be 
driven of such lengths and to such depths as the engineer may require. All 
piles shall_be capped during the driving to prevent brooming. 

LOG CULVERTS (U. S. FOREST ROAD SPECIFICATIONS) 

Log culverts shall be constructed in conformity^ with the plans,~or where 
directed by the engineer. 

Materials. — In the construction of log culverts the timber shall be of the 
species called for on the plans. All knots and projections shall be trimmed 
down even with the surface of the log, and all bark shall be peeled off before 
the logs are used. 

If Government owned stumpage is available the logs may be cut either from 
the right-of-way or adjacent Government land, as the engineer may direct, 
and the engineer will in all such cases indicate the trees to be used, which 
shall first have been designated by a forest official. The tops and branches 
of trees shall be disposed of as provided in the specifications for "Clearing 
and Grubbing," hereinbefore given. The stringer logs shall be straight. 

When suitable Government owned stumpage is not available the timber 
shall be furnished by the contractor at his own expense. 



MATERIALS 74 1 

Construction. — The stakes set by the engineer shall control the line and 
elevation for each structure. If practicable the backfill within and behind 
the abutments shall be made of stone. Where no stone is available, the 
logs of the abutment shall be more carefully hewn so as to form clos& joints 
that will hold a backfilling of earth. ^ In all cases the logs of the abutments 
shall be fastened together with five-eighths inch drift bolts. 

The stringer logs shall be laid close enough together to hold the fill without 
leakage and an occasional stringer shall be spiked to the abutment in order 
to hold the roof of the culvert in place. 

The crib wings shall be constructed in the same manner as the abutments. 

Where a floor is called for, it shall be constructed of stringer logs and in 
the manner shown on the plans. 

Payment. — Payment for log culverts shall be at the unit bid price per 
linear foot of culvert measured along the center line of culvert. The bid 
price for each size of culvert shall be payment in full for all labor and mate- 
rials entering into any culvert of that size and the necessary excavation and 
backfilling therefor. 

LOG BRIDGES (U. S. FOREST ROAD SPECIFICATIONS) 

Log bridges shall be constructed in conformity with the plans or where 
directed by the engineer. 

Materials. — The logs used in constructing log bridges shall be of the species 
called for on the plans. If Government owned stumpage is available, the 
logs may be cut either from the right-of-way or adjacent Government land, 
as the engineer may direct, and the engineer will in all such cases indicate 
the trees to be used, which shall first have been designated by a forest official. 
j The tops and branches of trees shall be disposed of as provided in the speci- 
' fications for "Clearing and Grubbing," as hereinbefore given. 

When suitable Government owned stumpage is not available the timber 
shall be furnished by the contractor at his own expense. 

The logs shall be straight, sound and free from defects of all kinds and 
shall be cut from live trees as far in advance of use as possible, but not ex- 
ceeding one year, and be allowed to season with the bark on. Immediately 
before use in the work all bark shall be peeled and the logs trimmed smooth 
of all knots and projections. 

All lumber for flooring, railings, etc., shall be of the kind and dimensions 
indicated on the plans and shall be free from shakes, wanes, black and un- 
sound knots, and from all other defects which would impair its strength in 
any way. 

The contractor shall furnish at his own expense all necessary bolts, drift 
bolts, spikes, nails and other material or hardware called for on the plans 
or in the specifications. 

Construction. — The contractor shall provide experienced workmen and 
ample and suitable equipment and tools for performing the work, and shall 
follow only well recognized methods in preparing the timber and framing 
and erecting the structure. 

Where concrete or masonry piers or abutments are called for on the plans, 
they shall be constructed in accordance with the requirements of the plans, 
and of the specifications hereinbefore given for the particiilar kind of con- 
crete or masonry called for. 

Payment. — Each log bridge superstructure complete will be paid for at 
the price bid per linear foot of bridge, as shown on the plans, which shall 
include all parts of the bridge except abutments and piers. This amount 
shall be payment in full for all materials, labor and incidenta,ls, required to 
construct the bridges in accordance with the plans and specifications. 

LOG ABUTMENTS FOR BRIDGES 

Log abutments for bridges will be built according to the specifications for 
"Log Cribbing," and as shown on the plans, and will be paid for as "Log 
Cribbing." 

LOG CRIBBING (U. S. FOREST ROAD SPECIFICATIONS) 

Log cribbing shall be built to the lines and grades given by the engineer 
and constructed in conformity with the plans or as directed by the engineer. 



742 SPECIFICATIONS I 

Materials.— The contractor shall secure and prepare or shall furnish at 
his own expense all necessary logs, timber, hardware, etc., under the condi- 
tions and as called for under the heading "Material" for "Log Bridges." 

Construction. — The cribbing shall be supported on mudsills with flattened 
lower surfaces placed as shown on the plans. 

All logs, including face logs, tie logs, mudsills and anchor logs, shall be 
properly notched together and drift bolted as shown on the plans. 

The minimum lengths and sizes of logs shall be as shown on the plans.; 
Each course of logs shall break joint with the adjacent courses. The length^ 
of tie logs required for the proper support and anchorage of the cribbing 
shall be as determined by the engineer. • 

The face and tie logs are to be so notched together, and hewn if necessary,' 
that the face logs will be in contact with each other throughout their entire 
length, except that in case a satisfactory rock backfill is placed against the 
face logs the engineer may permit open spaces not exceeding 4 inches in 
width between the face logs. When permission to use such spaces is given, 
the rock backfill shall be carefully placed, using the larger rocks adjacent 
to the logs and backing up with the smaller rocks in such manner that earth 
and finer material will not escape or be washed out. 

Payment. — Payment will be made by the linear foot of face logs in place 
complete at the unit bid price, which price shall include the furnishing and 
placing of transverse mudsills, tie logs, anchor logs and drift bolts. Such 
unit bid price shall be payment in full for all materials, labor, excavation, 
backfilling and incidental work required for the construction of the cribbing 
complete. The measurement of log cribbing shall include only the linear 
feet of face logs, or longitudinal mudsills when such are used, and will not 
include transverse mudsills, tie logs or anchor logs. 

CLEARING AND GRUBBING (WASHINGTON STATE 
SPECIFICATIONS) 

Clearing. — The right-of-way must be cleared to the width of feet 

on each side of the center line, or as shall be designated by the engineer; 
all trees, brush, and other vegetable matter within the space designated 
to be cut down, and the same, together with all other logs, brushwood, and 
fences already down, shall be burned or removed from the grounds, as 
the engineer may direct, so as not to injure the adjoining lands or to obstruct 
the line of the fences along the boundaries of the said right-of-way. When 
the embankments exceed two feet in height it will be required to cut the 
trees, brush, and stumps close to the ground. 

Light clearing shall include the removal of all standing trees of a size 
up to one foot in diameter, together with all other logs, brush, and other 
vegetable matter already down or lying loose on the ground. 

Heavy clearing shall include the removal of all standing trees over one 
foot in diameter, together with all other logs, brush, and other vegetable 
matter already down or lying loose on the ground. 

Grubbing. — From the space required for the roadbed and necessary 
slopes and side drains, and whatever additional space may be required by 
the engineer, except where the excavations are three feet or more in depth, 
or embankments two feet or more in height, all stumps and other wood or 
vegetable matter embedded in the ground shall be grubbed up, and removed 
or disposed of as the engineer may direct, and only the area so grubbed 
shall be estimated. 

Clearing and Grubbing (U. S. Forest Road Specifications). — This item 
shall include all clearing, grubbing and disposal of timber. 

The right-of-way must be cleared on each side of the center line of the 
road to the full width indicated by the plans, or as the engineer may require. 
All trees, brush and other vegetable matter within the space designated shall 
be cut down and all tree branches extending into the right-of-way which 
hang within 20 feet of the ground shall be cut off. The edge of the clearing 
shall present a fairly regular and uniform alignment, except that fine speci- 
mens of trees shall be left standing when in the judgment of the engineer 
they will not be injurious to the road. All stumps and all trees, the stumps 
of which are not to be grubbed, shall be cut not more than 2 feet above the 

From the space required for the roadbed and necessary slopes and side 
drains except where the embankments at the point in question are three feet 



METHODS 743 

or more in height, all stumps, large roots, and other imbedded wood or 
vegetable matter shall be grubbed or blasted from the ground. 

The contractor will be required to use merchantable timber cut from the 
right-of-way for the drainage or other structures for which it may be suitable 
and for which he would otherwise be compelled to cut merchantable timber 
from adjacent government land. All clear and sound logs or poles having 
a top diameter of four inches or more and a length of four feet or more will 
be considered as merchantable timber in the operations under these specifi- 
cations. The merchantable timber in excess of that needed in the construc- 

, tion of the road which must be cut in the_ clearing of the right-of-way shall 
be felled in the right-of-way, cleared of limbs and brush, sawed into such 
standard lengths as may be designated by the engineer and skidded into 
workmanlike piles at the edge of the right-of-way, before grading is under- 

, taken. The title to all such timber cut from National Forest lands shall 
remain with the United States subject to disposal by the Forest Service, 
U. S. Department of Agriculture, under its regular procedure. 

All other than merchantable trees, together with all brush, stumps, roots, 

. and other debris, must be placed in neat conical piles with the small material 
at the bottom and the large limbs and other materials stacked on the outside 
of the. pile in such a manner as to be completely consumed when the pile is 
burned. In case the burning is to precede the construction operations, the 
piles may be placed in the center of the right-of-way, otherwise the piles 

' should be placed in the most convenient place to the side of the right-of-way 

. where they may be burned without damage to the surrounding forest cover. 

;In no case will it be permissible to merely throw the refuse outside of the 
right-of-way or to place it in windrows at the side of the right-of-way. 

The material placed in piles shall be burned by the contractor at such time 
and in such manner as absolutely to prevent the fire from spreading to areas 
adjoining the right-of-way. 

Particular care must be exercised to avoid producing an unsightly appear- 
ance by burning or scorching green trees standing along the edge of the right- 
of-way. Any trees permanently defaced in this manner shall be cut down 
and disposed of as the engineer may direct. 

When upon the advice of the Forest Supervisor of the Natural Forest con- 
cerned the engineer determines that the proper protection of the National 

j Forest from fire demands that burning operations shall be discontinued, the 

] contractor shall make such disposal on the ground of the material as the 

(engineer may indicate. 

j 

EXCAVATION (WASHINGTON STATE SPECIFICATIONS) 

i Under the head of excavation shall be included all excavations required 
for the formation of the roadbed, the digging of all ditches, cutting new 
channels for streams, preparing foundations, the altering of all highway or 
private roads and all excavations in any way connected with or incidental 
to the construction of the road, and 'the expense of hauling and depositing 
same in embankments wherever required. 

Embankments. — Under the head of embankments "shall be included 
■all embankments for any of the purposes mentioned not formed from 
excavations taken from the prism of the road or other necessary excavations. 
] All grading shall be done and estimated by the cubic yard, measured 
in the excavation, except material borrowed for embankment, which shall be 
measured in embankment, and shall be comprised under heads, viz.: 
! Earth, Hard-pan, Loose Rock, Solid Rock, Shell Rock, and Solid Rock 
• Borrow. 

Earth. — Earth will include clay, sand, loam, gravel, and all hard material 
"^that can, in the opinion of the chief engineer, be reasonably plowed, and 
{all earthy matter or earth containing loose stones or boulders intermixed, 
> and all other material that does not come under the classification of hard- 
i pan, loose rock, solid rock, shell rock, and solid rock borrow. 
j Hard-pan.— Hard-pan will include _ material, not loose or solid rock, 
j that can not, in the opinion of the chief engineer, be reasonably plowed on 
.account of its own inherent hardness. 

i _ Loose Rock. — Loose rock will include all stone and detached rock, found 
!in separate masses, containing not less than one cubic foot, nor more than 
, one-half cubic yard, and all slate or other rock, soft or loose enough to be 
removed without blasting, although blasting may occasionally be resorted to. 



744 SPECIFICATIONS 

Solid Rock. — Solid rock will include all rock in place, and boulders meas-| 
uring one-half cubic yard and upwards, in removing which it is necessary* 
to resort to drilling and blasting. 

Shell-rock Excavation.— Shell-rock excavation will include all deposits^ 
composed entirely of rock in masses of less than one cubic foot which have 
broken off from the cliffs above the roadbed, but will only be estimated 
when in large deposits. 

Solid Rock Borrow. — ^Solid rock borrow shall consist of solid rock, accord- 
ing to above classification, excavated outside of the regular cross-sections 
of the cuts for the roadbed, and placed and measured in embankment. 

EXCAVATION (NEW YORK STATE SPECIFICATIONS, ITEMS NO. 2 

TO 46) 



Item 2 — Earth Excavation j 

Item 3 — Rock Excavation 

2.1. Under these items the Contractor shall grade the entire length of 
roadway, ditches and side slopes to the required lines and grades; shall make 
all excavations for culverts, under-drains, catch basins, leaching basins, and 
other structures except posts; shall grade connecting public highways as 
directed and remove spongy material from the sub-grade to the depths 
required — all as shown on the plans or as directed by the Engineer. 

This item includes the excavation, filling and rolling necessary to com- 
plete the road and all structures connected therewith except as noted above, 
and includes the removal of all objectionable material for the full width of 
the improvement except as noted under section i.i, and the filling to the 
required grade with acceptable material of all areas originally below the 
required grade, or excavated below grade under orders of the Engineer. 

Backfill for structures, old macadam excavated, and sod ordered removed 
from the site of a new embankment, shall be paid for as Earth Excavation. 

2.2. All suitable materials from the excavation shall be used so far as 
practicable in making embankments, building up low places on the sub- 
grade or shoulders, and such other places as directed. 

2.3. Surplus material shall be placed in embankments, shall be used for 
extending the shoulders or shall be deposited in spoil banks, as directed 
by the engineer. All surplus materials shall be removed and disposed of as 
directed by the engineer before the sub-grade or shoulder rolling is completed 
and before any stone is placed on the roadway. ^ 

2.4. If there is not sufficient suitable material to complete the grading 
and to bring the sub-grade to the required height,- the contractor shall 
borrow additional material from the sides of the roadway or from other 
borrow pits as directed by the engineer so that the established grade for 
the road, embankments, etc., will be secured. AU borrow pits outside the 
highway shall be acquired by the Contractor at his own expense, and any 
borrow pits in or adjacent to the highway shall be left in a neat and satis- 
factory condition and shall be thoroughly drained. 

2.5. The contractor shall remove boulders and all muck, quicksand, 
soft clay and spongy material which will not consolidate under the roller, 
from the sub-grade to a depth to be determined by the engineer, and refill 
the space with acceptable materials from the excavations, or_ with stone or 
gravel, as directed. If stone or gravel is used, the same will be paid for 
at the contract price bid for item "Foundation Course." After all drains 
have been laid and the surface of the sub-grade has been properly shaped, 
it shall be thoroughly rolled and compacted with an approved self-propelled 
roller weighing not less than 10 tons. Water puddling shall be resorted 
to in case the soil requires it. Care shall be taken not to roll clay founda- 
tions too much, thus developing a plastic condition. All hollows and 
depressions which develop shall be filled with acceptable material, and the 
sub-grade shall again be rolled. This process of filling and foiling shall be 
repeated until no depressions develop. In places where the character of 
the material makes the use of such a roller impracticable, a lighter one may 
be permitted. The sub-grade shall not be muddy, or otherwise unsatis- 
factory when the foundation course is placed upon it. All culverts, ditches, 
and drains shall be satisfactorily completed to effectively drain the highway 
before the placing of any pavement will be permitted.^ The shoulders 
shall be rolled and left in a compact and satisfactory condition at the com- j 
pletion of the pavement. 



METHODS 745 

2.6. Embankment shall be formed of suitable materials. If formed of 
stone, all reasonable precautions must be taken to insure a solid embank- 
ment. The upper surface of the embankment shall be rolled and left in a 
satisfactory condition and approximately true to line and grades. Large 
stone shall not project within 6 inches of the finished sub-grade, and all 
hollows, and depressions shall be filled with the smaller stone from the 
excavation, with gravel or with other acceptable material. Stone in em- 
bankments shall not be used nearer than 6 inches to the surface of shoulder. 

Where the filling is less than 2 feet in depth all vegetable matter shall be 
removed from the onginal surface. Where necessitated by the existing 
slope, the original surface shall be trenched or otherwise broken up before 
placing new embankment thereon. 

Embankment shall be . constructed in successive horizontal layers not 
exceeding 12 inches in thickness; when concrete is to be placed thereon, 
these layers shall not exceed 6 inches in thickness. Each layer shall extend 
across the entire fill and shall be thoroughly rolled and compacted by 
approved methods. If impracticable to use a heavy roller for this work a 
grooved roller shall be used. 

2.7. At all intersecting public highways the contractor shall grade back 
to a sufl&cient distance with acceptable materials, as directed by the engineer 
so that a smooth riding and satisfactory junction will be produced. 

2.8. The quantity of excavation to be paid for under Items 2 and 3 shall 
be the number of cubic yards of material, measured in its original position, 
excavated and disposed of as directed by the Engineer, and the limits shall 
not exceed those shown upon the plans or fixed by the Engineer. 

The price bid for Earth Excavation shall include the removal of all 

materials, as specified under section 2.1 — except as provided below for 

•'Rock Excavation," — the placing of same in embankment or spoil, the 

1 rolling, compacting, grading and all other work incidental thereto. 

i No direct payment shall be made under Items 2 or 3 for work in connection 

with contractor's plant, nor for his other requirements in carrying out the 

pi provisions of this contract, but compensation therefor shall be considered 

\ as having been included in the prices stipulated for the various items of 

, the contract. 

: The price bid for Item 3 shall include the removal of all boulders of more 
I than 13 cubic feet and all hard ledge rock and the placing of same in em- 
J bankment or spoil if not used under other items of the contract, and rolling, 
, compacting, grading and all other work incidental thereto. _ Boulders of 
less than 13 cubic feet, and all soft or disintegrated rock which can be re- 
. moved with pick and shovel, shall not be paid for under Rock Excavation, 
; but under "Earth Excavation." The price bid for the items shall include 
1 all labor, materials, supplies, and plant and incidentals necessary to com- 
3 plete the work. 

Item 4 — Overhaul 

4.1. If the haul on any riiaterial either from cuts or borrow pits made 
in accordance with directions from the Engineer exceeds 2000 feet it shall 
'i be classified as overhaul. 

For each 100 feet of haul greater than 2000 feet the Contractor shall 
receive the price bid for Overhaul per cubic yard of all material so moved, 
measured in its original position. 
] The price bid shall include all labor, appliances, and incidentals necessary 
i to complete the work. 

Item 5 — Vitrified Clay Pipe 

5. 1. Under this item the Cpntractor shall furnish and place vitrified 
pipe where directed by the Engineer. 

5.2. Pipe shall be first quality, double strength, salt glazed, sound, 
5! vitrified, stoneware sewer pipe with bell joints. (For dimensions and weight 

Iof vitrified pipe see page 560.) 
5.3. All pipe shall be laid true to line and grade with bells upstream, 
and shall have a full, firm and even bearing. The joints shall be filled with 
:j jute and mortar consisting of one part Portland cement and two parts sand. 
' S..4« The quantity to be paid for under this item shall be the number 
of linear feet of pipe incorporated in the work under the directions and 
' to the satisfaction of the Engineer. 
j The price bid shall include the furnishing and laying and all materials 



746 



SPECIFICATIONS 



and incidentals necessary thereto, except that all excavation in connection 
therewith will be paid for under item "Excavation." 

Item 6 — Vitrified Clay Underdrains 

6.1. Under this item the Contractor shall furnish and lay 6-inch salt 
glazed vitrified pipe wherever required for drainage. 

6.2. The pipe shall be laid true to line and grade with the bells up grade. 
A strap of burlap at least 6 inches wide and long enough to reach around 
the pipe and lap at least i foot shall be wrapped around each joint of pipe 
to give double thickness on the top and to act as a strainer. The pipe 
shall be covered as laid with clean gravel or broken stone of No. 2 or No. 3 
size placed around and above it to the surface of the sub-grade. 

6.3. The amount to be paid for under this item shall be the number of 
linear feet of i^ipe furnished and incorporated in the work._ 

The price bid shall include all labor, materials, and incidentals necessary 
to complete the work, except that the necessary excavation will be paid 
for under item "Excavation," and the necessary broken stone will be paid 
for under item "Broken Stone, Loose Measurement." 

Item 7 — Porous Tile Underdrain 

7.1. Under this item the Contractor shall furnish and lay 6-inch"porous 
tile wherever required for drainage. 

7.2. The tile must be whole and free from cracks and other defects, and 
must be satisfactory to the Engineer. 

7.3. The tile shall be laid true to line and grade and shall be covered 
as laid with clean gravel or broken stone placed around and above it to 
the surface of the sub-grade. 

7.4. The amount to be paid for under this item shall be the number 
of linear feet of pipe furnished and incorporated in the work. 

The price bid shall include all labor, materials, and incidentals necessary 
to complete the work, except that the necessary excavation will be paid 
for under item "Excavation," and the necessary broken stone will be paid 
for under item "Broken Stone, Loose Measurement." 

Item 8 — Concrete Leaching Basins 

8.1. Under this item the Contractor shall build at places indicated on 
the plan or ordered by the Engineer, concrete leaching basins of a type 
shown on the detail plans.^ 

8.2. The concrete used in these basins shall be second-class concrete. 

8.3. The grating shall be of cast iron of the quality specified in item 
"Miscellaneous Iron and Steel." 

8.4. For each basin completed, the Contractor shall receive the price bid. 
The price bid shall include all concrete, stone, grating, and all material, 

labor and incidentals necessary to complete the work, except that the 
excavation will be paid for under item "Excavation." 

Item 9 — Vitrified Leaching Basins | 

9.1. Under this item the Contractor shall build at places indicated on ! 
the plans or ordered by the Engineer, leaching basins of a type shown on 1 
the detail plans. 

9.2. Vitrified pipe shall be of double thickness, sound, and thoroughly 1 
tamped in place. i 

9.3. The broken stone used for filling shall be No. 4 broken stone or gravel. | 

9.4. The grating shall be of cast iron of the quality specified in item 1 
"Miscellaneous Iron and Steel." ; 

9.5. For each basin completed in accordance with plans and under orders \ 
of the Engineer, the Contractor shall receive the price bid. i 

The price ^ bid shall include all materials, labor and appliances, and all 
expenses incidental to completing the work, except the excavation — which 
last will be paid for under item "Excavation." 



METHODS 747 

Item 10 — Catch Basins 

10. 1. Under this item the Contractor shall build catch basins as shown 
on the plans, as directed by the Engineer. 

10.2. The catch basins may be built of second-class concrete or of accept- 
able brick at the option of the Contractor. If bricks are used they shall be 
sound, hard burned brick of acceptable quality, and shall be laid by a 
competent mason and in a workmanlike manner. Mortar of one part 
Portland cement .and two parts sand shall be used. 

10.3. For each catch basin. complete with cast iron top, as shown on plans 
and ordered by the Engineer, the Contractor shall receive the price bid.^ 

The price bid shall include all labor, materials and^ incidentals required 
to complete each basin, except that the excavation will be paid for under 
item "Excavation." 

DROP INLETS 

Drop inlets shall be constructed where shown upon the plans, or directed 
by the Engineer. The details of construction shall be such as he may direct. 

Payment for drop inlets will be made under appropriate items at the 
contract price for the materials entering into their construction; that is, 
payment will be made for the various amounts of _ excavation,^ concrete, 
cast iron, cast-iron pipe, etc. Payment under these items shall include all 
labor and materials necessary to complete the work. 

Item II — Changing Elevation of Manholes and Catch Basins 

11. 1. Under this item the Contractor shall raise or lower to the grade 
given all existing covers of catch basins or manholes. 

1 1.2. All changes shall be made with acceptable brick laid in Portland 
i cement mortar of one part cement and two parts sand. 

All work shall be done in a workmanlike manner by competent masons. 

1 1.3. For each manhole or catch basin raised or lowered as directed by 
' the Engineer, the Contractor shall receive the unit price bid. 

The price bid shall include all labor, materials and incidentals necessary 
to complete the-work. If any manhole or catch basin heads or .covers are 
broken through carelessness on the part of the Contractor, they shall be 
replaced at his expense. — 



Item 12 — Cast-iron Pipe 



12. 1. Under this item the Contractor shall furnish and place cast-iron 
pipe as directed for culverts, drains and other necessary uses, and of the 
sizes and weights ordered. 

12.2. Pipe shall be of class A unless otherwise called for by the plans or 
ordered in writing by the Division Engineer, and may be second quality; 

{ but it shall be free from all defects impairing its strength or utility. The 
iron must be of good quality, uniform in thickness and of full strength. 
The pipe shall be coated with coal-pitch varnish mixed with linseed oil to 
form a firm, tough coating. Joints shall be formed by caulking into the 
hubs a gasket of jute or oakum and then filling with mortar composed of 
equal parts of Portland cement and clean, sharp sand. It shall be laid true 
to line and grade and shall have a full, firm, even bearing. 

I ^ 12.3. The number of tons of cast-iron pipe to be paid for under this 

: item shall be the actual weight in place in the work as directed by the 
Engineer when of class A, or an equal weight when of heavier class; except 
that_ when a heavier weight is used under written order of the Division 

\ Engineer, such weight shall be paid for. 

The price bid shall include the furnishing, delivering, handling, laying, 
cutting and all work and materials necessary to complete the work. 

Item 13 — Relaying Old Pipe 

13. 1. Under this item the Contractor shall as directed carefully remove, 
preserve and relay old pipe found in existing culverts. 



748 



SPECIFICATIONS 



13.2. The old pipe when relaid shall be true to line and grade and have a. 
lull, firm, even bearing, and the work shall be in every way the same as if 
new pipe were being laid. 

13.3. Any old pipe in good condition which is damaged in removing, 
due to the carelessness of the Contractor, shall be replaced with new pipe 
at the Contractor s expense. 

Any old pipe which is, in the Engineer's judgment, unfit for relaying may' 
be destroyed before removing. 

13.4. The amount to be paid for under this item shall be the number; 
of linear feet incorporated in the work. New pipe furnished to replace' 
old pipe which is destroyed through the carelessness of the Contractor shall' 
be paid for as if the old pipe had been preserved and relaid. 

The price bid shall include all labor, materials and incidentals necessary! 
to complete the work, except that the excavation necessary will be paid for. 
under the item "Excavation." j 

i 

Item 14 — Stone Filling 

14. 1. Under this item the Contractor shall furnish and place acceptable 
stone of either quarry, field or cobble stone for filling crib work, and similar 
work as required. 

14.2. Stone filling shall be of acceptable quarry, field or cobble stone. 
The larger stones shall be properly embedded at the bottom of the fill; all 
stones shall be so placed as to make a fill of maximum stability. 

14.3. The quantity to be paid for under this item shall be the number 
of cubic yards measured in its final position and incorporated in the work 
as directed by the Engineer. The price stipulated shall include the cost 
of obtaining the stone, placing, and all materials and expenses incidental 
thereto. 

Item IS — Piles 

1 5. 1. Under this item the Contractor shall furnish and drive piles of 
acceptable material and lengths for foundations, revetment and elsewhere 
as required. 

15.2. Piles shall be furnished to fit the localities. The Contractor shall, 
when required, drive preliminary test piles, each of which will be paid for 
at the contract price therefor. After the test piles are driven a statement 
will be furnished the Contractor by the Engineer, showing for the informa- 
tion of the Contractor the probable number of piles of the different kinds 
required, grouped between certain lengths in feet. 

15.3.^ Piles shall be driven by hammer or cornbination of hammer and 
water jet methods, and the driving shall be satisfactory to the Engineer 
in every case. In driving piles the heads shall be protected from injury 
by a cap or shall be banded if required. The fall of the hammer shall not 
exceed 20 feet, and shall be regulated so as not to injure or shatter the pile. 
Driving shall continue until the penetration and bearing values are satis- 
factory to the Engineer. 

15.4. The tops of all piles shall be sawed level and true to the elevation 
fixed by the Engineer. 

15.5. Broken, split or misplaced piles shall be drawn and properly re- 
placed. Piles driven below the grade fixed by the Engineer shall be drawn 
and replaced by new, and if necessary, longer, piles. No payment will be 
made for driving or withdrawing piles so injured or misplaced. 

15.6. The number of linear feet paid for under this item shall be the total 
length of piles driven in accordance with plans or orders of the Engineer. 

The price bid shall include the furnishing and delivering upon the work, 
the peeling, banding, tenoning, framing, driving, painting and all other 
labor and incidentals necessary to complete the work. 

Item 16 — Timber and Lumber 

16. 1. Under this item the Contractor shall furnish timber and lumber 
of various sizes as may be ordered for sills or platforms beneath the road, 
for culverts, bridges, reinforcing existing structures and for other similar 
purposes as ordered by the Engineer. 

16.2. Timber and lumber shall be of short leaf yellow pine or spruce 



METHODS 749 

or other acceptable kind, sound, square-edged, free from shakes, loose 
knots or decay, and shall be planed, and tongued-and-grooved if required. 

16.3. No payments will be made under this item for timber or lumber 
for forms, moulds, or centers, for sheeting or bracing, scaffolds, fences, 
guard rails or any part of the contractor's temporary bridges, roads, or 
plant; but payment for timber and lumber used in the above cases shall be 
included under the appropriate items covering the same. 

16.4. The quantity of timber and lumber to be paid for shall be the 
number of thousand feet, board measure, actually placed in accordance 
with orders of the Engineer. If any round timber is used it shall be esti- 
mated as square timber of the largest size, omitting fractions of an inch, 
which can be inscribed in the small end of the log. 

No second hand timber shall be used except with the approval of the 
Engineer. The price bid shall include all bolts, spikes and other fastenings 
and all other material expenses incidental to furnishing, framing and placing 
the timber and lumber satisfactorily. 

Item 17 — Rip-rap 

17. 1. Under this item the Contractor shall furnish and place rip-rap 
for slope protection where shown upon the plans or ordered by the Engineer. 

17.2. Rip-rap shall consist of field stone or rough, unhewn quarry stones 
as nearly cubical in form as is practicable, placed upon a slope not steeper 
than the angle of repose, and so laid that the weight of the large stones is 
carried by the soil and not by the stones adjacent. Fifty per centum of the 
mass shall be large stones of two cubic feet or more. The largest stones 
shall be placed first, roughly arranged and in close contact; the stones shall 

; rest upon a 6-inch bed of stone chips or gravel or other acceptable porous 
material, where ordered by the Engineer. The spaces between the larger 
I stones shall be filled with spalls of suitable size. 

17.3. The quantity of rip-rap to be paid for under this item shall be the 
number of cubic yards placed in accordance with the plans or as directed 

i by the Engineer. When a porous bed is placed in accordance with the 
directions of the Engineer, the quantity of the same shall be included in the 
quantity of rip-rap and paid for as such. 

The price bid shall include all labor, materials and incidental expenses 

■j necessary to satisfactorily complete the work. 

\ CONCRETE JVLASONRY 

Item 18 — First-Class Concrete 

Item 19 — Second-Class Concrete 

Item 20 — Third-Class Concrete 

'\ 1 8. 1. Under Items 18, 19 and 20 the Contractor shall place concrete 

I' of the class indicated on the plans or ordered by the Engineer, for culverts, 

'■ abutments, wing walls and in other structures as directed by the Engineer. 

; This item shall not include concrete used in curbs, catch-basins, edging, 

.; sign posts, guard railing, resetting old curb, concrete pavement foundations 

or "Concrete Pavements" or in other structures for which there is a contract 

item, unless it is specifically stated under that item that such shall be the 

case. All concrete placed in the work, whether included under Items 18, 

19, or 20 or under other items, shall conform to the requirements for concrete 

of the class specified. 

18.2. Concrete shall consist of approved Portland cement, a fine aggregate 
i^ of sand, and a coarse aggregate of broken stone or gravel, mixed in the 
■ proportions specified for the various classes given below. Samples of all 
I these ingredients shall be submitted to and approved by the Bureau of 
\ Tests, and shall be acceptable to the Engineer before being used in the work. 
I 18.3. Concrete will be classified as follows: 

I First-class concrete shall be made of one part Portland cement, two parts of 
] No. I or No. 2 sand (see page 718) and four parts of coarse aggregate. 

Second-class concrete shall be made of one part Portland cement, two and 
one-half parts of No. 2 or No. 3 sand, and five parts of coarse aggregate. 
Third-class concrete shall be made of one part of Portland cement, three 
1 parts of No, 3 sand, and six parts of coarse aggregate. 



750 SPECTFTCATTONS 

Cement, fine and coarse aggregate shall be proportioned by loose volumes. 
For this purpose one bag of cement shall be considered as ®^loo oi a cubic 
foot. The fine and coarse aggregate shall be measured separately. 

PORTLAND CEMENT 

18.4. All the cement used in the work shall conform to the requirements 
given under" Materials of Construction," pages 717-718; it shall be 
subject to rigid inspection, shall be sampled by the Engineer at once on 
delivery, and shall conform to the prescribed tests made at the testing 
laboratories of the Bureau of Tests. All cement which is rejected because 
of failure to stand the required tests shall be immediately removed at the 
expense of the contractor. 

18.5. Cement barrels shall contain 376 pounds of Portland cement. 
Each bag of P9rtland cement shall contain 94 pounds net. 

18.6. Provision shall be made by the Contractor for storing cement 
in a dry place, 

fine aggregate 

18.7. Fine aggregate shall conform in all respects to the requirements 
given under "Materials of Construction," page 718. Sand which 
contains foreign matter shall be satisfactorily washed before using. Screen- 
ings shall not be used except when they have been submitted by the Division 
Engineer to the Bureau of Tests, have been accepted by the Bureau of 
Tests, and their use has been approved by the First Deputy Commissioner 
in writing, and then only under the restrictions laid down under " Mate- 
rials OF Construction," page 719. 

/ COARSE aggregate 

18.8. Coarse aggregate shall conform in all respects to the requirements 
given under " Materials of Construction," page 719. Materials which 
contain foreign matter shall be satisfactorily washed before using. 

mixing, depositing and finishing concrete 

18.9. Approved batch mixers shall be used in all cases where required 
by the Engineer. No continuous mixer shall be used. Mixing shall con- 
tinue through at least twelve revolutions of the mixer, and until every 
face of every particle of stone of gravel is completely coated with mortar. 
In all machine mixing the batches of concrete shall be proportioned to the 
size of the mixer to produce the best results. 

18.10. If hand mixing is permitted the following method shall be used; 
The sand and cement shall be thoroughly mixed dry and. made into a 

thin mortar. After the mortar has been brought to the proper consistency, 
the broken stone or gravel, having been just previously drenched with water, 
shall be added, and the whole thoroughly mixed to the satisfaction of the 
Engineer. The mixing shall be done upon water-tight platforms, in a 
satisfactory manner; after the materials are wet, the work shall proceed 
rapidly until the concrete is in place, and is so thoroughly manipulated that 
water flushes to the surface and all the interstices between the stones are 
entirely filled with mortar. 

18. 11. All mortar and concrete shall be used while fresh and before 
the initial set has begun. Any mortar or concrete in which the initial set 
has begun shall be removed from the mixing boards or receptacle and not 
used in the work. No retempering of mortar or concrete shall be allowed. 

18.12. The quantity of water to be used in making concrete shall be 
determined by the Engineer, but in general a wet mixture shall be used as 
tending to produce a uniform, dense and impervious concrete. Excess water, 
however, must be avoided. 

18.13. When required by the Engineer, concrete shall be deposited 
In layers averaging not more than six inches in thickness before compacting. 
In joining new concrete to old, or to concrete that has already set, the work 
already in place shall have its surface cut over thoroughly with picks to 
remove all laitance, loose and foreign material; this surface shall then be 
washed and be scrubbed with wire brooms before the new concrete is placed, i 



METHODS 751 

In order to bond the successive courses, horizontal keys shall be formed at 
the top of the upper layer of each day's work and at such other levels as 
work is interrupted until the concrete has taken its initial set. Rough stone 
may, at the discretion of the Engineer, be embedded instead of using the keys. 

Whenever concreting is suspended on any section for more than one 
hour, all edges which will be exposed in the finished work shall be brought 
to a level. 

In any given layer the separate batches shall follow each other so closely 
that each one shall be placed and compacted before the preceding one has 
set, so that there will be no line of separation between the batches. 

After the concrete has begun to set, it shall not be walked upon in less 
than twelve hours. 

The operation of compacting the concrete shall be conducted so as to 
form a compact, dense, impervious artificial stone which shall show a 
smooth face on exposed surfaces. The weight of rammers, if used, shall be 
satisfactory to the Engineer. If any monolith, the concrete of which is 
found porous, has been plastered or is otherwise defective, it shall be removed 
and replaced in whole or in part, as directed by the Engineer, entirely at 
the Contractor's expense. 

18.14. The Contractor shall construct suitable forms, the cost of which 
shall be included in the contract price per cubic yard for the concrete, the 
interior shape and dimensions of which shall be such that the finished con- 
crete shall be of the form and dimensions shown on the plans. Lagging 
for faces shall not be less than two (2) inches in thickness before being 
dressed, except where used for curved or special surfaces. Especial atten- 
tion must be paid to bracing, and where the forms appear to be insufficiently 
braced, or iinsatisfactorily built, either before or during concreting, the 
Engineer shall order work to be stopped until the defects have been corrected 
to his satisfaction. If desired, small rods to hold the forms may be embedded 
in the concrete, but in all such cases provision must be made by sleeve 
nuts or other satisfactory methods for the removal of the two inches nearest 
the surface. All holes thus left shall be immediately and completely filled 
with cement mortar and the surface left smooth and even. All forms 
shall be set and maintained true to the lines designated until the concrete 
is sufficiently hardened. All forms shall be satisfactory to the Engineer 
and shall remain in place as long as he deems necessary. The interior 
surfaces of the forms which come in contact with the surfaces of the concrete 
which will be exposed in the finished work shall be of lumber dressed on 
both faces and both edges and having water-tight joints, and shall be so 
constructed as to leave all such exposed surfaces of the concrete with a 
smooth even finish. Forms reused shall be Maintained at all times in good 
condition as to accuracy of shape, strength, rigidity, watertightness and 
smoothness of surface. Forms unsatisfactory in any respect shall not be 
used, and if condemned shall be removed immediately from the work. 

18.15. Boulders and fragments of rock may be bedded in a large mass of 
third-class concrete. Each stone before being bedded or placed shall be 
thoroughly washed and scrubbed, if necessary, to free it from all dirt. 
Stones bedded in concrete shall be at least three inches apart at all points, 
and no stones shall be placed within three inches of any face of the concrete. 
Stones shall be laid on their largest bed and worked down into the concrete 
by bars so as to exclude the air from any pockets in the lower surface of 
the stone. 

18.16. The Contractor shall construct weep holes in all retaining walls 
at such points as are indicated on the plans or designated by the Engineer. 
Selected stones shall be placed by hand at the inner end of the holes to 
assist drainage in escaping and to prevent the overflow of earth. Payment 
for all labor and materials required to construct and protect these weep 
holes will be included in the contract price for concrete. 

18.17. Whenever directed by the Engineer, newly laid masonry shall 
be protected to prevent freezing, and the protection shall be in all respects 
satisfactory to him. 

The Contractor shall be responsible for all damage to concrete by freezing, 
and any concrete so damaged shall be cut out and replaced at the Con- 

1 tractor's expense as directed by and to the satisfaction of the Engineer. 

j When the temperature falls below 35 degrees Fahrenheit the fine aggre- 

2 gate, water and stone shall be heated, and the newly laid concrete shall be 
} covered with canvas or otherwise protected from freezing. No concrete 



y52 SPECIFICATIONS 

foundation for pavement or concrete pavement shall be laid when the 

T^rior to'the finTac^eptance of the work shall be remedied by the Contractor 
JrSI.. own expense and to the satisfaction of the Engineer. 
^ t8 TO No Secfof stone shall be left within one inch of any face a broad- 
tinedfoVkorTther implement, if approved, being thr^^^ b^^ween the form 
o^^ the concrete to pry the fragments of stone back from the face. 

The to^sSf ace of concrete shall be formed immediately after the under- 
1vinacou?srfs completed and before this course takes its mitial set The 
too surfacf shalf b?formed by cutting off the excess with a^ temp ate and 
shSll then bfrubbed smooth and hard with a wooden float by skilled men. 
A^fsoon as the concrete has sufficiently set and the Engineer shall so direct, 
thplXis shall brremoved and all exposed faces immediately finished by 
We rubbed smootW^^ a mortar block and water. No plastering of 
^nv surface will be allowed, the required finish being obtained by rubbing 
doln theTrrlgularities of the face.\All exposed '^^^--^'^^^^rXl'Zi^^^ 
S^nQP without pits, irregularities, blow holes or bubbles., ihe surtace 
of all fi^sheTLd^u^^^^^ work shall be kept wet for a period of six days 

"tlfedSf Tol^^^^^^^^^^^ will be exposed in the finished 

structurf shin be rounded. A radius of one inch shall be used unless other- 
wLe designated on the plans or directed by the Engmeer. 

t8 20 Concrete shall not be laid in water nor exposed to the action 
of the water^before- setting, except by written permission of the Engineer, 
and then in such manner as he may specially direct. ^.^^^ ..i.„ .t-_„ 

t8 9t Where concrete is to rest on any excavated surface, other than 
rock sD^ckl care shall be taken not to disturb the bottom of the excavation 
Ind the final removal of material to grade shall not be made until just 
blrl"conc?ete is laid, except in concrete ^--dations for pavemen 

The excavation lines and bases of structures shown on the plans snau 
be consider!! as only approximate; and they may be ordered m writing 
hi ?hf Engineer to be placed at any elevation or of any dimensions that 
wTll Sfvf a satfsfactory foundation. Any additional concrete that may be 
reqmVed by thlEnSneer below or beyond the lines shown on the plans 

" NoXc^tu?e shalfbeTo'mmen^cTd'without the Engineer's approval. . 

AU mck o^ Lrdpan foundation surfaces shall be freed from loose pieces. 
riit to firm surfaces and cleaned to the satisfaction of the Engineer, before 
laying concrete All seams shall be cleaned out and filled with concrete or 
mortfr; and payment for such cleaning out and filling shall be made at 
the contract price for the class of concrete used. j ^« .-Uoii ^o 

UmfJs nor for an/concrete whose placing is rendered necessary owing to 

'* Th°e orTcrBiffor Items 18. 19 and 20. respectively, shall include all 
materia?s forms labor and other incidental expenses necessary to satis- 
Sctorly comSIte the work as specified in the foregoing paragraphs for 
first°class-concrete, second-class concrete and third-class concrete respectively. 

Item 21 — Stone Masonry 

21 I. Under this item the Contractor shall f""-°i=h and build all stone 
masonry in structures or elsewhere, as shown upon the plans or ordered 

SllSX7mfnfm-rta^"^^edf/;sTecp^^^^^^ 

-S^^hVs?o^-hSf^el^iS^n^?s^ftuTa!^^^^^^^^ 

presenting a neat and finished appearance Spalls f.^^ p mners shaU not 
bP allowed to show on the face of the wall, and shall be used only wnere 
nLessaTy The le^^h of stretchers shall not exceed three times their rise; 
?he with of stretchers shall in no case be less than their rise At least o^^^^ 
fourth of the stone in the face shall be headers, and these shall be evenly 



METHODS 753 

distributed; the length of headers shall not be less than the thickness of 
the wall, where the wall is four feet or less in thickness; where the wall is 
more than four feet in thickness, the length of the headers shall not be 
less than two feet and eight inches, and not more than two-thirds of the 
thickness of the wall; the width of the headers shall not be less than their 
rise. All stones shall be laid to break joints six inches or more and to 
thoroughly bond the work. ^ No joint of the face shall be over one inch in 
width. Backing shall consist of good-sized, well-shaped stone so laid as 
to break joints. All spaces between the stone shall be filled with spalls 
set in mortar. The rear faces shall present approximately plain surfaces. 

21.4. End walls of culverts and retaining walls shall be capped with 
concrete or with stone, roughly squared, extending across the entire, width 
of the wall, and on steps of wing walls the coping shall extend under the 
step next above it at least eight inches. 

21.5. On all exposed faces, the joints shall be raked out and cleaned 
to a depth of two inches and then pointed with Portland cement mortar 
mixed in a proportion of one to one. 

21.6. The quantity of stone masonry to be paid for under this item shall, 
be the number of cubic yards measured in the completed work, and the 
limits shall not exceed those shown upon the plans or fixed by the Engineer. 

The price bid shall include all labor, materials and incidental expenses 
necessary to satisfactorily complete the work. 

Item 22 — Stone Cxirbing and Headers 

22.1. Under this item the Contractor shall furnish and place stone curbing 
and headers where shown on the plans or ordered by the Engineer. 

22.2. Stone curbing and headers shall be of approved bluestone, sand- 
stone or granite, sound, uniform, free from seams or other imperfections, and 
shall be nowhere less than 5 inches thick, 15 inches deep, and 3 feet long. 

The upper face shall be evenly cut and the front face shall be dressed 
for the full depth to an even surface with no projections or depressions ex- 
ceeding one-quarter inch. The bottom shall be roughed off parallel to the 
top so that there will be no projections exceeding 2 inches beyond the 
required depth. 

^ The ends shall be squared and dressed to form joints not exceeding one- 
eighth inch for a depth of at least 2 inches from top and front face. The 
backs shall be rough dressed for full depth and dressed the same as the 
face for a depth of 2 inches from the top. The joints of circular curbing 
shall be cut on radial lines. 

22.3. The curb or header shall be set in third-class concrete, as shown 
on the plans. It shall be true to line and grade and settled so as to have a 
firm and uniform bearing. 

22.4. If required by the plans, porous drain-tile shall be placed under 
stone curbing and firmly embedded and covered with cinders, gravel or 
broken stone. 

22.5. After the curb or header has been set the trenches shall be filled 
with earth and thoroughly tamped. 

22.6. The quantity to be paid for under this item shall be the number 
of linear feet of curbing or headers set in accordance with plans and directions 
of the Engineer. 

The price bid for this item shall include the furnishing and setting of 
the curb or header, all concrete, tile, broken stone or gravel, and all labor, 
materials and incidental expenses necessary to complete the work. 

. Item 23 — Resetting Old Curbing 

23.1. Under this item the Contractor shall remove and reset old curbing, 
as shown upon the plans or ordered by the Engineer. 

23.2. Care shall be taken in removing old curbing so that there shall be 
. no" unnecessary breakage, and any curbing damaged in removing, hauling, 

or storing, due to the carelessness of the Contractor, shall be replaced with 
new curbing at his own expense. 

23.3. All joints and tops shall be redressed, if directed by the Engineer, 
to obtain a sanooth top surface and to obtain joints of the same class as 
specified for new curbing. 



754 SPECIFICATIONS 

23.4. The quantity to be paid for under this item shall be the number of 
linear feet removed, stored, hauled, and reset in accordance with the plans 
and as directed by the Engineer. 

The price bid shall include all concrete, tile, removing, redressing, hauling, 
storing, resetting, and all materials, labor and incidental expenses necessary 
to complete the work. 

Item 24 — Concrete Curbing 

24.1. Under this item the Contractor shall place concrete curbing, of 
the type shown on the plans, where shown on the plans or ordered by the 
Engineer. 

24.2. All curbing shall be constructed of first-class concrete. The con- 
crete shall be of such consistency, and be so spaded and worked, that a 
smooth mortar face will be produced. The coarse aggregate for concrete 
curbing shall be approved No. 2 stone or gravel. 

24.3. Curbing shall be moulded in place in sections 6 feet long and pro- 
vision made at each joint for expansion of one-sixteenth inch. 

24.4. All forms shall be set true to line and grade and held rigidly in 
position. They shall be either of metal or of acceptable planed and matched 
lumber, and of such construction that a smooth surface will be provided. 

The forms shall be left_ in place until the concrete has set sufficiently 
so that they can in the opinion of the Engineer be removed without injury 
to the curbing. The curbing shall immediately upon the removal of the 
forms be rubbed down to a smooth and uniform surface, but no plastering 
will be allowed. For this work a competent and skillful finisher shall be 
employed. 

24.5. The Contractor shall protect the curbing and keep it in first-class 
condition until the completion of the contract. Any curbing which is 
damaged at any time previous to the final acceptance of the work shall be 
removed and replaced with satisfactory curbing at the Contractor's ex- 
pense. (Also see section 18.1.) 

24.6. The quantity to be paid for under this item shall be the number of 
linear feet placed in accordance with the plans or directions of the Engineer. 

The price bid for concrete curbing shall include the furnishing and placing 
of all concrete, tile, porous filling, forms, and all other materials, labor and 
incidental expenses necessary to complete the work. 

Item 25 — Concrete Edging 

25.1. Under this item the Contractor shall furnish and mould in place 
concrete edging of the type shown on the plans and where designated on 
the plans or ordered by the Engineer. 

25.2. The concrete edging shall be composed of second-class concrete. 
The top shall be troweled to an even surface and the material shall be 
rammed and spaded so that a dense concrete and a smooth surface will 
result. (Also see section 18. i.) 

25.3. The forms shall be set and held true to line and grade, and shall 
not be removed until the concrete has set sufficiently, in the judgment of 
the Engineer, so that no harm will result therefrom. The edging shall be 
protected from injury until the completion of the contract. 

After the removal of the forms, the trenches shall be back-filled with 
earth and thoroughly tamped. ^ 

25.4. The quantity to be paid for under this item shall be the number of 
linear feet of concrete edging completed as shown on the plans or ordered 
by the Engineer. 

The price bid shall include the furnishing and placing of concrete and 
forms, and all other materials, labor and incidentals necessary to complete 
the work. 

Item 26 — Cobble Gutters 

26.1. Under this item the Contractor shall furnish and place cobble 
gutters where shown on the plans or ordered by the Engineer. 

26.2. Cobble gutters shall consist of rounded "hardheads," quarry 
or field stone, and shall be laid on edge. If hardheads are used they shall 
be 4 inches to 8 inches in diameter. The largest stones shall be selected 



METHODS 755 

and set along the edges of the gutter. All stones except where embedded in 
mortar shall be set in sand, and shall be laid to line and grade with close 
joints by skilled workmen using regular paving tools. The whole shall 
then be thoroughly rammed in place and brought to a uniform surface. 
All joints shall be swept full of sand. On grades exceeding 6 per centum and 
elsewhere if called for by the plans or ordered by the Engineer, cobble gutters 
shall be laid in Portland cement mortar, mixed one to three, as shown upon 
the plans. 

26.3. The quantity of cobble gutter to be paid for under this item will 
be the number of square yards of exposed surface laid in accordance with 
the plans and as directed by the Engineer. 

The price bid shall include the furnishing and placing of all stones, sand, 
mortar, and all other materials, labor and incidental expenses necessary 
to complete the work. 

Item 27 — Concrete Gutters 

27.1. Under this item the Contractor shall furnish and place concrete* 
gutters where shown upon the plans or ordered by the Engineer, 

27.2. Concrete gutters shall be of first-class concrete and shall conform 
to all requirements therefor as elsewhere specified. They shall be of the 
shape and length shown upon the plans, and shall be placed true to line 
and grade as directed. (See section 18. i.) 

27.3. The quantity for which the Contractor will be paid shall be the 
number of square yards of concrete gutters placed in accordance with the 
plans and ordered by the Engineer. 

The price bid shall include the furnishing and placing of all _ concrete, 
the prepara-tion of foundation, together with all other labor and incidental 
expenses necessary to satisfactorily complete the work. 

Item 28 — Brick Gutters 

28.1. Under this item the Contractor shall furnish and place brick gutters 
where shown upon the plans or ordered by the Engineer. 

28.2. Brick gutters shall be constructed of approved brick, shall conform 
to the dimensions shown upon the plans, and shall be laid true to lines and 
grades upon a suitable bed of sand. 

28.3. Where brick gutters are to be laid next to a curbing in connection 
with a pavement having a concrete foundation, they shall be constructed 
in full conformity to the specificatfons for brick pavement, and shall be 
paid for as such. _ 

28.4. The quantity for which the Contractor will be paid shall be the 
number of square yards of brick gutters placed inaccordance with the plans 
a,nd ordered by the Engineer. 

The price bid shall include the furnishing and placing of all materials 
and the preparation of bed, together with all other labor and incidental 
expenses necessary to satisfactorily complete the work. 

Item 29 — Metal Reinforcement 

29.1. Under this item the Contractor shall furnish and place metal bar 
and metal mesh reinforcing material where shown upon the plans or directed 
by the Engineer. 

29.2. All metal reinforcement shall, when embedded, be free from mill 
scale, grease, injurious rust, dirt or other foreign substance. 

29.3. AH metal reinforcement shall be securely held in place so that it. 
will be in the prescribed position after the concrete has been thoroughly 
compacted. 

29.4. Unless otherwise designated upon the plans,'^all bar reinforcement 
shall be of open hearth steel, and shall consist of approved "deformed" 
bars or rods which shall have an elastic limit of not less than 30,000 nor 
more than 45,000 pounds per square inch, and an elongation of not less than- 
20 per centum in a length of 8 inches. 

Deformed bars shall not contain more than ^00 of one per centum of 
sulphur nor more than Hoo of ope per centum of phosphorus. In small 
culverts and other structures of minor importance standard commercial de- 
formed bars acceptable to the Engineer may be used. 

All deformed bars shall be uniform in quality, and shall endure bending 



7S6 



SPECIFICATIONS 



1 80 degrees, when cold, around a circle whose diameter is equal to the 
diameter or thickness of the test piece, without fracture on the outside of 
the bent portion. 

Bars shall overlap each other by 30 diameters. 

29.5. Unless otherwise designated upon the plans, all metal mesh rein- 
forcement shall be of an approved kind and quality, and of the cross-section 
shown upon the plans and acceptable to the Engineer, and equal in all 
respects to the best standard commercial products. Sheets of metal mesh 
shall overlap each other as directed by the Engineer or as shown upon 
the plans. 

29.6. The quantity of metal reinforcement for which the Contractor 
will be paid shall be the number of pounds incorporated in the work ^'n 
accordance with the plans or directions of the Engineer. 

The bid price shall include all labor, materials, and other expenses nec- 
essary to satisfactorily complete the work. 

; Metal reinforcement used in rails and posts shall not be included in 
this item, but shall be considered as being included in the price bid for 
appropriate items. 

Item 30 — Miscellaneous Iron and Steel 

30.1. Under this item the Contractor shall furnish and place all cast 
iron, wrought iron and steel not especially included in other items as shown 
on the plans and for miscellaneous structures as ordered by the Engineer. 
This item shall include beams, channels, and other structural shapes, as 
well as miscellaneous iron castings, wrought iron, etc. 

30.2. All structural steel, bolts, etc., shown on the plans may be of 
stock steel. Stock steel shall be subjected only to surface inspection and 
cold bending tests. Test pieces cut from finished materials shall endure 
bending cold, without signs of cracking, 180 degrees around a circle whose 
diameter is equal to the thickness of the test piece. 

Iron castings shall be made of the best tough gray iron of uniform quality 
and shall be free from defects and uneven shrinkage. No mill cinder iron, 
white or burnt iron or scrap of any kind shall be used. They shall be 
clean, out of wind, and true to dimensions. Castings having blow holes 
plugged or filled with putty or crust shall not be used. 

Wrought iron shall be tough, fibrous and uniform in quality and shall be 
manufactured by approved methods. Steel scrap shall not be used in its 
manufacture. Finished material shall be clean, smooth, true to shape and 
free from defects. 

All iron and steel except cast iron shall be given a shop coat of red lead 
and oil, and after being placed shall be given two coats of approved paint. 

30.3. The quantity of iron, wrought iron and steel to be paid for under 
this item shall be the number of pounds furnished and placed in accordance 
with the plans or instructions of the Engineer. The price bid shall include 
the furnishing, placing, painting and all other labor, materials and incidental 
expenses necessary to satisfactorily complete the work. 

Item 31 — Wooden Guard Railing 

3 1. 1. Under this item the Contractor shall furnish and erect wooden 
guard railing of the type indicated, where shown on the plans or ordered by 
the Engineer. 

31 . 2. The posts shall be of seasoned white oak, cedar, locust, tamarack, 
white pine, or chestnut. ^ They shall be at least 6 inches square, or if round 
Ihey shall be 6 inches in diameter at the smaller end after the bark is removed, 
and 7 feet long. Round posts shall be shaved to even surfaces free from bark 
or skin. The lower part of the posts to a point 3 feet from the top shall be 
dipped while dry in suitable bituminous material heated to a temperature 
of 300 degrees Fahrenheit, or shall be charred as directed. The posts if 
dipped shall be thoroughly dry before being set in the ground . 

31.3' Rails shall be of seasoned, planed spruce or other ^satisfactory 
wood, and be properly secured to the posts, all in a workmanlike manner. 

31.4. The joints of the rails and posts shall be given one coat of white 
lead and linseed oil before being put together; the beveled tops of posts shall 
receive two heavy coats of the same. The entire surface exposed above the 
ground shall be painted with three coats of white lead and linseed oil. 



METHODS 757 

31 .5. The white lead and the Unseed 9!! shall be delivered separately on 
the road in original containers; before being mixed and used a pint sample 
of each, covering each lot, shall be forwarded to the Bureau of Tests, and 
neither ingredient shall be used until accepted by the Commission. The 
mixing of the ingredients shall be as directed by the Engineer. This specifi- 
cation shall apply to all paint used under this contract. 

31.6. The quantity of wooden guard railing to be paid for under this 
item shall be the number of linear feet completed in place. 

The price bid shall include the furnishing and erecting of all posts and rail, 
the excavation, painting, dipping, hardware and all expenses and incidentals 
necessary to complete the work. 

Item 32 — Special Guard Railing 

32 . 1. Under this item the Contractor shall furnish and erect, true to line 
and grade, guard railing of the special design shown upon the plans, at the 
places indicated by the plans or ordered by the Engineer. 

32.2. Except as otherwise provided by the plans, each class of work 
necessitated under this item shall be governed by the clauses of other items 
which are specially applicable thereto. 

32 .3. The quantity of guard railing to be paid for under this item shall 
be the number of linear feet placed in accordance with the plans and ordered 
by the Engineer. 

The price bid shall include all excavation, concrete, metal reinforcement, 
hardware, backfilling and all other materials, labor and incidental expenses 
necessary to satisfactorily complete the work. 

Item 33 — Pipe Railing 

33 .1. Under this item the Contractor shall furnish and erect pipe railing 
of the type indicated where shown upon the plans or ordered by the Engineer. 

33 . 2. Pipe railing shall consist of wrought iron pipe, rails, posts and pipe 
rail fittings of the sizes shown on the plans. All threaded joints shall be 
coated with lead and oil before being assembled. All parts shall be painted, 
after being put in place, with two coats of white lead and linseed oil. 

33 .3. The quantity of pipe railing to be paid for under this item shall be 
tlie number of linear feet placed in accordance with the plans and ordered 
by the Engineer. 

The price bid shall include the furnishing and erecting of all materials, the 
painting and all expenses and incidentals necessary to complete the work. 

Item 34 — Guide Signs 

34. 1. Under this item the Contractor shall furnish and erect guide signs 
of the type indicated wherfe shown upon the plans or ordered by the Engineer. 

34 . 2. Permanent guide signs shall be for the purpose of furnishing perma- 
nent directions to traffic after the completion of the contract. Permanent 
guide signs shall be constructed of kiln dried white pine and of the dimensions 
shown on the plans. They shall first be given four coats of white lead mixed 
with linseed oil. After the last coat has become thoroughly dried the letters 
shall be painted with black enamel paint, and when this is thoroughly 
dry they shall be given one coat of the finest white shellac. 

34.3. Temporary guide signs shall be for the purpose of guiding traffic 
along a detour during construction. Temporary guide signs shall be 
constructed of kiln dried white pine and of the dimensions shown on. the 
plans. They shall first be given three coats of white lead mixed with linseed 
oil. After the last coat has become thoroughly dried the letters shall be 
painted with black enamel paint. 

34.4. The number of guide signs to be paid for under this item shall be 
the number of signs placed in accordance with the plans and ordered by the 
Engineer. All signs become the property of the State upon payment for this 
item. 

The price bid shall include the furnishing pf all labor and materials neces- 
sary to satisfactorily erect permanent guide signs on sign posts and temporary 
guide signs including sign posts, each guide sign complete in place. 



7S8 



SPECIFICATIONS 



Item 35 — Highway Number Signs 



35. 1. Under this item the Contractor shall paint on the concrete sign 
post highway number signs of the type indicated where shown upon the 
plans or ordered by the Engmeer. 

35 . 2. Highway number signs shall be painted on all concrete sign posts 
with letters which shall first be formed of two coats of fiat black mixed in oil 
and afterward retraced with black enamel. 

35- 3- The number of highway number signs to be paid for under this 
item shall be the number placed in accordance with the plans and ordered 
by the Engineer. 

The price bid shall include the furnishing of all labor and materials to 
satisfactorily complete the work. 

Item 36 — Danger Signs 

36.1. Under this item the Contractor shall furnish and erect danger 
signs where shown upon the plans or ordered by the Engineer. These 
shall be of the type called for by the plans. 

^ 36 . 2. Danger signs shall be constructed of a material and painted 
similar to that specified for guide signs and shall be of the dimensions and 
lettered as shown on the standard plans. These signs shall be placed on 
the standard concrete sign posts and set at an angle of forty-five degrees 
to the center line. When the standard sign is used the arrow shall point in 
the direction of the danger. 

36 . 3. . The number of completed danger signs for which the Contractor 
will receive payment will be the number placed in accordance with the plans 
and ordered by the Engineer. 

The price bid sh#ll include the furnishing of all labor and materials neces- 
sary to complete each danger sign in a satisfactory manner. 

Item 37 — Concrete Sign Posts 

^ 37.1. Under this item the Contractor shall furnish and erect concrete 
sign posts of the type indicated, where shown upon the plans or ordered by 
the Engineer. 

37 .2. Concrete sign posts shall be made of first-class concrete and of the 
dirnensions and materials shown on the standard plans. To these posts 
shall be securely fastened guide boards and signs. 

37.-3. The number of completed concrete sign posts to be paid for under 
this itern shall be the number erected in accordance with the plans and 
ordered by the Engineer. 

The price bid shall include all concrete, reinforcement, forms, excavation 
and backfill, and the furnishing of all other labor and materials necessary 
to complete each concrete sign post in a satisfactory manner. 

LOOSE STONE 

Item 38 — Screened Gravel — ^Loose Measure 

Item 39 — Broken Stone — Loose Measure 

38.1. Under these items the Contractor shall furnish and place upon 
the road, as directed by the Engineer, broken stone and gravel of the sizes 
designated on the Itemized Proposal. This stone and gravel will be used 
for general repair work and for miscellaneous work. 

38.2. The stone or gravel delivered shall be of approved quality and shall 
conform to the general requirements for broken stone and gravel, and thev 
shall be of the sizes ordered. 

'u^?^'l' T^® quantity to be paid for under Items 38 and 39 respectively 
shall be the quantity of broken stone or gravel furnished and delivered on the 
work at the places and in the condition specified by the Engineer. When 
the material is produced by the contractor on the work, it shall be measured 
in cubic yards; it shall be measured in tons of 2000 lbs. when the material is 
imported and the weight is obtainable from reliable sources such as certified 
quarry orTaiiroad figures. 

The priceibid shall, include furnishing and delivering the stone or gravel 



METHODS 759 

as directed by the Engineer and all labor, appliances and expenses incidental 
thereto; also the spreading, rolling or incorporating of the stone or gravel 
in the work, when required by the Engineer. 

FOUNDATION COURSE 

Item 40 — Foundation Course — **Run of Bank" Gravel 
Item 41 — Foundation Course — Field or Quarry Stone 

40.1. Under these items the Contractor shall furnish and place a founda- 
tion course of stone or gravel of the depth and in the places called for by the 
plans, or as ordered by the Engineer in accordance with section 2.5, "Prepa- 
ration of Subgrade" of item "Excavation." 

40.2. No stone or gravel shall be placed on the road until the culverts are 
completed and proper drainage provided. 

40.3. When field or quarry stone is used for constructing the foundation 
course it shall be of a hard, sound and durable quality, acceptable to the 
Engineer; the stones shall be placed by hand so as to bring them in as close 
contact as possible. When quarry stones are used they shall be placed on 
edge. The depth of the stone shall in no case be greater than the depth 
specified for the course, the width shall not be greater than the depth, 
nor more than six inches; and the length shall not be greater than one and 
one-half times the depth, nor more than 12 inches. The distribution of the 
stone shall be of a uniformity satisfactory to the Engineer. The long dimen- 
sion shall always be placed crosswise the road. After laying, this course 
shall be thoroughly rolled with an approved roller weighing not less than 
ten tons, and shall then be filled with stone or gravel as directed and again 
rolled until the stones are bound together and thoroughly compacted; but 
no gravel shall be used for filling except under written permission of the 
Engineer. All holes or depressions found in rolling shall be filled with mate- 
rial of the same quality and the surface shall be re-rolled until it conforms to 
the lines and grades shown on the plans. When field stone is used approved 
tailings may be used for filling. In all cases a sufficient amount, of fine mate- 
rial shall be used to fill all voids. In limited areas where the use of a roller 
is impracticable heavy tampers may be used to consolidate the material. 

40.4. Wherever gravel is used for the foundation course it shall conform 
in all particulars to the gravel specifi^ed in section 2 of Bottom Course "Run 
OF Bank" Gravel. . ' . . 

40.5. The quantity to be paid for under this item shall be the number of 
cubic yards of compacted material in place. The amount to be estimated 
shall be computed by multiplying the finished cross-section of the foundation 
course as shown upon the plans or ordered by the Engineer, by the length of 
the foundation course measured along the axis of the pavement. 

The price bid shall include the furnishing, placing, filling, rolling of the 
material and all labor and incidental expenses necessary to complete the 
work. 

Item 42 — Foundation Course — Telford Base 

42.1. Under this item the Contractor shall furnish and place a founda- 
tion course of field or quarry stone laid on edge, in accordance with the plans 
or as ordered by the Engineer. 

42.2. No stone shall be placed on the road until the culverts are com- 
pleted and proper drainage has been provided. 

42.3. Field or quarry stone of approximate rectangular_ shape shall be 
used. The stone shall be not less than one and one-half inches thick, in 
depth equal to the depth of the course, and in length not more than one and 
one-half times the depth. 

42.4. The pieces shall be placed on edge by hand in as close contact as 
possible with long dimension crosswise of the road. After being placed, 
all pieces projecting more than one inch above the established plane of the 
surface shall be broken off flush so as to obtain a true and uniform surface. 
This course shall then be rolled with an approved self-propelled roller weigh- 
ing not less than ten tons, and shall then be filled with approved screenings 
and again rolled until the course is thoroughly compacted. Material other 
than screenings for filling this course shall not be used except under the writ- 
ten order of the Engineer. 



76o 



SPECIFICATIONS 



42.5. The quantity to be paid for under this item shall be the number 
of cubic yards of compacted material in the cornpleted course. The amount 
to be estimated shall be computed by multiplying the finished cross-section 
of the foundation course as shown upon the plans or ordered by the Engineer, 
by the length of the foundation course measured along the axis of the pave- 
ment. The price bid shall include the furnishing, placing, filling, rolling of 
the material and all labor and incidental expenses necessary to complete the 
work. 

BOTTOM COURSE 

Item 43 — "Run of Bank" Gravel 

43.1. Under this item the Contractor shall furnish and place approved 
"Run of Bank" gravel either upon the properly prepared sub-grade or 
upon the foundation course. The work shall be performed in full conformity 
to the specifications given under sections 44.-2 to 44.9 inclusive, so far as 
same are not inconsistent with the use of such gravel. 

43.2. All gravel shall be of hard, durable stone satisfactory to the Engineer. 
The particles shall be of such size as will pass through a 3>^-inch circular 
hole, and shall be well graded. Gravel shall be of such nature that the 
material passing a 3'i-inch screen shall not be more than 5 peri centum in 
excess of the voids in the remaining material after its separation therefrom. 
Before using "Run of Bank" gravel in the work the same shall be tested to 
determine its suitability. Should at any time during the work and for any 
reas9n the gravel fail to maintain suitable proportions of the coarse and fine 
particles, the Contractor shall by the addition of selected material and satis- 
factory manipulation produce a material meeting the above requirements. 

_ 43. 3. The depth of loose stone or gravel in all cases, whether in founda- 
tion, bottom or top courses, shall be gauged by the use of cubical blocks of 
suitable size. (See page 591.) 

43.4. The spreading of any layer or course of broken stone, gravel or 
filler, whether in foundation, bottom or top courses, shall be done from 
suitable spreader wagons or from piles dumped along the road as directed 
by the Engineer. 

No segregation of large or fine particles will be allowed, but the stone as 
spread shall be well graded with no pockets of fine material. 

43.5.. The quantity to be paid for under this item shall be the number 
of cubic yards of compacted material in place in the completed course. 
The amount to be estimated shall be computed by multiplying the finished 
cross-section of the bottom course as shown on the plans or ordered by the 
Engineer, by the length of the bottom course measured along the axis of 
the pavement. 

The price bid shall include the furnishing, placing, rolling and filling the 
material, and all other labor, materials and incidental expenses necessary 
to satisfactorily complete the work. 

Item 44 — Bottom Course — Screened Gravel 
Item 45 — Bottom Course — Broken Stone 

44.1. Under these items the Contractor shall furnish and place stone or 
gravel, conforming to the general requirements for same, either upon the 
properly prepared sub-grade or upon the foundation course. This stone or 
gravel shall be of sizes specified below. 

44.2. After the sub-grade or foundation course shall have been properly 
prepared and proper drainage provided, a course of broken stone or gravel 
of graded No.^ 3 or No. 4 or a uniform mixture of same shall be spread evenly 
so that it will have after rolling the required thickness. If specifically 
allowed by the Engineer a limited amount of No. 2 stone may be used in 
the bottom course. (For the meaning of these numbers in connection 
with size see page 720). ^ 

In cases where the finished thickness of the bottom course is to be more 
than S inches, the broken stone or gravel for it shall be spread, rolled and 
filled in two separate layers neither of which shall be of a greater depth than 
6 inches measured loose. 

^ Not feasible, see page 156. 



METHODS 761 

44.3. The depth of loose stone or gravel in all cases, whether in founda- 
tion, bottom or top courses, shall be gauged by the use of cubical blocks of 
suitable size. (See page 591.) 

44.4. The spreading of any layer or course of broken stone, gravel or 
filler, whether in foundation, bottom or- top courses, shall be done from 
suitable spreader wagons or from piles dumped along the road as directed 
by the Engineer. 

No segregation of large or fine particles will be allowed, but the stone 
spread shall be well graded with no pockets of fine material. 

44.5. After the bottom course of stone or gravel has been laid loose it 
shall be thoroughly rolled with an approved' roller weighing not less than 
ten tons. 

This rolling must begin at the sides and continue toward the center 
and shall continue until there is no disturbance of the stone ahead of the 
roller. After the stone is thoroughly compacted No. i stone or gravel, 
and screenings or sand, or a mixture of these, shall be uniformly spread 
upon the surface and swept in with rattan or steel brooms and rolled dry. 
After the completion of the rolling no teaming other than that necessary 
for bringing material for the next course shall be allowed over the rolled 
material. It is the intention to bind this course with the small stone, but 
not to use so much that a good bond will not be secured between the bottom 
and top courses. 

44.6. When two courses of bottom stone are laid each course shall be 
treated by rolling and adding fine material as described above. 

44.7. If the sub-grade material shall become churned up into or mixed 
with the bottom or sub-bottom courses through the Contractor's hauling 

. over it or working on it when the sub-grade is in a wet condition, the Con- 
tractor shall at his own expense remove such mixture of sub-grade material 
and broken stone and replace it with clean broken stone of the proper size, 
and shall roll or otherwise compact the material so as to produce a uniform, 
firm and even bottom course. 

If the above condition occurs through no fault of the Contractor, the 
Contractor shall be paid both for excavating and replacing under the items 
"Excavation" and "Bottom Course" respectively. 

44.8. All filler for top and bottom courses shall be delivered and piled 
alongside the road before the course in which it is to be used is placed. 

44.9. The quantity to be paid for under these items respectively shall 
be the number of cubic yards of compacted material in place in the com- 
pleted course.^ The amount to be estimated shall be computed by multi- 
plying the finished cross-section of bottom course as shown upon the plans 
or ordered by the Engineer, by the length of the bottom course measured 
along the axis of the pavement. 

The price bid for the respective items shall include the furnishing, placing, 
filling, rolling of the material and all labor and incidental expenses necessary 
to complete the work. 

Item 46 — Concrete Foundation for Pavement 

46.1. Under this item the Contractor shall furnish and place upon a 
propery prepared sub-grade, concrete foundation f9r pavement of the 
thickness shown upon the plans or ordered by the Engineer. 

46.2. Concrete foundation shall not be placed on any sub-grade until 
the sub-grade has been properly drained, thoroughly rolled and cornpacted, 
and is true to line and grade in horizontal and transverse cross-section. 

46.3. Concrete shall consist of a mixture of Portland cement. No. 2 
or No. 3 sand and broken stone or gravel. The coarse aggregate shall 
consist of a well-mixed product of No. 2 and No. 3 stone or No. 2 and No. 3 
gravel. The fine aggregate shall consist of No. 2 or No. 3 sand. All of 
these materials shall conform in all respects to the requirerrients_ given under 
"Materials of Construction," pages 717 to 720. All specifications relating 
to second-class concrete shall apply to work done under this item, in so far 
as they are not inconsistent with the special specifications given below. 

46.4. The concrete shall be mixed in the proportions of one volume 
of cement to two and one-half volumes of sand and five volumes of broken 
stone or gravel. The relative proportions of fine and coarse aggregate 
may be varied slightly, as a result of tests for voids by the Engineer, to 



762 



SPECIFICATIONS 



the end that the resulting concrete shall be as dense as possible. The 
concrete shall in all cases approximate a i : 2>^ : 5 niix. 

46.5. The concrete shall be mixed in approved mechanical batch mixers. 
Mixing shall be continued through at least 12 revolutions and until every 
particle is coated with mortar and until the batch is of uniform color and 
consistency. After the materials are once wetted the work shall proceed 
rapidly until the concrete is in place. The quantity of water used shall be 
as directed by the Engineer and suitable measuring tanks shall be provided 
by the Contractor so that the same amount of water may be used in the 
separate batches. 

46.6. Before any concrete :fs placed, the sub-grade shall be sprinkled 
sufficiently to dampen it, but a muddy condition shall not be allowed. 
As soon as possible after mixing, the concrete shall be deposited in place 
and thoroughly spaded and rammed so as to bring the mortar flush to the 
surface. Especial care shall be taken to keep the concrete uniform and to 
prevent pockets of stone or mortar. 

46.7. The surface, when completed, shall conform to the lines and grades 
shown upon the plans, and shall be free from depressions or irregularities. 
No stone shall project above the general surface. _ All ramming and shaping 
shall be done before the concrete has taken its initial set. 

46.8. When the work is stopped for any reason a vertical joint shall 
be put in and the work completed up to this joint. 

46.9. No concrete foundation for pavement shall be laid when the tem- 
perature falls below 35° F. 

46.10. As soon as the concrete has taken its initial set the surface shall 
be covered with a one-inch layer of suitable material and this shall be kept 
moist for a period of at least seven days. For covering concrete foundations 
on which a sand cushion is called for, the sand cushion may be used for 
the cover coat if the contractor so elects; in case this is done the sand cushion 
shall be put in acceptable condition before preparing for laying the blocks; 
any portions which have become excessively dirty shall be removed and 
replaced with acceptable material to the satisfaction of the Engineer. 

In those cases where material other than sand cushion is used as a cover 
coat it shall be cleaned off after a period of ten days. 

46.11. The quantity to be paid for under this item shall be the number 
of cubic yards of concrete foundation for pavement incorporated in the 
work in accordance with the plans or as directed by the Engineer. 

The price bid shall include the furnishing and placing of all materials; 
all mixing, tamping, finishing, and all labor, appliances and incidental 
expenses necessary to complete the work. The amount to be estimated 
shall be computed by multiplying the cross-section of concrete foundation 
as shown upon the pUns or ordered by the Engineer by the total length of 
concrete foundation measured along the axis of the pavement. 



METHODS 763 



Series of 1917 
IOWA STATE HIGHWAY COMMISSION 

AMES, IOWA 

Standard Specifications For 

Earth and Gravel Road 

Construction 



Revised series of 191 7 distributed by the State Highway Commis- 
sion under Chapter I-A, Title VIII, Supplement to the 
Code 191 3 as amended by Acts of the Thirty- 
Sixth General Assembly 

Section Three 
EARTH ROADS 

1. Alignment. — The center of the finished roadway shall conform in align- 
ment to the center stakes. These stakes shall follow, as nearly as possible, 
the center line of the right-of-way. 

2. Grade Lines. — The grade line shown on the profiles shall denote the 
crown of the finished roadway at its center line. 

3. Cross- section. — Unless otherwise provided the cross-section to be used 
is the standard cross-section of the Highway Commission for the road system 
on which the work is located. 

Note. — The Commission will approve changes in the standard cross-sec- 
tion to meet local conditions, on specific improvements, but a change ap- 
proved for one road shall not be construed to apply to other roads. In each 
case the proposed change should be submitted to the district engineer who 
will make a field examination to determine the feasibility of the changes 
proposed. 

4. Grading. — Under this head will be included all excavation and em- 
bankments required for the formation of the earth roadway, cutting all 
ditches along or contiguous to the road, forming the approaches to all side 
roads and farm entrances, changing of stream channels, and all other exca- 
vations and embankraents comiected with or incident to the construction of 
the road. Grading will be estimated under the following heads, viz.: 

Solid rock excavation. 
Loose rock excavation. 
Earth excavation. 
Solid rock excavation will include all rock in masses which cannot be re- 
moved without blasting, also all detached rock or boulders measuring not 
less than one cubic yard each. 

Loose rock excavation will include all slate or other rock which can be 
quarried or removed without blasting, also all detached rock or boulders 
measuring not less than one-fourth nor more than one cubic yard each. 



764 



SPECIFICATIONS 



Earth excavation will include all loose stones, boulders, and other material 
of every description as found, which are not included in the above specifica- 
tions as solid and loose rock. 

5. Excavation. — Excavation shall be made in all cases to the required 
alignment and cross-section. Any roots, stumps, or other timber encoun- 
tered in the excavation shall be removed and burned or otherwise disposed 
of as directed by the engineer, but shall not be placed in the embankments. 
All materials taken from excavations shall be deposited in the embankments 
unless otherwise specified or directed by the engineer. The cost of moving 
the same when the average length of haul does not exceed five hundred (soo) 
feet will be considered as included in the price per cubic yard for excavation. 

6. Provision for Drainage. — If it is necessary in the prosecution of the 
work to interrupt or obstruct the natural drainage of the surface, or the 
flow of artificial drains, the contractor shall provide for the -same during the 
progress of the work in such a way that no damage shall result to either 
public or private interests. He shall then be held liable for all damages 
which may result from any neglect to provide for either natural or artificial 
drainage which he may have interrupted. 

7. Intercepting Ditch. — In cuts along sidehills where there is a possbilityi 
of surface water causing damage by flowing down the side slope of the cut, 
a ditch shall be constructed to intercept the surface water and prevent it 
from flowing into the cut. The contractor will be paid for this work as an 
extra. 

8. Borrow Pits. — When sufficient material for the embankments is not 
obtainable within the side ditches and excavations as staked out, the con- 
tractor shall make up the deficiency from borrow pits laid out by the engineer. 
Borrowing must be done from regular shaped borrow pits in order to admit 
of ready and accurate measurements, care being taken not to unnecessarily 
injure or disfigure the land. ^ The banks must be sloped, the pits so con- 
structed that surface water will drain out and the premises left in a condition 
satisfactory to the engineer. The right-of-way for borrow pits will be fur- 
nished by the county. 

9. Berms. — Wherever it becomes necessary to make an excavation along 
the side of the road as in the construction of borrow pits, ditches, etc., a 
berm not less than four feet in width shall be left between the toe of slope 
of the roadway embankment and the top of the excavation bank. 

10. Waste. — When the amount of cut exceeds the amount of fill the excess 
material shall be deposited as directed by the engineer. Such material shall 
preferably be used in widening the adjacent fills so as to reduce the side 
slopes thereon. 

11. Embankments. — Embankments shall be carried up in horizontal 
layers, each of which shall be carried out to its proper width in the cross- 
section of the roadway. _ Sod obtained in the cuts may be deposited in the 
embankments provided it is so placed as to be not closer than twelve (12) 
inches to the finished roadway or subgrade. Stones obtained from cuts 
shall be so distributed in the embankments as to not form pockets or 
cavities. All existing slopes and surfaces of embankment shall be plowed 
where additional fill is to be made, so that the new material will bond with 
the old. 

12. Guard Rail. — Where the height of an embankment is over six feet, 
substantial guard rails shall be constructed along the shoulders. Such guard 
rail will be paid for at the price bid per lineal foot of rail. Where the height 
of the embankment is six feet or less, the side slopes shall be flattened to a 
slope not steeper than three to one (3 : i) unless otherwise shown on the plans. 

13. Sod in Blade Grader Work and Shallow Fills. — In blade grader work 
and in fills so shallow that the sod cannot be kept at least twelve (12'') inches 
below the finished roadway, such sod, after being cut loose with blade grade 
or plows, shall be disked and harrowed until it is reduced to small pieces 
which will not interfere with trafiic. These small pieces of sod shall not be 
deposited in the middle of the road but shall be deposited near the shoulders 
and shall be covered with earth. The middle portion of the road shall be 
formed of earth free from sod. The disking and harrowing of sod is included 
in the price bid for excavation. 

14. Side Ditches.— The side ditches shall be excavated to the depth, 
alignment, and cross-section shown on the drawings. Care shall be taken 
to secure a uniform grade on the ditches so that the water will readily drain 
out, and to secure smooth, uniform slopes on the ditch banks in strict con- 
formance with the drawings. 



METHODS 765 

15. Clearing and Grubbing. — The ground included in the highway must 
be cleared of trees, stumps, brush, weeds and grass to the full width of right- 
of-way, unless otherwise directed. All timber, stumps, brush, and other 
vegetable matter must be burned unless otherwise directed by the engineer. 
Such material shall not be placed in the embankments. 

Where embankments are to be more than two and one-half feet in height, 
it will be sufficient to cut all trees, stumps, and brush close to the ground. 
Where embankments are to be less 'than two and one-half feet in height, 
and in all excavations, all stumps and large roots must be grubbed out and 
burned or removed. 

Unless otherwise specified, clearing and grubbing will be paid for as extra 
work, as provided in Section Two, paragraph 22. Allowance will be made 
for all grubbing in excavations for the roadbed, all grubbing in borrow pits 
ordered and staked out by the engineer to supply material for the embank- 
ments, and all grubbing in embankments less than two and one-half feet 
high, but will not be allowed for embankments over two and one-half feet 
high, or in borrow pits made by the contractor without having been so 
ordered by the engineer. 

16. Hedge rows. — Hedges, under these specifications, are rows of trees or 
bushes, used for fence purposes or wind breaks, containing at least three 
bushes or trees per rod. For removing such hedges the contractor will be 
paid the price bid per rod. 

17. Measurements. — Grading shall be estimated and paid for by the 
cubic yard at the prices specified in the tender. Measurements of grading 
quantities will, in all cases, be made from the cuts or pits from which the 
material is taken, by cross-sectioning before and after excavation, and the 
volumes determined by the average end area method. 

18. Haul and Overhaul. — The average length of haul shall be determined 
by locating the center of gravity of the cut and the center of gravity of the 
corresponding fill. If the center of gravity of the cut is more than five 
hundred (500) feet from the center of gravity of the corresponding fill, over- 
haul at the rate of one cent per cubic yard per 100 feet will be allowed for 
the entire amount of material in the cut for the distance between the centers 
of gravity in excess of five hundred (500) feet. 

Note. — Should the engineer desire to eliminate any payment for overhaul, 
a stipulation to that effect may be inserted in the instructions to bidders, 
as provided in Section Two, paragraph 25. 

19. Tile Sub-drains. — Tile sub-drains shall be put in wherever shown on 
the plans. The tile used shall meet the requirements of the standard speci- 
fications for farm drain tile adopted in 19 16 by the American Society for 
Testing Materials. The tile shall be laid true to grade and alignment 
established by the engineer. ^ For furnishing and laying tile drains, the con- 
tractor will be paid at the price bid for such work. 

Note. — The first requirement of road construction is to get a well-drained 
roadbed. For this reason, county engineers are instructed to require tile 
drainage on all portions of the highways where there is any question regard- 
ing the adequacy of the surface drainage or the stability of the soil. 

If possible, the flow line of the tile shall be placed a minimum depth of 
five feet below the elevation of the roadway shoulders. No tile less than 
six inches in diameter shall be specified. 

Where the grade of the side ditch is less than one per cent., inlets to the 
tile shall be provided at intervals of about five hundred feet. These inlets 
shall be constructisd by filling the trench for a length of about three feet 
with coarse gravel, broken stone, or other suitable proous material. The 
top of the porous material shall be raised about eight inches above the top 
of the trench. 

20. Finishing Stakes. — The engineer shall set suitable finishing stakes to 
guide the contractor in finishing the road. 

Note. — One of the most common defects in earth road construction is the 
failure to bring the earth shoulders up to the proper grade and alignment. 
The shoulders are often left low and irregular, thus resulting in an unsightly 
road having too much crown in the center. This defect can be obviated 
only by setting stakes, giving the grade and alignment of the shoulders. In 
finishing, the contractor should use a templet to fit the crown of the road, 
and in this case stakes need be set only along one shoulder or along the center 
line. If no templet is used, finishing stakes should be set along each shoulder 
and on the center line. 

Finishing stakes on fills should be set above the established grade so as to 



766 



SPECIFICATIONS 



allow the proper amount of shrinkage. Under average conditions the follow- 
ing percentages for shrinkage should give satisfactory results: 

Depth of Fill ^irSe°' 

Up to 5.0 feet IS % 

5.0 feet to 12.0 feet 12 % 

12.0 feet to 18.0 feet ! 10% 

21. Finishing. — If the road is not to be surfaced with gravel, the contractor 
shall, after having brought it substantially to grade, complete the work in 
such a manner that the finished road will be smooth and true to cross-section, 
grade and alignment.^ No extra compensation will be allowed for finishing 
as this work must be included in the price bid for excavation. 

If the road is to be surfaced with gravel, the earthwork necessaiy for 
forming the sub-grade shall be executed in the manner specified for the class 
of gravel surfacing to be used. _ The preparation of the sub-grade for the 
gravel surfacing is not included in the price bid for earthwork. 

22. Installing Temporary Culverts.— ^-Temporary culverts will be construed 
to mean corrugated culverts, boiler pipe culverts, concrete tile culverts, or 
cast iron culverts not over thirty-six inches in diameter, and placed without 
permanent bulkheads. The county will furnish and deliver temporary cul- 
verts at the railroad station. The contractor will be required to haul, 
properly place, and fill over such culverts. For this he will be paid at the 
price bid per lineal foot. 

Section Four 
MATERIAL 

1. Gravel. — The gravel used in the construction of Class A or Class B 
gravel roads shall be a pit or bank gravel conforming to the following speci- 
fications as to grading: 

Passing a 2" mesh screen 100 % 

Passing a 2" , retained on \" mesh screen % to % 

Passing a \" , retained on y^" mesh screen % to % 

Passing a y^." , retained on yi," mesh screen % to % 

Passing a yi!' mesh screen 25 % to % 

The clay content shall not exceed fifteen per cent. (15 %) by dry weight. 

Engineer's Note. — The county engineer should make a careful sieve 
analysis of the gravel available for the work under consideration and should 
insert in the above blank spaces the percentages which will secure the best 
results, from the material at hand. A desirable road gravel should have a 
grading within the following limits: 

Passing 2" mesh screen 100 % 

Passing 2" mesh, retained on 1" mesh 20-40 % 

Passing i" mesh, retained on y^^" mesh 10-30% 

Passing 3^" mesh, retained on Y^" mesh iS-35 % 

Passing >^" mesh 25-40 % 

A gravel having over 60 % passing a Y^" screen should not be used in gravel 
road construction, although such a material might be used in a sand-clay 
road. 

2. Clay Content. — If the gravel used contains insufficient clay to bind it 
properly, additional clay shall be added in the manner specified for the class 
of road being constructed. If the gravel used contains too much clay, clean 
gravel or sand shall be added until the clay content is reduced to the proper 
percentage. 

Note. — The county engineer shall carefully test the available gravel sup- 
ply to determine the amount of clay binder, the percentage of oversized 
stones, and other information to enable the contractor to make intelligent 
bids on the work under consideration. 

3. Gravel Supply. — The source of the gravel supply shall be stated in the 
instructions to bidders. Where the gravel is to be shipped in, the contractor 
will be required to furnish such material and pay all freight charges and costs 



METHODS 767 

therefor. A price per cubic yard or per ton for such gravel on board cars 
at the station where it is to be unloaded shall be stipulated in the tender. 

Where the gravel is to be secured from local deposits, such deposits shall 
be bought or optioned by the county. The right-of-way for a suitable road 
reaching such gravel deposits shall also be provided by the county. 

4. Stripping the Gravel Pits. — Where the gravel pits are furnished by the 
county, the contractor shall do the necessary stripping, back-filling, and 
the necessary grading on the road leading to such pit. For this stripping, 
back-filling, and grading he will be paid at the price bid per cubic yard for 
earth excavation. 

5. Loading Gravel. — The contractor shall use precautions in loading the 
gravel so as to secure the grading specified. The loading shall be done in 
such £C way that the clay which is left on top of the gravel will be uniformly 
distributed throughout the material. ^ Large lumps of clay or loam in the 
gravel will not be permitted. Oversized stones shall be removed during 
the loading. 

Note. — If gravel is being secured from deposits that are quite variable, 
the county should station a man at the pit to see that a uniform mixture 
is secured in the loading, or should require the contractor to adopt a method 
of loading which will secure such uniformity. 

6. Right-of-way for Hauling Equipment. — It is understood and agreed 
that in transporting the surfacing material, the contractor shall have the 
right to lay tracks on, or operate equipment over, any public highway, pro- 
vided that the tracks shall be so laid as not to interfere with traffic; that the 
contractor is responsible for any accidents which may occur due to such 
railway having been laid on the highway, or to damages resulting from the 
highway being placed in an improper or dangerous condition, and that the 
public highway will be left in as good condition after the hauling is finished 
as when the same was started. 

The contractor shall maintain at his own expense the road leading to the 
gravel pit and shall repair any damage to public roads because of his hauling 
over the same. 

Motor trucks used in hauling shall not have a loading in excess of 400 
pounds per inch width of tire. This loading shall include the weight of 
the truck as well as the material being transported. 

7. Crushing Oversized Stone. — The contractor under these specifications 
shall not be required to crush any oversized stones unless a clause to that 
effect is inserted in the instructions to bidders. If such a requirement is 
made, the contractor shall furnish all equipment, material, and labor neces- 
sary to crush such stone, so that it will meet the requirements of Section 
Four, Paragraph No. i, with reference to size. Suitable means shall be 
provided for mixing this crushed material with the other gravel so that a 
uniform product is secured. 

Where crushing of oversized stone is required, a price per cubic yard for 
such crushing shall be received. 

Section Five 

CLASS A GRAVEL SURFACING 

1. Class A Gravel Surfacing. — Class A gravel surfacing shall consist of 
two courses of gravel of the thickness and width shown on the plans. The 
sub-grade and each course of gravel shall be compacted by rolling. (See 
Plate No. 34» page 140.) 

2. Earthwork. — Before any gravel surfacing is laid, the earth road shall 
have been brought to grade and cross-section, and the sub-grade prepared in 
in the manner specified. 

3. Preparation of Sub-grade and Shoulders. — The sub-grade for the lower 
course shall be shaped by excavating to the width shown on the cross-section 
for the lower course, and to a depth such that the top surface of the lower 
course will conform to the grade and cross-section shown on the plans. The 
material excavated shall be used for constructing the shoulders for the upper 
course. The edge of the trench shall be true to alignment and shall be as 
nearly vertical as the nature of the soil will permit. Before the upper course 
of gravel is placed, the earth shoulders for that course must be brought to 
the proper alignment and to such height that they will compact under 
rolling to the proper thickness for this course. 



768 



SPECIFICATIONS 



4. 'Lateral Drains. — -In clay soils, lateral drains shall be constructed at j 
intervals of from 50 ft. to 100 ft. as may be directed by the engineer. These 
drains shall be about 12" wide and shall be cut to such depth that they will 
drain freely from the sub-grade of the lower course to the side ditch. About 
S" of coarse gravel shall be placed in the trench and shall be covered with 
earth to the level of the shoulder. On hills over four per cent. (4%) grade, 
the lateral drains shall slope down hill at an angle of seventy degrees with 
the center line and shall be cut through to the center of the road. 

5. Rolling the Sub-grade. — After the sub-grade for the lower course has 
been properly shaped, it shall be rolled until thoroughly compacted and the 
roller leaves no perceptible track thereon. If, during the roiling, soft places 
appear, this material shall be removed and replaced with new material 
which can be properly compacted under the roller. If sandy places are 
encountered, sufficient clay shall be added to permit proper rolling. 

6. Placing the Lower Course. — The gravel for the lower course shall be 
placed on the sub-grade and spread uniformly to a depth such that when 
rolled it will have the thickness shown on the plans for this course. Ruts 
or depressions in the sub-grade caused by hauling over the same must be 
kept filled so as to present a smooth, uniform surface for receiving the gravel. 
After being evenly spread, the lower course of gravel shall be harrowed three 
times, or more if necessary, to secure a uniform distribution of the fine and 
coarse particles. Any oversized stones which are brought to the surface 
by the harrowing shall be raked out and placed on the sub-grade, or in the 
lateral drains, or removed from the road entirely. 

7. Rolling the Lower Course. — After the lower course has been harrowed 
it shall be rolled until thoroughly compacted, and the roller leaves no per- 
ceptible track thereon. The additional sub-grade for the second course shall 
be shaped before the rolling for the lower course begins. The rolling for ., 
the lower course shall begin on the additional sub-grade for the upper course I 
and the roller shall be worked gradually towards the middle of the road, ! 
after which it shall be taken to the opposite side and the other half of the J 
road rolled in the same manner. ' 

To aid in the compaction of the gravel, the rolling must be done when the j 
material has been wetted sufficiently by sprinkling or by rain to secure the ■ 
maximum compaction possible with the gravel being used. All hollows that ' 
develop during rolling shall be filled with the same grade of gravel and 
rerolled. 

8. Placing the Upper Course.— The upper course of gravel shall be spread 
and harrowed in the manner specified for the lower course. Ruts caused by 
hauling over the gravel must be kept filled by frequent use. of the grader, 
drag, or planer. If it appears that the gravel contains insufficient clay to 
bond properly, clay in the proper quantities shall be added to the lower course 
prior to placing the upper course. 

9. Rolling the Upper Course. — After the upper course has been placed, 
the earth shoulders therefor shall be built up to such a height that when 
compacted by rolling they will be true to cross-section and elevation. The 
upper course of gravel shall be heavily sprinkled and then rolled until thor- 
oughly compacted and the roller makes no appreciable track therein. If a 

"gravel deficient in binding material has been used, rolling shall continue until 
the clay which was previously spread on the lower course is forced up through 
the upper course and the gravel is well bonded. If excess clay should 
appear in the surface, sand shall be spread over the surface as directed by 
the engineer and the rolling continue until there is no apparent excess clay. 
Depressions which may appear during the rolling of the upper course of 
gravel shall be removed by smoothing the surface with the blade grader 9r 1 
planer or by adding additional gravel of the same quality as that used in | 
the upper course. ^ 

In rolling the upper course the roller shall start at least two feet out on 
the earth shoulder and shall be gradually worked towards the crown of the 
road, after which it shall be taken to the opposite side and the other half of 
the road completed in the same manner. 

10. Material. — See Section Four. 

11. Cleaning Side Ditches and Shaping Earth Shoulders. — After the roll- 
ing of the upper course is completed, the earth shoulders shall be neatly | 
finished true to cross-section, grade and alignment, the side ditches shall be 
cleaned true to grade and cross-section, and, if necessary, the outlets shall 
be improved to allow free discharge of surface water. 



METHODS 769 

12. Machinery. — (a) Roller. The roller used on this work shall be a 
self-propelled, three- wheeled roller, weighing not less than eight nor more 
than twelve tons, (b) A spiked tooth harrow weighing not less than eight 
pounds per tooth and having teeth of sufficient length to reach to the full 
depth of each layer of gravel, shall be used, (c) Sprinkler. The sprinkling 

I tank shall be equipped with a suitable spray designed to sprinkle a strip of 

I at least six (6) feet wide. 

I 13. Items Included in Prices Bid. — See Section Seven. 

Section Six 
CLASS B GRAVEL SURFACING 

1. Class B Gravel Surfacing. — Class B gravel surfacings shall consist of a 
single course of gravel of the thickness and width shown on the plans. Un- 
less otherwise specified in the instructions to bidders, Class B gravel surfaces 

, shall be constructed without rolling. (See Plate No. 34, page 140.) 

2. Earthwork. — Before any gravel surfacing is laid, the earth road shall 
, have been brought to grade and cross-section, and the sub-grade prepared in 
' the manner herein specified. 

3. Preparation of Sub-grade. — Along the center line of the finished earth 
^ roadway the crown on the road for the proper width shall be shaped to con- 
: form with the sub-grade shown on the gravel cross-section. The finished 

sub-grade shall present a smooth, uniform surface, parallel to the grade line 

■ shown on the plans._ It shall be excavated to such a depth, or the earth 
. shoulders shall be raised to such a height that the crown of the finished road 
; shall conform from shoulder to shoulder to the crown shown on the standard 
- cross-section. 

; 4. Lateral Drains. — Where necessary, lateral drains shall be cut through 

; the shoulders of the earth roadway, into the side ditches. These drains 

shall be constructed as specified in Section Five, paragraph 4. These drains 

shall be placed at low places in the grade and at such additional points as 

; may be directed by the engineer. 

5. Placing the Gravel. — After the sub-grade is prepared, sufficient gravel 
?' shall be placed thereon to give the required thickness when compacted. 

'i Note. — By placing the loose gravel 6'' thick at the middle and 5'' thick 
at each edge, the compacted gravel surfacing should conform substantially 
n to the standard cross-section for Class B road. 

6. Earth Shoulders. — Suitable earth shoulders shall be constructed to pre- 
vent the gravel from spreading beyond the width shown on the cross-section. 

: These shoulders may be constructed by excavating a trench in the earth 
; roadway and using the material thus excavated to finish the earth shoulders, 
or the shoulders may be constructed by bringing up additional earth from 
. the sides of the road. 

5 7. Spreading and Harrowing the Gravel. — The gravel may be spread with 
I shovels after being placed, or a quantity may be placed and spread with a 

■ road machine. After the material has been spread to a uniform thickness 
it shall be harrowed not less than three times with a spiked tooth harrow 
weighing not less than eight pounds per tooth, and having teeth of sufficient 

; length to stir the material to its entire depth. All over sized pebbles which 
appear during the harrowing shall be carried ahead and placed on the sub- 
1 grade or in the lateral drains, or shall be removed from the road entirely. 
18. Material." — See Section Four. 

9. Adding Clay Binder. — By order of the_ engineer, additional binder in 
' the quantities designated shall be spread uniformly over_ the surface of the 

gravel. The clay. and gravel shall then be thoroughly mixed by harrowing, 
\ discing, or other suitable means. The mixing shall be done only after the 
I road has been" wetted either by sprinkling or by rain. Care shall be taken 
i in adding the binder, as sod, foreign material, or material deficient in binding 
I properties will not be permitted on the gravel road. 

10. Cleaning Side Ditches and Shaping Earth Shoulders. — After the 
I gravel surfacing is completed, the earth shoulders shall be neatly finished 
I true to cross-section, grade and alignment, the side ditches shall be cleaned 
I true to grade and cross-section, and, if necessary, the outlets shall be im- 
proved to allow free discharge of surface water. 

11. Rolling. — If rolling is specified in the instructions to bidders, the sub-^ 
grade and gravel surface shall be rolled as specified in Section Five for Class' 

I A gravel surfaces. 

I 12, Items Included in Price Bids. — See Section Seven. 



770 SPECIFICATIONS 



Section Seven 
ITEMS INCLUDED IN PRICES BID 

1. Loose Rock, Solid Rock, Earth Excavation. — The contract price for 
excavation per cubic yard shall include the excavation of the material, the 
loading, transportation (provided the average haul does not exceed 500 
feet), the deposition of the excavated material in the manner described in 
these specifications, the finishing of. the earth roadway, side ditches and 
slopes, the discing and harrowing of sod where required, the repair and 
replacing of all fences carelessly or unnecessarily damaged or removed by 
the contractor, maintaining the dirt roads as specified in Section Two, para- 
graph 16, and such incidental work as may be required to make the grading 
work complete. 

No extra payment shall be made for hauling material when the average 
length of haul does nor exceed the free haul limit of five hundred (500) feet. 

2. Removing and Replacing Fences. — The price bid for removing and 
replacing fences will include removing the posts, removing and caring for the 
wire, digging the necessary holes, replacing the posts, replacing the wire, 
furnishing any additional staples used, and such incidental work or materials 
as may be necessary to replace the fence in as good condition as before the 
same was removed. 

3. Constructing Guard Rail. — The price bid per lineal foot for guard rail 
shall include the furnishing of all lumber, posts, hardware, and other mate- 
rial, and constructing the railing complete as specified. 

4. Removing Hedge Rows. — The price bid per rod for removing hedge rows 
shall include cutting the trees or plants, grubbing the stumps, piling and 
burning or otherwise disposing of the brush, roots, and timber as directed 
by the engineer, and all other work incident to removing such hedges. 

5. Placing Temporary Culverts. — The price bid per lineal foot for placing 
temporary culverts shall include shaping the ditch bed to receive the culvert, 
placing the culvert in position, connecting the various sections, making the 
necessary fill, and such incidental work as may be required to place such 
temporary culverts. The price bid will not include the making or placing 
of any bulkheads. 

6. Laying Drain Tile.-;— The price bid per foot for laying drain tile shall 
include furnishing the tile at the site, digging the trench, laying the tile, 
back filling the trench, and all incidental work necessary to make the tile 
drain complete. 

7. Loading Gravel at the Pit. — The price bid for loading the gravel at 
the pit shall include the supplying of all necessary equipment, materials, 
and labor for loosening, loading such gravel on to the cars, trucks, or wagons 
used, removing the oversized stone and pebbles, screening and re-propor- 
tioning any material where it is specified in the form of tender that such 
screening and reproportioning will be necessary, and all necessary incidental 
work. Payment for loading will be made on all gravel handled including 
the oversized material. Unless otherwise specified in the instructions to 
bidders the amount of gravel handled will be determined by cross-sectioning 
the gravel pit after the necessary stripping has been done and cross-sectioning 
it after the grayel has been removed. 

8. Hauling tlie Gravel. — The orice bid per cubic yard per mile for hauling 
the gravel shall include the furnishing of all labor, materials, and supplies 
necessary for such hauling work, the necessary maintenance of any roads 
over which hauling is being done so as to keep such roads in proper condition, 
and all incidental work necessary in doing such hauling. Unless otherwise 
specified in the instructions to bidders, the quantity of gravel hauled will 
be determined from the estimates for loading. If the oversized material 
is left in the pit then the amount of gravel hauled will be determined by 
deducting the oversized material from the estimate on loading. If the over- 
sized material is crushed and hauled to the road, then the amount of gravel 
hauled will be equal to the estimate on loading. The length of haul on 
which payment shall be made is the average length of such haul for the con- 
struction of any given mile of road. 

Note. — If in the construction of any given mile of road, the end of such 
mile nearest the pit is two miles distant therefrom by the road over which 
hauling is being done, then the length of haul on which payment will be 
made for this mile is two and one-half miles. 



METHODS 771 

9. Class A Gravel Surfacing. — The price bid per square yard for Class A 
gravel surfacing in place shall include the excavation of the necessary trench 
for the lower course, rolling the sub-grade, dumping, spreading, harrowing, 
sprinkling, and rolling the first course of gravel, shaping the earth shoulders, 
dumping, spreading, harrowing, sprinkling, and rolling the upper course of 
gravel, cleaning the side ditches, shaping the earth shoulders, maintaining 
the finished work as specified in Section Two, paragraph 16, and such inci- 
dental work as niay be necessary to make the sub-grade, earth shoulders, 
^nd gravel surfacing complete. The width of surfacing on which payment 
will be based is the width of the top course of gravel as shown on the plans. 

10. Class B Gravel Surfacing. — The price per square yard for Class B 
gravel surfacing in place shall include the shaping of the sub-grade and earth 
shoulders, dumping, spreading, and harrowing the gravel, cleaning the side 
ditches, maintaining the finished work as specified in Section Two, paragraph 
16, and such incidental work as may be necessary to make the sub-grade, 
earth shoulders, and gravel surfacing complete. 

If rolling for Class B gravel surface is specified in the instructions to 
bidders, the price bid per square yard for the gravel surface in place shall 
include the rolling. ^ 

11. Adding Bindmg Material. — The price bid per cubic yard for adding 
clay binding material shall include the excavation, loading, hauling, dump- 
ing, spreading and mixing of such clay binding material and all other work 
incidental to the addition of such material. Should the average length of 
haul on such clay binder exceed 500 feet, overhaul will be allowed as specified 
in Section Three, paragraph 18. 

12. Constructing Lateral Drains. — ^The price bid each for the construction 
of lateral drains shall include the excavation of the necessary trench, placing 
the coarse gravel therein, filling the trench, and such incidental work as is 
necessary to make each lateral drain complete. 

The price bid per cubic yard for crushing the oversized stone and pebbles 
will include the furnishing of all labor and equipment for elevating, crushing, 
screening, and loading such stone ready to be hauled to the road. 

13. Crushing Oversized Stone. — The price bid for crushing shall apply 
only to that percentage or quantity of the material which is too large to 
pass a two-inch (2") ring without crushing. 

CHERT SURFACE (ALABAMA STATE SPECIFICATIONS) 

Description. — On the sub-grade, prepared as hereinbefore specified, shall 
be constructed a chert surface of the cross-section and compacted thickness 
shown on the plans. 

Chert. — Before any chert is used in the construction of the road surface, 
it shall first have been approved by the Engineer. ^ In general, the special 
provisions accompanying the proposal forni will indicate the locations from 
which satisfactory chert may be obtained and also indicate whether crushing 
and screening of the chert will be required. Any large particle of chert 
that may be spread on the road, and that would fail to pass a two (2) inch 
ring, shall be broken by harnmering, or otherwise, before the surface is rolled. 
Unless otherwise provided in the special provisions, chert quarries will be 
furnished by the County free of charge to the contractor, but the contractor 
must provide and maintain roads to such quarries at his own expense. 

Construction Methods. — The chert shall be spread on the sub-grade to 
such depth that when compacted the surface will have the compacted thick- 
ness shown on the plans. It shall be dumped, spread and rolled in the man- 
ner hereinbefore specified for dumping, spreading and rolling No. i and No. 
2 crushed stone in the case of crushed stone surfaces. Where, in the judg- 
ment of the engineer, the conditions are such that a well bonded surface is 
not secured by rolling as above specified, the contractor shall sprinkle the 
surface with water while the rolling is in progress, and the sprinkling shall 
be done in such quantity and in such manner as the engineer may direct. 

Basis of Payment. — The contract price per cubic yard f or_ chert for sur- 
facing shall be full compensation for quarrying, crushing, loading, spreading, 
rolling, sprinkling, hauling the chert one (i) mile or less, and maintaining 
the surface until the road is accepted. Measurement of chert will be made 
in trucks, wagons, or cars as the chert is delivered. Stripping of chert 
quarries will be paid for at the contract price for common excavation. The 
bid price for overhaul of chert will be paid on all chert necessarily hauled 



77^ SPECIFICATIONS 

a distance greater than one (i) mile. The method of determining overhaul 
will be in all respects similar to that provided for determining overhaul in 
the case of crushed stone surfaces. 

GRAVEL SURFACE (ALABAMA STATE SPECIFICATIONS); 

Description. — On the sub-grade, prepared as hereinbefore specified, shall 
be constructed a gravel surface of the cross-section and compacted thickness 
shown on the plans. 

Gravel. — Before any gravel is used in the construction of the road surface, 
it shall first have been approved by the Engineer. All gravel pits will be 
furnished by the County, and in general, those which are acceptable will be 
indicated in the special provisions accompanying the proposal form. The 
contractor, however, must provide and maintain roads to such pits at his 
own expense. 

When gravel for the surface is to be shipped in, it will, unless otherwise 
specified in the special provisions, be furnished by the County, f. o. b. cars 
at such sidings as the engineer and contractor may agree upon. The con- 
tractor shall unload cars promptly, even though the gravel has to be dumped 
on the ground and re-handled. Gravel will be furnished as it is needed by 
the contractor, in so far as the County can secure the desired service from 
the railroads, but the County will not be responsible for any damage which 
the contractor may sustain on account of delays or irregularities on the part 
of railroads in furnishing cars or in delivering the gravel at the sidings. 
The contractor shall be responsible for any and all demurrage charges made 
by the railroads on account of delays in unloading cars. When the County 
has to pay demurrage charges resulting from failure on the part of the con- 
tractor to unload the cars promptly, the amounts so paid will be charged 
to the contractor and deducted from amounts that may be or become due 
the contractor for work performed or materials delivered. 

If it is deemed advisable to add screened gravel or clay to the gravel before 
it is used as surfacing material, it will be so specified in the special clauses 
accompanying the proposal form. The screened gravel or clay will be 
selected by the engineer and furnished by the County, either in pits or at 
railroad sidings, according to the conditions specified in the preceding para- 
graph. The work of admixing the screened gravel or clay with the gravel, 
shall be done by the contractor and as hereinafter specified under construc- 
tion methods. 

Construction Methods. — The gravel shall be spread on the sub-grade to 
such depth that when compacted the surface will have the compacted thick- 
ness shown on the plans. It shall be dumped and spread in the manner 
hereinbefore specified for dumping and spreading No. i and No. 2 crushed 
stone, in the case of crushed stone surfaces. If rolling is to be required it will 
be so specified in the special clauses accompanying the proposal form and 
shall be done in the manner hereinbefore specined for rolling crushed stone 
surfaces. 

When the specifications call for admixing clay with the gravel, this shall 
be done in strict accordance with the following directions: 

1. The proportion in which the clay shall be added is to be determined by 
the engineer, and the engineer may change the proportion from time to 
time, as the exigencies of the case may warrant. 

2. If practicable, the loading of the clay and gravel shall be so managed 
that each load hauled to the road will contain the proper proportion of 
each, so mixed in loading that m_ dumping and spreading each material will 
be uniformly distributed. If it is impracticable to load the two materials 
at the same time, they may be hauled to the road separately, in which case, 
the engineer will determine the order in which the clay shall be spread and 
the depth of layer required. 

3. Wherever clay is to be mixed with the gravel, as above provided, and 
no matter whether the gravel and clay are hauled together or separately, 
as soon as the materials for four or five hundred (400 or 500) linear feet, of 
surface have been spread, the entire mass shall be thoroughly mixed by 
means of plowing and harrowing, and the plowing and harrowing shall con- 
tinue until the entire surface is free from lumps or pockets of clay and the 
engineer is satisfied that the two materials are uniformly distributed through- 
out the mass. As soon as the mixing is completed to the engineer's satis- 
faction, the surface shall be shaped to conform with the plans, and rolled, 
if rolling is specified. 



METHODS 773 

When screened gravel is to be added to the surfacing gravel, the method 
of mixing the two materials shall be similar in all respects to that specified 
for admixing clay with surfacing gravel. 

Basis of Payment. — The contract price per cubic yard for gravel for sur- 
facing shall be full compensation for loosening, loading, spreading, rolling 
(if rolling is specified), hauling the gravel one (i) mile or less, and main- 
taining the surface true to cross-section until the road is accepted. Meas- 
urement of gravel will be made in trucks, wagons or cars as the gravel is 
delivered. Stripping of gravel pits will be paid for at the contract price for 
common excavation. The bid price for overhaul of gravel will be paid on 
gravel necessarily hauled a distance greater than one (i) mile. The method 
of determining overhaul will be in all respects similar to that provided for 
determining overhaul in the case of crushed stone surfaces. 

Where the specifications call for clay or screened gravel to be admixed 
with the surfacing gravel, these will be paid for at the contract rates for 
surfacing gravel and according to the schedule outlined in the preceding 
paragraph. The contract price for admixing clay or screened gravel will 
be full compensation for all plowing, harrowing, etc., that may be necessary 
in securing a thorough mixture of the two materials. 

TOP SOIL OR SAND-CLAY SURFACE (ALABAMA STATE 
SPECIFICATIONS) 

Description. — Upon the sub-grade, prepared as hereinbefore specified 
shall be constructed a top soil or sand-clay surface of the cross-section and 
compacted thickness shown on the plans. 

Surfacing Material. — The surfacing material shall consist of top soil or 
natural sand-clay obtained from fields or pits designated by the engineer, 
and as near the right-of-way as practicable, or, in the event that it is im- 
practicable to secure suitable top soil or natural mixed sand-clay, the sur- 
face shall consist of an artificial mixture of sand and clay, the materials for 
whiph artificial mixture shall be obtained from^ places designated by the 
engineer. Before any surfacing material is used it shall first have been ap- 
proved by the engineer. The surfacing material shall be free from trash or 
other foreign matter and contain no stones or boulders that would fail to pass a 
one and one-half (i^^) inch ring. Should any such non-read building material 
be placed on the road, it shall be removed by the contractor at his own expense. 

The fields or pits from which the surfacing material is to be obtained will 
be furnished by the County free of cliarge to the contractor, but the con- 
tractor must provide and maintain at his own expense, all necessary roads 
for hauling the surfacing material to the roa'd. 

Construction Methods — Case i. — Where the surfacing material consists 
of either top soil or natural sand-clay that has been approved for use without 
the admixture of any other material, it shall be evenly spread on the sub- 
grade to such depth that when compacted the surface will have the com- 
pacted thickness shown on the plans. The material shall be dumped on 
the sub-grade in longitudinal rows containing not more than one- third (3^^) 
of a cubic yard to lo lineal feet, and the number of rows shall be such that 
when the material is spread, the desired cross-section and thickness of sur- 
face will be obtained. After sufficient material has been dumped in this 
way for one hundred or two hundred (lOO or 200) feet of road surface, and 
before any part of the rows have commenced to pack, it shall be spread 
approximately to the required cross-section and harrowed to secure uniform- 
ity. The spreading may be done by hand or with a road machine in the 
following manner: i. The machine shall be run over the road with the blade 
set so as to scrape off the tops of the piles and fill in the spaces between; 2. 
The outside edges shall be gone over with the blade set so as to pull the top 
soil or sand-clay toward the center; 3. The grading machine shall be run 
over the shoulders so as to pull the shoulder material up against the surfacing 
material and thus bring the entire road surface approximately to the required 
cross-section. The surfaced portion of the road shall then be harrowed with 
either a tooth or disc harrow until unifonn density is secured, after which 
the road shall be brought to the required cross-section and so maintained 
until accepted. The shaping or reshaping of the surface shall be undertaken 
only when the weather conditions are such that the loosened surfacing or 
shoulder material will be readily compacted by traffic to form a well bonded 
surface. 



774 SPECIFICATIONS 

Case 2. — When the surfacing material is to consist of an artificial mixture 
of sand and clay, made by mixing the material of the roadbed with sand or 
clay from some other source, the construction shall proceed in the following 
manner: 

1. The surface of the roadbed shall be thoroughly loosened by plowing 
and harrowing to a depth of from 4 to 8 inches, according to the nature of 
the two materials to be mixed, and as the engineer may direct. 

2. The material to be added shall be dumped and spread in the manner 
described for Case i. 

3. The added material shall be thoroughly mixed and incorporated with 
the material of the road-bed. The mixing shall be done by means of plowing 
and harrowing and shall continue until the engineer is satisfied that the two 
materials are thoroughly mixed in proper proportion. A part of this mixing 
shall be done when the road is wet so that the surface will be puddled. 

4. If, after mixing the two materials as above described, a deficiency of 
the added material is apparent at any point, such deficiency shall be imme- 
diately corrected by spreading more of the added material at that point and 
continuing the mixing as above described. 

5. After the mixing is complete, as above specified, the road shall be 
shaped and maintained as provided in Case i, except that wherever a poor 
mixture is observed, it shall be corrected by additional mixing or by adding 
necessary material and mixing. 

Case 3. — When the surfacing material is to consist of an artificial mixture 
of sand and clay, both of which materials are to be obtained from without 
the road, the construction shall proceed in the following manner: 

1. The materials shall be spread in successive layers on the road and mixed 
in place. The engineer will determine the order in which the two materials 
shall be spread, as well as the depth of layer for each material. 

2. The dumping and spreading of the materials shall be done as specified 
for Case i. ^ 

3. The mixing of the two materials and the shaping and maintaining of 
the road shall be done as specified for Case 2. 

Basis of Payment. — The contract price per cubic yard for top soil or 
natural sand-clay surfacing material shall be full compensation for loosening, 
loading, spreading and harrowing, and for hauling the^ surfacing material 
one (i) mile or less, as well as for shaping and maintaining the surface true 
to cross-section until the road is accepted. In the case of an artificially 
mixed surface the materials brought on to the road will be paid for at the 
contract price per cubic yard for top soil or natural sand-clay surfacing 
material, which will include all the items mentioned above except harrowing, 
and the contract price per square yard for mixing will be full compensation 
for all necessary harrowing, plowing or other mixing. Measurement of all 
top soil or sand-clay surfacing materials will be made in trucks, wagons or 
cars, as it is delivered on the road, except that where the surfacing material 
is hauled in scrapers or shoveled on to the road, it will be measured compacted 
in place on the road. 

Stripping of surfacing materia! pits will be paid for at the contract price for 
common excavation. 

The bid price for overhaul of sand-clay will be allowed on all sand-clay 
materials necessarily hauled a distance greater than one (i) mile. The 
method of determining overhaul will be in all respects similar to that provided 
for determining overhaul in the case of crushed stone surfaces. 

TOP COURSE (NEW YORK STATE SPECIFICATIONS, ITEMS 47 to 55) 
Item 47 — Top Course — Water Bound Macadam — Gravel 

47.1. Under this item the Contractor shall furnish and place upon the 
bottom course, gravel of an approved character to form the top course. 

47.2. The top course shall consist of approved gravel of the character 
hereinbefore specified and of the thickness shown on the plans, together 
with the binder necessary to^ properly fill and bind the course. For this 
purpose gravel of No. 3 size with, when approved by the Engineer, a certain 
amount of No. 2 size, may be used. (Seepage 72of or meaning of these numbers 
as to size.) Run of bank gravel shall not be used except by written permis- 
sion of the Division Engineer; this permit must be given in advance, shall 
specify the locality from which it is to be taken, and contain a proviso that 
if the material should at any time become unsatisfactory its use shall at once 



METHODS 775 

cease and proper material be furnished without additional recompense even 
if it has to be imported. ^ A copy of any such permit must be filed with the 
State Highway Commission, and on this permit must be the written and 
signed acceptance of all the conditions by the Contractor. 

47.3. The gravel shall be spread evenly upon the bottom course, using 
cubical blocks for gauging, to such a depth as to insure the required thick- 
ness after it shall ^ have been thoroughly rolled and compacted with an 
approved roller weighing 10 to 12 tons. Care shall be exercised to prevent 
any depressions or surface irregularities after rolling the gravel and binder. 

47.4. When the gravel consists of screened material the binder shall 
consist of a mixture of the sand screened out and the No. i size, with enough 
clay added when necessary to make a percentage of 12 to 17, but not to 
exceed 1 7 per cent._ The binder shall be added as directed by the Engineer and 
thoroughly swept into interstices thereof until they are filled. After sprink- 
ling the surface it shall be thoroughly rolled. The adding of binder where 
necessary and the sweeping, sprinkling and rolling shall continue until the 
course is compacted. The pavement shall then be opened to traffic and 
shall be in a first-class and satisfactory condition at the time of its acceptance. 

47.5. When the gravel consists of run of the bank the binder | shall be 
the fine particles contained in the material in its natural state except that 
when so ordered in writing by the division Engineer a small percentage 
of clay or loam may be added, when necessary to properly bind the course. 

The particles shall be of such size as will pass through a 3 3'^ -inch circular 
hole, and shall be well graded. Gravel shall be of such nature that the 
material passing a 3^-inch screen shall not be more than five per centum (not 
feasible, see page 138) in excess of the voids in the remaining material after 
its separation therefrom. Should at any time during the work and for any 
reason the gravel fail to maintain suitable proportions of the coarse and fine 
particles, the Contractor shall by the addition of selected material and satis- 
factory manipulation produce a top course meeting the above requirements. 

Care shall be taken to keep the large stone away from the surface. 

After sprinkling the surface it shall be thoroughly rolled. ^ Additional 
material forbinder shall be added where necessary and the sprinkling and 
rolling shall continue until the course is compacted. The pavement shall 
then be opened to traffic and shall be in a first-class and satisfactory con- 
dition at the time of its acceptance. 

47.6. The quantity to be paid for under this item shall be the number 
of cubic yards of compacted material in place in the completed course. 
The amount will be computed by multiplying the finished cross-section 
of the top course as shown on the plans or ordered by the Engineer, by 
the length of the top course measured along the axis of the pavement. 

The price bid under this item shall include the furnishing, placing, rolling, 
filling, and puddling of the material, and all labor, material and incidental 
expenses necessary to complete the work. 

Gravel or screenings remaining loose on the surface after the work is 
completed shall not be estimated as a part of the depth of the top course, 
but payment therefor shall be included in the price bid for this item. 

Item 48 — Top Course — Water Bound Macadam — ^Broken Stone 

48.1. Under this item the Contractor shall furnish and place upon the 
bottom course broken stone to form the top course. 

48.2. The top course shall, except as noted below, consist of No. 3 broken 
stone as shown on the plans and of the thickness shown thereon, together 
with the binder necessary to properly fill and bind the course. The binder 
shall consist of screenings and No. i stone mixed. 

48.3. The No. 3 stone shall be spread evenly upon the bottom course, 
using cubical blocks for gauging, to such a depth as to insure the required 
thickness after it shall have been thoroughly rolled and compacted. Care 
shall be used in the spreading of the stone that no irregularities in the contour 
shall develop in the rolling; every such irregularity that does occur the 

1 Contractor shall remove before adding the smaller material. The rolling 
i shall be done with a 10 to 12 ton self-propelled roller of approved pattern, 
' and shall be continued until the layer of stone does not creep or wave ahead 
I of the roller. 

After the stone has been compacted to the satisfaction of the Engineer, 
a light coating of binder shall be spread on dry by shoveling from piles 



776 SPECIFICATIONS 

previously placed alongside the pavement, and immediately swept in and 
thoroughly r9lled. Care must be taken throughout t9 add the binder only 
in light coatings and to thoroughly sweep each coating in order that the 
maximum amount of binder may be worked in to fill the voids. The spread- 
ing and sweeping and rolling shall be continued until no more binder will 
go in dry, after which the macadam shall be sprinkled tmtil saturated, the 
sprinkler being followed by the roller. If the sub-grade should become 
wet to such an extent that the pavement becomes unstable and waves 
under the roller, the roller shall be taken off and this portion left to dry out 
before puddling is resumed. 

More screenings shall be added where necessary, and the sweeping, 
sprinkling, and rolling shall continue until a grout has been formed that 
shall fill all the voids and be pushed into a wave by the wheels of the roller. 
After the wave of grout has been produced over the whole section of the 
macadam this portion shall be left to dry out, after which it shall be opened 
to traffic. The macadam shall be repuddled and back-rolled on succeeding 
days as much as may be necessary to secure satisfactory results. The 
macadam shall then be covered with a wearing carpet of screenings at least 
three-eighths of an inch thick; this wearing carpet shall be maintained and 
renewed until the whole road is accepted. During all the working hours 
when the roller is not needed for rolling the fills, sub-grade, shoulders 
and unfinished courses of the pavement, it shall be employed in back-rolling 
the earlier portions of the macadam. 

48.4._ The quantity to be paid for under this time shall be the number 
of cubic yards of compacted material in place in the completed course. 
The amount to be estimated shall be computed by multiplying the finished 
cross-section of the top course as shown on the plans or ordered by the 
Engineer, by the length of the top course measured along the axis of the 
pavement. 

The price bid shall include the furnishing, placing, rolling, filling and 
puddling of the material, and all labor, material and incidental expenses, 
necessary to complete the work. 

No. I stone or gravel, chips or screenings remaining loose on the surface 
after the work is completed shall not be estimated as a part of the depth of 
the top course, but payment therefor shall be included in the price bid for 
this item. 

Item 49 — Cleaning Old Pavement 

49.1. The purpose of the work called for under this item is to prepare 
an old macadani or old concrete surface for the application of a new top 
course or a wearing carpet. 

49.2. Under this item the Contractor shall clean the old macadam or 
concrete surface by the use of seal hand brooms or by the use of mechanical 
sweepers of approved type, as directed by the Engineer, so as to completely 
uncover but not dislodge the embedded stones of the pavement. 

All mud, dust, and other dirt so swept off shall then be removed and 
deposited in such places and in such" manner as the Engineer may direct. 

49.3. Ruts and depressions of a greater depth than one inch below the 
general surface of the pavement shall be completely swept out by hand 
brooms until all loose material has been removed and the embedded stones 
are fully uncovered. 

This operation of cleaning out the ruts and depressions and filling them' 
with thoroughly compacted stone and binder to the general level of the 
surface, shall precede the general operation of cleaning the macadam surface. 
. 49.4. The amount to be paid for under this item shall be the actual 
number of square yards of old macadam or concrete, including ruts and 
depressions, cleaned in accordance with the above sections and to the 
satisfaction of the Engineer. 

The price bid shall include all labor, tools, appliances, the removal of mate- 
rial cleaned from the surface, and all other expenses incidental thereto. 

Item 50 — Scarifying and Reshaping Old Macadam 

50.1. The purpose of the work under this item is to prepare old macadam 
pavement for the application of a top course. 



METHODS 777 

50.2. Under this item the Contractor shall thoroughly scarify the old 
macadam by hand picking or by means of a mechanical scarifier of approved 
type. Unless specifically authorized by the Engineer, the use of a roller 
with spiked wheels will not be permitted. 

The loosened stones shall then be forked, or raked over as directed by 
the Engineer, after which the macadam shall be compacted by rolling 
with a self-propelled roller weighing not less than 10 tons until an even 
and firm surface is produced. If necessary in order to satisfactorily com- 
pact the stones, the macadam shall be sprinkled during the process of 
■ rolling. 

50.3. The quantity to be paid for under this item shall be the actual 
number of square yards, scarified, reshaped,^ rolled and compacted to the 
satisfaction of the Engineer, and the price stipulated shall include all labor 
appliances and expenses incidental thereto. 

Item 51 — Sixrface Treatments with Bituminous Material 

5 1. 1. Under this item the Contractor shall apply bituminous material 
and shall apply broken stone or gravel of specified sizes as a wearing carpet 
to a new or old pavement of macadam, concrete, or any other substance or 
type, as shown on the plans or ordered by the Engineer. 

51.2. If the pavement to be treated is a newly built macadam or concrete' 
after it shall have become thoroughly dried and hardened, it shall be swept 
clean of all dust, dirt or other loose material; if ordered by the Engineer, 
the sweeping of the macadam shall be continued until the voids are exposed 
in the surface to a satisfactory depth, not exceeding one-half inch. The price 
bid, under this item, shall include the aforesaid cleaning of the pavements. 

If the pavement to be treated is an old macadam or old concrete, the 
cleaning shall be paid for under item "Cleaning Old Pavement." 

5 1. 3. After the pavement shall have been cleaned to the satisfaction 
of the Engineer, and when dry, the bituminous material shall be uniformly 
sprayed over the surface by means of an approved pressure distributor. 
The bituminous material for hot application shall be heated to a tem- 
perature between 250 degrees and 350 degrees F. as required, and when 
tar is used, it shall be heated to a temperature between 200 degrees and 
250 degrees F. as required. 

The amount of bituminous material to be used in any one application 
shall not be less than one-sixth nor more than one-half gallon per square 
yard, the precise quantity depending upon the character of the pavement, 
the materials and the local conditions. The Contractor shall, therefore, 
be subject entirely to the direction of the Engineer in this respect. 

5 1. 4. The bituminous material applied as above specified shall then 
be immediately covered, while soft, with a uniform layer of approved broken 
stone of No. 2 or No. I size, after which the stone shall be rolled with a self- 
propelled roller of approved weight. If ordered by the Engineer another 
application of bituminous material shall then be made to be followed by an 
application of approved No. 2 stone or approved No. i stone, and again 
rolled to the satisfaction of the Engineer. 

The quantity of No. 2 stone and of No. i stone to be used shall be suf- 
ficient to completely cover the bituminous material and shall be spread in 
two or more thin applications, the roller being used after each spreading. 
The total amount of stone to be used after each application of the bituminous 
material being that which will become imbedded under the pressure of the 
roller. The final application of the stone shall be of No. i size. 

5 1.5. Gravel, which has been tested and approved for use, may be sub- 
stituted for broken stone if screened to produce particles corresponding 
with No. 2 and No. i sizes. 

5 1.6. No bituminous material for surface treatment shall be placed 
between October 15th and May 15th, except by written permission of 
the Engineer, nor when the air temperature on the work is below 50 degrees F., 
nor when the pavement is damp or in an otherwise unsatisfactory condition. 

51.7. Under this item the Contractor shall be^ paid for the number of 
gallons of bituminous material furnished in and incorporated in the work 
in accordance with these specifications and the orders of the Engineer. 
Bituminous material, that has been wasted or that has been rendered 
unfit for use by over-heating or by long-continued heating, shall not, be 
paid for, For purposes of measurement, a gallon shall be a volume of 



778 



SPECIFICATIONS 



231 cubic inches and measurement shall be based on the volume of the 
bituminous material at a temperature of 60 degrees F. 

The price bid shall include the furnishing, hauling, heating and applying 
the bituminous material, and shall also include the spreading, rolling and 
incorporation of the stone into the wearing carpet. 

This item shall not include the furnishing of the No. i and No. 2 stone 
or gravel, nor the delivery of same along the side of the road; these will be 
paid for under Items Screened Gravel or Broken Stone Loose Measure, 
respectively. 

Item 52 — Top Course Bituminous Macadam — Penetration Method 

52.1. Under this item the Contractor shall furnish and lay a broken 
stone top course composed of fragments of the specified sizes, and incor- 
porate therewith bituminous material introduced from the surface by means 
of an approved pressure distributor. 1 

1 Hand spreading from pots or hods is more satisfactory for the first coat 
but not for the flush coat. 

52.2. After the bottom course shall have been completed to the satis- 
faction of the Engineer, a course of approved No. 3 broken stone shall be 
evenly spread thereon in such quantity that after the application of the 
bituminous material and broken stone of smaller sizes, hereafter specified, 
the final compacted thickness of the top course shall be as called for on the 
plans or ordered by the Engineer. 

The No. 3 stone shall then be smoothed out by passing over it a few 
times a self-propelled roller weighing approximately 10 tons, after which 
bituminous material of the kind specified in the proposal, heated to a tem- 
perature between 250 degrees and 350 degrees Fahrenheit if asphalt is 
used, and between 200 degrees and 250 degrees if tar is used, shall be evenly 
spreading over the surface. The quantity of bituminous material to be 
used in the first application shall be the amount ordered by the Engineer, 
which will approximate ifi gallons per square yard for a top course 3 
inches thick, with a proportional reduction in the quantity for thinner courses. 

The surface shall then be immediately covered with a layer of approved 
No. 2 broken stone, after which it shall be compacted with a self-propelled 
roller weighing approximately 10 tons; during the rolling process, additional 
No. 2 broken stone shall be applied and broomed about until the voids in 
the No. 3 stone are entirely filled. * The rolling shall be continued until the 
course of stone is thoroughly compacted and its surface is true and even to 
the established grade and conforms in all respects to the requirements 
specified for finishing and testing the surface of "Top Course Bituminous 
Macadam, Mixing Method — Type i." 

52.3. After this portion of the work shall have been completed to the 
satisfaction of the Engineer, all loose stone shall be swept from the surface 
and a sealing coat of one-half gallon of bituminous material per square 
yard shall be applied by means of an approved pressure distributor. After 
this it shall be immediately covered with approved No. i broken stone, 
spread and broomed about by experienced workmen, and again rolled; the 
rolling shall be continued and additional No. i stone shall be applied until a 
smooth, uniform surface is produced. 

52.4. Before being opened to traffic a layer of No. i broken stone approxi- 
mately one-half inch thick shall be spread loose on the surface for wearing 
course". 

52.5. The quantity to be paid for under this item shall be -the number 
of cubic yards of compacted material in place in the completed course. 
The amount to be estimated shall be computed by multiplying the finished 
cross-section of the top course, as shown upon the plans or ordered by the 
Engineer, by the length of the top course measured along the axis of the 
pavement. 

The price bid shall include the heating and placing of the bituminous 
material, the furnishing, placing, rolling and filling of the broken' stone, 
and all labor, materials, and incidental expenses necessary to complete the 
top course. 

This item shall not include the furnishing and delivery of the bituminous 

*Too much roiling is injurious while the oil is hot; better results are 
obtained by waiting till the next day to compact ; the course should be rolled 
early in the morning for 10 days and gradually hardened down. 



METHODS 779 

material; such furnishing and delivering will be paid for under the item 
covering such material. 

No. I broken stone or gravel, chips or screenings remaining loose on 
the surface after the work is completed shall not be estimated as a part of 
the depth of the top course, but payment for these shall be included in the 
price bid for item 52. 

Item S3 — Top Course — Bituminous Macadam — Mixing Method. Type i 

53.1. Under this item the Contractor shall construct a top course of 
broken stone mixed with a bituminous material, upon a previously con- 
structed bottom course of concrete, broken stone, quarry or field stone, 
or gravel. The surface laid shall be in conformity with the lines and grades 
shown upon the plans or ordered by the Engineer. A smooth finished 
surface will be insisted on free from irregularities and waviness. The entire 
top course shall consist of a wearing course finished over with a flush or 
sealing coat. 

53.2. The broken stone used in this course shall be of approved material. 
When the top course is to be 2 inches or less in thickness in the completed 
work, the stone shall be of No. 2 size. When the top course is to be over 
2 inches in thickness in the completed work, No. 2 and No. 3 stone shall be 
used, proportioned as directed by the Engineer. The sealing coat therefor 
shall be of stone of No. i size. (For stone sizes corresponding to these 
numbers, see page 720.) 

53.3- Gravel of approved quality and corresponding to the same sizes 
as broken stone may be used in the top course. If used, it shall conform 
to the general requirements for broken stone and gravel for water-bound 
and bituminous macadam work. 

53.4. The broken stone for the wearing course shall be heated, before 
entering the mixer, to between 225 degrees Fahrenheit and 300 degrees 
Fahrenheit in revolving dryers of an approved type. The stone shall be 
continuously agitated during the heating. 

,S3.5. The bituminous material to be used in this course shall conform 
with the specifications for "Bituminous Material A for Mixing Method 
— Type I." 

53-6. The bituminous material shall be heated in kettles so designed 
as to admit of even heating of the entire mass, with an efficient and positive 
control of the heat at all times. Bituminous material "A" shall be heated 
as directed to a temperature between 275 degrees Fahrenheit and 350 degrees 
Fahrenheit; all material heated beyond 350 degrees Fahrenheit, either 
before or during mixing with the broken stone, shall be rejected. Bitumi- 
nous material "T" shall be heated as directed to a temperature between 200 
degrees Fahrenheit and 275 degrees Fahrenheit; all bituminous material 
*'T" heated beyond 275 degrees Fahrenheit either before or during mixing 
with the broken stone, shall be rejected. No tar shall be heated in kettles 
containing any_ asphalt cement, and no asphalt cement shall be heated in 
kettles containing any tar; before changing from one type of ^material to 
the other, kettles shall be scrupulously cleaned in order to avoid mixtures 
of the two; any such mixtures shall be rejected. 

53.7. When thoroughly heated to the proper temperatures, the bituminous 
material and the broken stone for the wearing course shall be mixed as 
directed from time to time, using approximately 18 gallons of biturninous 
material per cubic yard of loose stone. (The amount of bitumen in the 
completed work shall be from 5 to 73'^ per centum of the total weight of the 
completed course.)^ The Contractor shall provide approved means for 
accurately proportioning the mixture. Excess of bituminous^ material 
shall be prevented; and any such excess shall be cause for rejection of the 
course unless satisfactorily cprrected previous to laying. The mixer used 
shall be of satisfactory design, having revolving blades^ and .efficient 
means for keeping the temperature at the desired point without burning 
the liquid. The mixing shall continue until every particle of the broken 
st9ne is thoroughly coated with the bituminous material and a uniform 
mixture has been obtained, which when discharged shall have a temperature 
between 200 degrees and 300 degrees Fahrenheit for bituminous material 
**A" and between 200 degrees and 250 degrees Fahrenheit for bituminous 
material "T." 

The use of batteries of small batch mixers will not be allowed. 



78o SPECIFICATIONS 

53.8. The bituminous mixture, heated and prepared as specified above, 
shall be delivered from the mixer to the point of deposition in the pave- 
ment, if at a considerable distance, in suitable trucks or wagons, provided 
with canvas covers for retaining the heat. To prevent undue compacting 
on long hauls, partitions may be required for large truck loads. As deliv- 
ered, the mixture shall have a temperature of at least 150 degrees Fahren- 
heit. Material having a lower temperature than this shall not be laid in 
the pavement. The mixture shall be immediately spread over the founda- 
tion course by men experienced in such work, so that when rolled it shall 
have the required thickness and shall be free from surface depressions and 
irregularities. ^ The paving shall be done as continuously as practicable, to 
reduce to a minimum the number of joints between hot and cold materials. 
Such joints shall be constructed in an approved manner. The hot paving 
mixture shall not be dumped in large masses on the bottom course. It shall 
be dumped upon platforms and shoveled with hot shovels into position in 
the pavement. 

53.9. The wearing course, placed as above specified, shall be rolled at 
once, while the material is still warm and pliable, beginning at the edges and 
working toward the center. Acceptable means shall be provided to prevent 
the asphalt frorn sticking to the roller. Rolling shall continue without 
interruption until all roller marks disappear and the surface shows no 
further compressibility. Places which the roller cannot effectively reach 
shall be compressed with hot iron tamps. 

53.10. As soon as possible after the compacting of the wearing course, 
when the surface is clean and dry, a sealing coat of hot bituminous material 
*'A" shall be evenly spread oyer the wearing course by means of approved 
pressure distributors. The bituminous material "A" shall be applied at a 
temperature not less than 275 degrees Fahrenheit nor more than 350 degrees 
Fahrenheit, at a rate of ^^ to ^ gallon per square yard, as directed. A thin 
and uniform layer of dry, clean No. i stone shall be immediately spread 
over the bituminous material "A" by machines or skilled workmen, sufficient 
to more than take up all the excess bituminous material "A." The spread- 
ing of the No. I stone shall not lag more than 20 feet behind the placing of 
the asphalt coating. The pavement shall then be again thoroughly rolled. 
The surface of the wearing course shall be kept scrupulously clean until 
the sealing coat is applied. The Contractor shall not permit any hauling 
over the surface before the completion of the sealing coat. 

53.11. Before placing the sealing coat, the pavement shall be tested 
with a ten foot straight edge laid parallel with the center line of the pave- 
ment, and any depressions exceeding one-half inch shall be satisfactorily 
eliminated or the pavement relaid. 

53.12. Rollers used for the bituminous wearing course and the sealing 
coat shall be well balanced, self-propelled rollers of satisfactory design, 
weighing between eight and ten tons. They shall give a compression under 
the rear roller of between 200 and 350 pounds per linear inch of roll, and 
shall be provided with an ash pan which shall prevent ashes from dropping 
upon the pavement. 

53.13. No top course bituminous material shall be mixed or placed be- 
tween October 15 and May 15 except by written permission of the Engineer, 
nor when the air temperature in the shade is below 50 degrees Fahrenheit, 
nor when the foundation is damp or otherwise unsatisfactory. 

53.14. The Contractor shall provide a sufficient number of accurate 
efficient thermometers for determining the temperatures of the bituminous 
material and the broken stone at all stages of the work. 

53.15. The quantity to be paid for under this item shall be the number 
of -square yards of compacted material in place in the^ completed course. 
The amount to be estimated shall be computed by multiplying the finished 
width of the top course as shown upon the plans or ordered by the Engineer, 
by the length of the top course measured along the axis of the pavement. 

The price bid shall include the furnishing (bituminous material excepted) , 
the heating, placing, rolling and compacting of all materials, together with 
all other labor and incidental expenses necessary to satisfactorily complete 
the work. 

The furnishing of the bituminous material will be paid for under the 
appropriate item therefor as shown on the proposal sheet. 



i 



METHODS 781 

Item 54 — Top Course — Bituminous Macadam — Mixing Method. Type 2 

54. 1. Under this item the Contractor will be required to construct a 
top course consisting 'of a compacted mixture of broken stone, sand and 
bituminous material "A" laid to conform to the required grade and cross- 
section, as shown on the plans and ordered by the Engineer. 

54- 2. Broken stone for this course shall be of the character specified 
all of which shall pass a one-half -inch screen and shall be so graded that 
when combined in a bituminous mixture containing not less than thirty 
(30) per centum of the sand specified in section 54.3 it shall produce a 
bituminous mixture coming within the limits specified in section 54.8. 

54-3. The sand shall be clean, hard grained and sharp. It shall all 
pass a ten (10) mesh screen, and shall contain at least fifteen (15) per 
centum of material retained on a forty (40) mesh screen and at least 
twenty (20) per centum of material that will pass an eighty (80) mesh 
screen except as hereinafter provided for. If the sand does not contain 
the required amount of fine material, approved stone dust may be added 
to make up the deficiency. 

54.4. The bituminous material to be used, in this course shall conform 
with the specifications for bituminous material "A" for Type 2. 

54.5. The broken stone and sand shall be heated as directed, before 
entering the mixer, to between 225 degrees Fahrenheit and 325 degrees 
Fahrenheit in revolving dryers of an approved type._ The broken stone and 
sand shall be continuously agitated during the heating. 

54.6. The bituminous material shall be heated in kettles so designed 
as to produce an even heating of the entire mass, with an efficient and 
positive control of the heat at all times. It shall be heated as directed to a 
temperature between 275 degrees Fahrenheit and 350 degrees Fahrenheit. 
If heated beyond 350 degrees Fahrenheit either before or during the mixing 
with the broken stone it shall be rejected. 

54.7. The Contractor shall provide a sufficient number of accurate, 
efficient, stationary thermometers for determining the temperature of the 
asphalt cement in the kettles. 

54.8. When thoroughly heated to the temperature directed, the bi- 
tuminous material and the broken stone and sand shall be mixed in the 
following proportions by weight : 

Bitumen ^ , from 7 to 11 % 

Mineral aggregate, passing 200 mesh. from 7 to 11 % 

Mineral aggregate, passing 40 mesh. from 45 to 55 % 

Mineral aggregate, passing 10 mesh from 16 to 25 % 

Mineral aggregate, passing 4 mesh from 8 to 15 % 

Mineral aggregate, passing 2 mesh less than 10 % 

the sieves being used in the order named. A mixer shall be used, having 
revolving blades, and so designed and operated as to produce and discharge 
a thoroughly coated and uniform mixture of non-segregated broken stone, 
sand and bituminous material. When discharged the mixture shall have a 
temperature not more than 325 degrees Fahrenheit and not less than 225 
degrees Fahrenheit as directed. 

54.9. All defective areas in the cement concrete foundation shall be 
repaired as directed at least ten (10) days in advance of laying the bituminous 
concrete. Before laying the bituminous concrete the surface of the founda- 
tion shall be dry and thoroughly cleaned. 

54.10. The mixture heated and prepared as specified in section 54-8, 
shall be delivered direct from the mixer to the point of deposition on the 
foundation in trucks or wagons, provided with canvas covers for retaining 
the heat. As delivered, the bituminous concrete shall have a temperature 
of at least 200 degrees Fahrenheit: material having a lower temperature 
than this shall not be laid upon the foundation. Before the mixture is 
placed, all contact surfaces of curbs, edgings, manholes, etc., shall be well 
painted with hot asphalt cement. The hot mixture shall be dumped upon 
platforms, constructed as directed, and shoveled with hot shovels into 
position on the foundation. It shall be immediately spread as directed 
over the foundation course by men experienced in such work, so that when 
rolled it shall have at no i)lace less than the required thickness and shall be 
free from surface depressions and irregularities. Joints between hot and 



782 



SPECIFICATIONS 



cold materials shall be constructed as directed. The paving shall be done 
as continuously as practicable, to reduce to a minimum the number of 
such joints. 

- 54- II' Rollers used on the bituminous concrete shall be well balanced, 
self-propelled, tandem rollers, weighing between seven (7) and eight (8) 
tons each. Each shall have a compression under the rear roller of between 
two hundred (200) and three hundred (300) pounds per linear inch of roll, 
and shall be provided with an ash pan which shall prevent ashes from drop- 
ping into the bituminous concrete or sealing coat. 

54.12. The surface of the top course shall be tested with a ten (10) foot 
straight edge laid parallel with the center line of the road upon any portion 
of the surface, and any depression or other irregularity exceeding one-half 
(K) inch [3'!" is a better limit] shall be satisfactorily eliminated as directed. 

54.13. After the pavement has been satisfactorily finished and has thor- 
oughly dried out, Portland cement shall be dusted over the surface in a 
quantity sufficient to^ form a complete film_ over all parts of the pavement. 
This film shall remain undisturbed by rain or otherwise until it has set; 
in case of disturbance before setting, it shall be renewed. 

54. 14. No top course material shall be mixed or placed between October 
15th and May isth, except" by written permission of the Engineer, nor 
when the air temperature in the shade is below 50 degrees Fahrenheit nor 
when the foundation is damp or otherwise unsatisfactory. 

54.15. The quantity to be paid for under this item shall be the number 
of square yards of compacted material in place in the completed pavement. 
The amount to be estimated shall be computed by multiplying the width of 
top course as shown on the plans or ordered by the Engineer, by the length 
of the top course measured along the axis of the road. 

The 'price bid for this item shall include the furnishing of the sand ; the 
furnishing, crushing and screening of the broken stone; the heating, mixing, 
placing and rolling of the broken stone, sand and bituminous material, 
and the cement film and all work and expense incidental to the completion 
of the work except the furnishing of the bituminous material, which shall 
be paid for under the item Bituminous Material "A" for Mixing Method, 
Type 2. 

Item 55 — Bitulithic Pavement 

55.1. Under this item the Contractor shall furnish the necessary stone, 
bituminous material, machinery, labor and other equipment, and shall 
construct upon a properly prepared foundation a bitulithic pavement com- 
posed of an accurately proportioned aggregate of carefully graded broken 
stone properly heated and mixed with separately heated Warren's Puritan 
Brand bitulithic cement, placed and rolled _ and covered with Warren's 
quick drying bituminous flush coat composition, followed by two coats of 
hot stone chips thoroughly rolled into the surface. 

55.2. The several grades and sizes of mineral aggregate shall be accurately 
measured in proportions previously determined by laboratory tests to give 
the best results; that is, the most dense mixture of mineral aggregate and 
one having inherent stability; heated in a rotary mechanical heater so 
designed as to keep each batch by itself until heated, or after heating the 
stone in a rotary mechanical heater to a temperature of about 250 degrees 
Fahrenheit, it shall be elevated and passed through a rotary screen, having 
sections with various sized openings. The difference in the width of open- 
ings in successive sections shall not exceed one-fourth (3^^) inch in sections 
having openings smaller than one-half (j^i) inch, and shall not exceed (}^i) 
inch, in sections having openings greater than one- half (>^) inch. The 
several sizes of stone thus separated by the screen sections shall pass 
into a bin containing sections or compartments corresponding to screen 
sections. From these compartments the stone shall be drawn into a weigh- 
ing-box, resting on a scale having seven beams. The stone from these com- 
partments shall be accurately weighed, using the proportions which have 
been previously determined by laboratory tests to give the best results; 
that is, the most dense mixture of mineral aggregate, and one having inherent 
stability. If the crushed stone in the wearing course does not provide the 
best proportions of fine-grained particles, such deficiency must be sup- 
plied by the use of not to exceed 25 per centum hydraulic cement, pulverized 
stone, or very fine sand. 

55.3. The mineral aggregate, composed of differing sizes accurately meas- 
ured or weighed as above, shall pass into a "twin pug " or other approved 



I 



METHODS 783 

form of mixer. In this, mixer shall be added a sufficient quantity of Warren's 
Puritan Brand, bituminous water-proof cement, or bitulithic cement, to 
thoroughly coat all the particles of stone and to fill all voids in the mixture. 
The bituminous cement shall, before mixing with the stone, be heated to 
between 200 degrees and 250 degrees Fahrenheit, and the amount used in 
each batch shall be accurately weighed and used in such proportions as 
have been previously determined by laboratory tests to give the best re- 
sults — that is, to coat all particles of stone and fill the voids in the mineral 
aggregate.^ The mixing shall be continued until the combination is a 
uniform bituminous concrete. In this condition it shall be hauled to the 
street, and there spread on the prepared foundation to such a depth that, 
after thorough compression with a steam road roller, it shall have a thickness 
of two (2) inches. The proportioning of the varying sizes of stone and 
bituminous cement shall be such, that the compressed mixture shall, as 
closely as practicable, have the density of solid «tone. 

55.4. After rolling the wearing surface, there shall be spread over it, 
while it is still warm, a thin coating of Warren's Quick Drying Bituminous 
Flush Coat Composition, by means of a suitable flush coat spreading machine, 
so designed as to spread quickly over the surface a uniform thickness of 
flush coat composition. This spreading machine shall be provided with a 
flexible spreading band and an adjustable device for regulating, to any 
desired amount, the quantity and uniformity of flush coat composition 
to be spread. 

There shall be spread over the flush coat composition, in at least two 
coats, fine particles of hot crushed stone, in sufficient quantity to com- 
pletely cover the surface of the pavement. These _ stone chips shall be 
spread by means of a suitable stone spreading machine, so designed as to 
provide a storage receptacle of at least five (5) cubic feet capacity and to 
rapidly and uniformly cover the surface of the pavement with the desired 
quantity of stone. This spreading machine shall be provided with an 
adjustable attachment for regulating uniformly the quantity of stone spread 
at each operation. The hot stone chips shall be immediately and thoroughly 
rolled into the surface until it has become cool. The purposes of the flush 
coat composition and the fine particles of hot crushed stone are to not 
only fill any unevenness in the surface, but also to make the surface water- 
proof and gritty, thus providing a good foothold for horses. _ 

On grades a mineral flush coat may be used in place of the liquid flush coat. 

55.5. Warren Bros., owners of the^atents used in the construction of 
Bitulithic pavement, have filed with the State Commission of Highways a 
properly executed binding agreement to furnish any contractor to bid for 
the work all the necessary surface material mixed and ready for use, and 
bituminous flush coating cement necessary for coating the wearing surface, 
delivered on wagons of the Contractor at the mixing plant (which will be 
located within three miles of the point of use) at a stipulated price per 
square yard for each contract. Such price for Bitulithic pavement mixture 

; and flush coating composition will include a license to use all the patents 
required in the construction of the pavement as herein specified. 

The filing of a bid under these specifications will be construed as an 
acceptance of the terms of the license agreement filed by the Warren Bros. 
Company, at the price fixed in said agreement, which is on file with the- 

, secretary of the Commission. 

55.6. The quantity of pavement to be paid for under this item shall be 
I the number of square yards of Bitulithic pavement placed in accordance 
' with the plans, or as directed by the Engineer. The bid price shall include 
' the furnishing and placing of all materials, the mixing, spreading, rolling 

and all labor and incidental expenses necessary to complete the work. 



GENERAL SPECIFICATIONS FOR AMIESITE PAVEMENT 



Foundation. — The excavation, filling or embankment, drainage and 

I rolling of the sub-base shall be in full accordance with the standard speci- 
fications for street or highway paving before placing the foundation, the 
depth and nature of which is governed by existing conditions of the sub-grade. 
The foundation, whether in re-surfacing or new work, shall be, before 
.applying the Amiesite, even and compact and swept clean of all loose dirt 
iand foreign material. New stone, if put on, shall be thoroughly bonded 
)with screenings, sprinkled and rolled hard and uniformly. The foundation 
lust be uniform and be brought up to a true and even grade, parallel to 



784 



SPFXIFTCATIONS 



and inches below the elevation of the finished surface of the street 

or road. 

Application. — The bottom course shall be spread m a uniform layer, 
using blocks or strips to insure an even distribution, then rolled. (Size) 
Stone used in Amiesite Bottom Course-Graded — H'' to iW\ If -any 
depressions appear, due to foundation not being firm or any other 
reason, they must be filled with Amiesite and rolled until surface is even and 
to grade desired. 

After the preliminary rolling, the Amiesite top course, made of stone 
graded from W to W^ in size, shall be applied, not less than one inch 
(i") deep, loose measurement, and raked to an even depth so as to 
cover the underlying Amiesite and fill the voids. In no case shall the bottom 
course be spread over 300' in advance of the top course, nor shall over 
50' be left uncovered during the night. 

The compressed depth of finished Amiesite surface shall be: Preferably 
not less than 2H inches. 

Rolling. — After the top course has been evenly spread to a true grade, 
the surface shall be rolled with a standard ten ton road roller until the 
material is thoroughly compacted and ceases to creep in front of the roller. 
In rolling the roller must start from the sidelines of the street or road and 
work towards the center. Care must be taken that the shoulders are firm 
and solid, as otherwise the surface will iron out to a feather edge and crack. 
No rolling shall be done unless the Amiesite is free from water. 

Surface Finish. — After rolling as called for above, clean, sharp sand 
or stone dust (Limestone where obtainable) shall be spread in a thin layer 
and the road may then be immediately thrown open to traffic. 

General. — No Amiesite shall be spread when the road-bed contains 
depressions holding water. The Amiesite must at all times be kept clean. 
Dirt or other foreign material must not be allowed to mix with, under, or 
on the Amiesite while being unloaded from cars, spread and rolled. 

Should the bottom course become coated or partly coated with dust or 
dirt before the top course can be applied, the part thus coated must be 
swept and then given a light application of bituminous cement, that can be 
applied in a thin coating from a sprinkling pot so constructed that a thin 
and uniform application can easily be applied. 

The Amiesite may be steamed to facilitate its unloading from the cars. 
Steam pressure shall not exceed fifteen pounds to the square inch. The 
Amiesite should not be steamed more than fifteen minutes in any one place. 
This shall be done under the supervision of the inspector in charge. 

The Amiesite shall be unloaded from wagons upon iron sheets or boards, so 
as to insure the material being kept clean and being spread uniformly. 

Cross rolling shall be done, when ordered, to equalize the bond and 
prevent waves in the surface. Care must be taken that the bottom course 
is not rolled down hard before the top course is applied. 

The finished surface of the Amiesite after rolling shall be kept ^" 
higher than any permanent elevation, depending upon the traffic to ulti- 
mately compress or pound it down to grade. 

Grading slopes or shoulders shall not be carried on after the Amiesite 
course is started until completion of roadway. 

The street or road shall be closed to traffic when the Amiesite surface is 
being applied. 

Item 56 — Hassam Compressed Concrete Pavement 

56.1. Under this item the Contractor shall furnish all materials for and 
place upon a properly prepared sub-grade or sub-bottom course Hassam 
Compressed Concrete Pavement of the thickness shown upon the plans 
or ordered by the Engineer. 

56.2. Hassam Compressed Concrete Pavement will be placed on the 
sub-grade or on the sub-bottom course and shall not be placed until these 
are in first-class condition as required for macadam pavement. 

56.3. Hassam Compressed Concrete Pavement shall consist of a graded 
No. 3 and I^o. 4 stone (for the meaning of these numbers see page 720), of 
an approved quality, spread evenly and gauged by the use of cubical blocks; 
after rolling and thoroughly compacting with a lo-ton roller, it shall have 
the required depth and shall conform to the established lines, grades and cross- 
sections. Where any depressions or irregularities develop in rolling the 
surface shall be forked over and material added or taken away to the end 
that a smooth surface shall be provided after re-rolling. 

56.4. After the rolling has been satisfactorily completed and the surface 



METHODS 785 

of the broken stone has been brought to the required uniform surface, and 
before there is any displacement of the stone, the voids shall be filled with a 
grout consisting of one part Portland cement and two parts of approved 
sand. The sand shall be of such sizes that it will not separate readily from 
the cement, when placing the grout, and any batch of grout, when being 
placed, shall at all times be of a uniform product and of such consistency 
that it will flow readily but shall not be so wet as to cause a separation of 
the cement and sand. The rolling shall be continued during the process of 
grouting and until all the voids are filled. 

56.5. The grout shall be mixed in a Hassam Grout Mixer or other me- 
chanical mixer which will properly mix the ingredients and from which 
they can be deposited without a separation of the cement and sand. 

56.6. Immediately after the voids shall have been filled with grout, 
a thin layer of No. i broken stone or fine aggregate shall be spread over 
the entire surface and rolled until the grout flushes to the surface. 

56.7. After placing the surface stone the surface shall not be worked 
upon or disturbed for a period of ten days, during which time the surface 
shall be kept thoroughly wet. 

56.8. Any cracks either longitudinal or transverse which develop before 
the acceptance of the work shall_be thoroughly cleaned out and filled with 
acceptable bituminous material. 

56.9. The quantity to be paid for, under this item, shall be the number 
of cubic yards of Hassam Compressed Concrete Pavement incorporated in 
the work in accordance^ with the plans or as directed by the Engineer. 

The price bid shall include the furnishing and placing of all materials, 
all grouting, rolling, forms and all labor, appliances, royalties and incidental 
expenses necessary to complete the work. The amount to be estimated 
shall be computed by multiplying the cross-section of concrete pavement as 
shown upon the plans or ordered by the Engineer, by the total length of 
pavement measured along the axis of the pavement. 

Item 57 — Cement Concrete Pavement 

57.1. Under this item the Contractor shall furnish and place upon a 
properly prepared sub-grade or sub-bottom course, concrete pavement of the 
thickness shown upon the plans or ordered by the Engineer. 

57.2. Concrete pavement will be placed on the sub-grade or on the 
sub-bottom course, and shall not be placed until these are in first-class 
condition, as required for macadam pavement. 

57.3. Concrete shall consist of a mixture of Portland cement, No. i 
sand, and broken stone or gravel. All these materials shall conform in all 
respects to the requirements given under "Materials of Construction," 
and all the specifications relating to first-class concrete shall apply to work 
done under this item, in so far as same are not inconsistent with the special 
specifications given below. 

57.4. The concrete shall be mixed in the proportions of one volume 
of cement to four and one-half volumes of sand and broken stone or gravel. 
The volumes of sand and broken stone or gravel, shall be measured separately 
in approved hoppers. The relative proportions of fine and coarse aggregate 
will be varied slightly, as a result of tests for voids by the Engineer, to the 
end that resulting concrete shall be as dense as possible. The concrete 
shall in all cases approximate at i : 1 3^ : 3 mix. 

57.5. The coarse aggregate shall consist of a well-mixed product of 
No. 2 and No. 3 stone or No. i and No. 2 gravel. Gravel shall not be used 
except when it has been submitted by the Division Engineer to the Bureau 
of Tests, has been approved by the Bureau of Tests, and its use has been 
approved by the First Deputy Commissioner in writing — and then only 
under the restrictions laid down under "Materials of Construction." The 
fine aggregate shall consist of No. i sand. 

57-6. The concrete shall be mixed in approved mechanical batch mixers. 
Mixing shall be continued through at least 12 revolutions and until every 
particle is coated with mortar and until the batch is of uniform color and 
consistency. After the materials are once wetted the work shall proceed 
rapidly until the concrete is in place. The quantity of water used shall 
be as directed by the Engineer and suitable measuring tanks shall be pro- 
vided by the Contractor so that the same amount of water may be used in 
the separate batches. No concrete pavement shall be laid when the tem- 
perature falls below 35° F. 



786 



SPECIFICATIONS 



57.7. Substantial forms shall be placed along the edge of the concrete 
pavement and shall be set and held true to line and grade. 

57.8. Before any concrete is placed, the sub-grade shall be sprinkled 
sufficiently to dampen it but a muddy condition shall not be allowed. 
As soon as possible after mixing, the concrete shall be deposited in place 
and thoroughly spaded and screeded so as to bring the mortar flush to the 
surface. Especial care shall be taken to keep the concrete uniform and to 
prevent pockets of stone or mortar. 

57-9. Heavy screeds cut to the lines required for the finished surface 
and resting upon the side forms shall be used for consolidating and screeding 
the concrete, and the surface, when completed, shall conform to the lines 
and grades shown upon the plans, and shall be free from depressions or 
irregularities. No stone shall project above the general surface. All 
shaping and screeding shall be done before the concrete has taken its initial 
set. Any concrete which has not been shaped and finished previous to the 
time of initial set, shall be removed for the full depth of the roadway and 
replaced with satisfactory concrete. 

57.10. If a satisfactory finish can not be obtained with the screed, the 
screeding shall be immediately followed, and before the cement has taken 
its initial set, by rubbing down with a wooden float. The men employed 
for this work shall be competent and experienced and shall work from a 
platform which rests on the forms or shoulders. The surface, when finished, 
shall be such that no water will stand on the finished pavement. It shall 
then be slightly roughened by brooming. 

57.11. As soon as the concrete has taken its initial set the surface shall 
be covered with a one-inch layer of sand or other suitable material of which 
the shoulders are to be constructed and this shall be thoroughly sprinkled 
every morning and night, and more often if necessary, so^ that it will be 
kept moist for a period of ten days after placing; the material shall then be 
cleaned from the surface and the road may be opened to traffic if so directed 
by the Engineer. 

57.12. The concrete shall be deposited in sections 30 feet in length, 
and at the end of each section expansion joints of the type shown on the 
plans shall be placed. After starting any section, an effort shall be made 
to complete it at one operation. If for any reason this can not be done, a 
vertical joint shall be made when the work is stopped and the work com- 
pleted up to this joint. 

57.13. Any cracks, either longitudinal or transverse, which develop 
before the acceptance of the work, shall be thoroughly cleaned out ana 
filled with acceptable bituminous material. 

57.14. The quantity to be paid for under this item shall be the number of 
cubic yards of concrete pavement incorporated in the work, in accordance 
with the plans or as directed by the Engineer. 

The price bid shall include the furnishing and placing of all materials; 
all mixing,^ screeding, finishing, forms, expansion joints and all labor, appli- 
ances and incidental expenses necessary to complete the work. The amount 
to be estimated shall be computed by multiplying the cross-section of con- 
crete pavement as shown upon the plans or ordered by the Engineer by 
the total length of pavement measured along the axis of the pavement. 

Item 58 — Lignin or Sulphite Liquor 

58.1. Under this item the Contractor shall furnish and apply lignin 
or sulphite binder at the rate of one-half gallon of binder (not of the mixture) 
to the square yard. 

58.2. A quart sample, from each carload of the material to be used, shall 
be submitted to the Bureau of Tests for acceptance before it may be used. 

^ This rnaterial shall be a neutral or basic liquor secured by the extrac- 
tion of lignin from organic matter. It shall be concentrated by evapora- 
tion at a temperature not exceeding 210 degrees Fahrenheit until it has a 
specific gravity at 77 degrees Fahrenheit of not less than 1.23. When 
concentrated to a constant weight at 212 degrees Fahrenheit, it shall have 
a residue of not less than 45 per cent. It shall contain not more than 9 per | 
cent, of ash. It shall be 99.5 oer cent, soluble in cold water. j 

58.3. After the road has been thoroughly filled and brought to a puddle 
with water, the application of lignin or sulphite binder shall commence 
and the puddle continued, using a mixture of one part binder to not less 



METHODS 787 

than three parts water. This puddling shall continue until the road has 
received a treatment for its full width of one-quarter gallon of the lignin 
(not of the mixture) to the square yard. After the roadway has set, but 
not entirely dried out, the balance of one-quarter gallon of the lignin to the 
square yard shall be applied to 80 per cent, of the width of roadway, using a 
mixture of one part lignin to two parts water. _ 

58.4. Lignin or sulphite binder shall be applied to the roadway by means 
of an improved sprinkler which can be regulated so that a uniform distri- 
bution is obtained and so that not over one-half of the required amount of 
binder shall be spread to the square yard on each trip of the sprinkler. The 
sprinkler shall be equipped with necessary brooms so arranged as to sweep 
forward any excess material that does not immediately penetrate into the 
surface. 

58.5. The quantity of material to be paid for under this item shall be 
the actual number of gallons of lignin binder, measured before dilution, 
actually applied and incorporated in the work to the satisfaction of the 
Engineer. Binder that has been wasted or that has been applied not in 
accordance with the requirements of this specification or the orders of the 
Engineer, shall not be included in this item for payment. The price bid 
shall include the cost of furnishing hauling, applying and all necessary 
appliances and expenses incidental thereto. 

Item 59 — Wood Block Parement 

59.1. Under this item the Contractor shall furnish and place upon a 
properly prepared foundation wood block of the quality specified where 
shown upon the plans or ordered by the Engineer. 

This pavement shall be placed upon the old macadam, old concrete 
pavement, new concrete foundation or on other foundation as shown on 
the plans and ordered by the Engineer. 

59.2. The blocks shall be from 6 to 9 inches long and shall average 8 
inches; they shall be 3 inches in depth and from 3 to 4 inches in width; 
but all blocks in one piece of pavement shall be of uniform width. No 
variation greater than He -inch shall be allowed in the depth and ^-inch 
in the width of the blocks. 

59.3. Blocks shall be made from Southern yellow pine. North Carolina 
pine, Norway pine, black gum or tamarack; only one kind of wood, however, 
shall be used in one piece of pavement. 

Yellow pine block shall be made from what is known as Southern yellow- 
pine, well manufactured, full size, saw butted, all square edges, and shall 
be free from the following defects: 

Unsound, loose and hollow knots, worm holes and knot holes, through 
shakes and round shakes that show on the surface. In yellow pine timber 
the annular rings shall average not less than six to the inch and shall be in 
no case less than four to the inch, measured radially. 

Norway pine, gum. North Carolina pine and tamarack block shall be 
cut from timber that is first-class in every respect, and shall be of the same 
grade as that defined for the Southern yellow pine. 

59.4. The creosote oil with which the blocks shall be treated shall conform 
to either of the following specifications, designated as "A" and "B." 

The preservative to be used under this specification shall be a product of 
coal gas, water gas or coke oven tar, which shall be free from all adultera- 
tions and contain no raw or unfiltered tars, petroleum compounds, or tar 
products obtained from processes other than those stated. 

Specification **A" 

The specific gravity shall not be less than one and eight-hundredths 
(1.08) nor more than one and fourteen hundredths (1.14) at a temperature 
of thirty-eight (38) degrees centigrade. 

Not more than three and one-half (3H) per cent, shall be insoluble by 
continuous hot extraction with benzol and chloroform. 

On distillation, which shall be made exactly as described in Bulletin 
6s of the Railway Engineering and Maintenance of Way Association, the 
distillate, based on water free oil, shall not exceed one-half (3^^) of one (i) 
per centum at one hundred and fifty (150) degrees centigrade, and shall not be 



788 



SPECIFICATIONS 



less than thirty (30) nor more than forty (40) per centum at three hundred 
and fifteen (31S) degrees centigrade. 

The oil shall contain not more than three (3) per centum of water. 

Specification " B " 

It shall be completely liquid at tliirty-eight (38) degrees centigrade, 
and shall have a specific gravity at that temperature of not less than one 
and three hundredths (1.03) nor more than one and eight hundredths (1.08). 

It shall contain not more than two (2) per centum of matter insoluble by hot 
extraction with benzol and chloroform. 

On distillation, which shall be made exactly as described in Bulletin * 
No. 65 of the American Railway Engineering and Maintenance of Way ■ 
Association, the distillate based on water free oil shall be within the following \ 
limits: * 

At 210 degrees centigrade, not more than 5 per centum. 

At 235 degrees centigrade, not more than 35 per centum. J 

At 3x5 degrees centigrade, not more than 85 per centum. 

The oil shall yield a coke residue not exceeding three (3) per centum. 

The distillate, between 210 degrees centigrade and 235 degrees centigrade, ," 
shall yield solids on cooling to 15 degrees centigrade. The preservative ; 
shall contain not more than 3 per centum of water. 

59.5. The manufacturer of the oil shall permit full and complete inspection 
and sampling at the factory at which the oil is produced, of all materials- 
either crude or refined, entering into the manufacture of the finished product 
itself, in order that the materials used can be determined to be in accordance 
with the foregoing requirements. He shall also submit satisfactory proof 
of the origin of all materials entering into the composition of the finished 
product. 

Samples of the preservative taken by the inspector from the treating 
tank during the progress of the work shall at no time show an accumula- 
tion of more than 2 per centum of foreign matter, such as sawdust or dirt. 

59.6. The blocks shall be treated with the preservative above described, 
so that they shall contain at least sixteen pounds of the same per cubic 
foot of timber. 

The manufacturer of the block shall equip his plant with all necessary 
gauges, appliances and facilities to enable the inspector to satisfy himself 
that the requirements of the specifications are fulfilled. 

59.7. Upon the foundation shall be spread a bed of cement mortar at 
no place less than one-half inch in thickness, composed of one part Portland 
cement and four parts sand thoroughly mixed dry. This mortar bed shall 
be struck with a template to a true surface exactly parallel to the top of the 
proposed pavement surface and three inches below it. ^ This bed shall be 
sprinkled, immediately in advance of the block laying, with hand sprinklers. 

59.8. On the mortar surface prepared as described, the blocks shall be 
laid with grain vertical and at such angles with the curb as the Engineer may 
direct. The blocks shall be laid in straight and parallel courses and set 
snugly together but not driven together. Each course of blocks shall be 
of uniform width and depth, with end joints broken by a lap of not less than 
two and one-half inches. Only whole blocks shall be used except in starting 
courses, cutting closures, or where specially permitted by the Engineer. 

Closures shall be carefully cut and trimmed by experienced men, the 
portion of the blocks used shall be free from defects and the cut end shall 
have a surface perpendicular to the top of the block and cut at a proper 
angle to give a close joint. In laying block the pavers must stand on the 
block previously laid. 

After the laying is completed, defective blocks shall be carefully culled 
out, low blocks raised, the courses carefully aligned and the blocks spaced 
up. The pavement shall then be rolled by a steam tandem roller weighing 
not less than two and one-half tons nor more than five tons; the pavement 
being at the same time lightly sprinkled and the rolling continued until a 
uniform surface is obtained. Upon the completion of the rolling any 
defective blocks shall be removed and be replaced with sound blocks, and 
displaced blocks shall be realigned. The joints in the pavement shall then 
be immediately filled in the manner hereinafter described. If deemed 
advisable by the Engineer, portions of pavement laid with blocks which have 
become "dried out" shall be sprinkled with water at frequent intervals 
before joints of same are filled. 



METHODS 789 

59.9. After rolling, the blocks shall be flushed with an approved bituminous 
filler heated to at least 300 degrees Fahrenheit, which shall be poured over 
the whole surface and well forced into the joints by rubber squeegees. 
While the bituminous filler is still hot it shall be immediately followed with a 
thin coating of clean dry sand. Before turning traffic onto the pavement a 
coating of one-half inch in thickness of dry screened sand shall be spread 
over the entire surface. 

ASPHALTIC FILLER (CITY OF LIMA, OfflO) 

After rolling, the surface of the pavement shall be swept clean and the 
joints between the blocks and expansion joints shall be filled with an asphaltic 
filler which shall be free from water, coal-tar pitch, or any product of coal 
or water gas tar. It shall adhere firmly to the blocks, be pliable,' at all 
climatic conditions to which it will be subjected, and conform to the following 
requirements: 

It shall have a specific gravity of not less than nine hundred and sixty-five 
thousandths (0.965) at seventy-seven (77) degrees Fahrenheit. 

It shall have a melting point of not less than one hundred and ten (no) 
and not more than one hundred and sixty (160) degrees Fahrenheit. 

It shall have a penetration of not less than twenty (20) nor more than 
fifty (50). 

The bitumen of the asphaltic filler shall be soluble in carbon tetrachloride 
to the extent of at least ninety-eight (98) per cent. 

The asphaltic filler shall be heated to a temperature of not less than two 
hundred and eighty (280) degrees nor more than three hundred and fifty 
(350) degrees Fahrenheit, and shall be applied in such a manner that all 
spaces between the blocks will be completely filled, the temperature of heating 
to be varied within these limits according to the nature of the asphaltic 
filler used and at the discretion of the City Engineer. In applying the 
asphaltic filler care must be taken to use the least amount necessary to 
properly fill the joints and hold the top dressing. The blocks must be dry 
at the time of the application of the filler. 

PITCH FILLER (CITY OF LIMA, OHIO) 

After rolling, the surface of the pavement shall be cleaned and the joints 
between the blocks and expansion joints shall be filled with a "straight run" 
paving pitch obtained from gas-house tar. No pitch from coke-oven tar 
shall be used. It shall be of such quality and consistency as will be approved 
by the City Engineer. Thfe pitch shall contain not less than twenty (20) 
per cent, nor more than thirty (30) per cent, of free carbon, and shall have a 
melting point at a temperature of not less than one hundred and twenty (120) 
degrees and not more than one hundred and thirty (130) degrees Fahrenheit. 
The pitch must be used at a temperature of not less than three hundred 
(300) degrees and not more than three hundred and fifty (350) degrees 
Fahrenheit. In applying the pitch, care must be taken to use the least 
amount necessary to properly fill the joints and hold the top dressing. 

SAND FILLER (CITY OF LIMA, OHIO) 

After rolling, the surface of the pavement shall be swept clean and the 
joints, except as hereinafter provided, between the blocks shall be filled with 
clean, warm, fine sand, which shall be swept into the joints until the same 
are completely filled. 

The expansion joints and joints between the blocks in a space of two (2) 
feet in width adjacent to the gutters, a space of four (4) feet wide in the 
middle of the roadway and around all covers to sub-surface improvements 
shall be filled with a "straight run" paving pitch obtained from gas-house 
tar. No pitch from coke-oven tar shall be used. It shall be of such quality 
and consistency as will be approved by the City Engineer. The pitch must 
be used at a temperature of not less than three hundred (300) degrees and 
not more than three hundred and fifty (350) degrees Fahrenheit. The pitch 
shall contain not less than twenty (20) per cent, nor more than thirty (30) 
per cent, of free carbon and shall have a melting point at a temperature of 
not less than one hundred and twenty (120) degrees and not more than one 
hundred and thirty (130) degrees Fahrenheit. 



790 SPECIFICATIONS 

ALTERNATIVE fl 

For the purpose of automatic expansion and the prevention of slipperynessl' 
alternate bids will be received for Creosote Lug Blocks, or their equal-. 

On one end of each block there shall be one, and on one side of each block 
there shall be two ribs or projections extending the full depth of the block, 
and such ribs or projections shall be an integral part of the block. 

Such ribs or projections shall be of the size and shape and placed in such 
position on the block as the Engineer may determine. 

In all other respects such blocks shall conform to these general specifica- 
tions. Should there be any deviation therefrom, the contractor shall submit 
complete specifications of the kind of block he wishes to bid on and the 
method of manufacturing the same. 

59.10. The quantity to be paid for under this item shall be the number of 
square yards, including expansion joints, of pavement laid in accordance 
with the plans and as directed by the Engineer. 

The price bid shall include the furnishing and placing of the mortar bed, 
wood block, bituminous filler and sand surfacing and all other labor and 
incidental expenses necessary to complete the work. 

Item 60 — Asphalt Block Pavement 

60.1. Under this item the Contractor shall furnish and place upon a 
properly prepared foundation asphalt block of the quality specified where 
shown upon the plans or ordered by the Engineer. This pavement shall be 
placed upon the old macadam, old concrete pavement, new concrete founda- 
tion or on other foundations as ordered by the Engineer and shown upon 
the plans. 

60.2. The blocks shall be five inches in width, by twelve inches in length, 
by two inches in depth, and a variation of more than one-fourth of an inch 
in length and one-eighth of an inch in width or depth from these dimensions 
will be sufficient ground for rejecting any block. 

60.3. The blocks shall consist of the following materials: 
Asphaltic cement. 

Crushed trap rock or other approved crushed rock. 
Inorganic dust. 

The rock used in the blocks must be crushed so that every particle will 
pass a screen of one-fourth of an inch mesh. The blocks shall receive a 
compression in the moulds of not less than one ton per cubic inch of material 
in the blocks, and must weigh not less than ten and one-half pounds per 
block. The blocks shall have a specific gravity of not less than 2.40, and 
after having been dried for twenty-four hours at a temperature of 150 
degrees Fahrenheit, they shall not absorb more than i per centum of mois- 
ture when immersed in water for seven days. Whatever the character of 
the asphalt used, the block shall yield not less than 6H per centum of 
bitumen, when extracted with carbon bisulphide. 

The inorganic dust, or filler, shall be produced from sound limestone 
or other approved material, and shall be powdered to such a fineness that 
all of it shall pass a thirty mesh sieve and not less than 50 per centum of it 
shall pass a 200 mesh sieve. Sufficient inorganic dust shall be used to give 
a minimum percentage of voids in the block, and provide a sufficient medium 
for absorbing the asphaltic cement. 

60.4. The asphaltic cement shall be composed of natural or oil asphalt, 
and asphaltic oil, as approved. This asphaltic cement shall be of acceptable 
consistency and quality. 

The material shall have a specific gravity of at least 0.98 at 77 degrees 
Fahrenheit. Its penetration shall be not more than ten mm. when tested 
for five seconds at 77 degrees Fahrenheit, with a No. 2 needle weighted with 
100 grams. When twenty grams are heated tn a hot air oven in a flat- 
bottom dish two and one-half inches in diameter at 325 degrees Fahrenheit 
for five hours, the loss in weight shall not be more than eight per centum. 
It shall show an open flash point not less than 325 degrees Fahrenheit. Its 
solubility at air temperature in chemically pure carbon disulphide shall be 
at least sixty-six per centum. 

60. 5 Upon the foundation shall be spread a bed of the thickness shown 
upon the plans, composed of one part Portland cement and four parts sand, 
thoroughly mixed. 

This mortar bed shall be struck with a template to a true surface, exactly 
parallel to the top of the proposed pavement surface and two inches below it 



METHODS ^ 791 

This bed shall be sprinkled immediately in advance of the block laying 
with hand sprinklers. 

The blocks shall be laid while the mortar is fresh and before it has taken 
its initial set. All depressions and other irregularities in the surface shall 
be corrected by the Contractor immediately. 

The blocks shall be laid by the pavers standing upon the blocks already 
laid and not upon the bed of mortar. 

The blocks shall be laid at right angles with the line of the street, and 
in such a manner that all longitudinal joints shall be broken by a lap of 
at least four inches. The blocks shall be so laid as to make the lateral 
joints as tight as possible, consistent with keeping a good alignment of 
the courses across the street. When thus laid the blocks shall be imme- 
diately covered with clean, fine sand, perfectly dry, and screened through a 
one-eighth inch screen. This sand shall be spread over the surface and 
swept into the joints and be allowed to remain on the pavement not less 
than thirty days or for such time as the action of the traffic on the street 
shall have thoroughly ground the sand into all the joints. 

60.6. The materials incorporated into blocks shall be approved by the 
Engineer, and samples of all materials shall be sent to the Bureau of Tests 
and they shall pass the tests required by this Bureau for these materials. 

60.7. The method of work and materials used shall at all times be 
subject to the inspection and supervision of the Engineer or his representa- 
tive upon the work. 

60.8. The quantity to be paid for under this item shall be the number 
of square yards of asphalt block laid in accordance with the plans or as 
directed by the Engineer. The price bid shall include the furnishing and 
placing of all materials, mortar bed, and all labor and incidental expenses 
necessary to complete the work. Where placed upon old concrete founda- 
tion to receive the mortar bed will be paid for under item "Cleaning Old 
Pavement" or item "Scarifying and Reshaping Old Macadam." 

Item 61 — Brick Pavement (Sand Cushion Type) 

6 1. 1. Under this item the Contractor shall furnish and place the number 
of square yards of brick pavement required in accordance with the plans or 
as ordered by the Engineer. The item will include the furnishing and plac- 
ing of all the block, sand cushion, grout, expansion joints and all material, 
labor and other expenses incidental thereto but will not include the concrete 
foundation, edging, curbing, manholes, catch basins, etc., which will be 
paid for under the especially designated items therefor. 

61.2. All bricks or blocks used must be vitrified and especially burned 
for street paving and of the very best quality as regards hardness, dimensions, 
toughness, straight lines and non-absorption of water. 

61.3. The paving bricks shall be subjected to modulus of rupture test 
and to abrasion tests conducted by the Commission in the manner and with 
rattlers of the type adopted February 7, 191 1, by the National Paving Brick 
Manufacturers Association. One sample shall be tested for every two hun- 
dred thousand ('200,000) bricks and less than this when conditions warrant. 
An average loss in weight in a rattler test exceeding twenty-four (24) per 
centum, or an average absorption of three and one-half (3H) per centum of 
water shall cause the rejection of the total quantity that the test represents, 
provided, however, *that if permitted the bricks may be carefully recuUed, 
and new samples taken and tested. If this second test passes the require- 
ments, the bricks represented by' it may be used. If this second test fails, 
no further test shall be permitted but the entire lot shall be rejected. To 
ensure the furnishing of bricks of uniformly acceptable quality, any "brand" 
of brick shall be rejected and shall not be further considered if three lots, 
each of ten thousand (10,000) bricks or more, offered consecutively for ac- 
ceptance tests, fail to meet the requirements for this section without recuUing 
them. 

Modulus of Rupture. — When tested on edge as laid on the pavement, the 
modulus of rupture shall be not less than two thousand (2000) pounds per 

WL 
square- inch. Computed by formula R = 3-T-j^in which R is the modulus 

of rupture in pounds per square inch, L the length between supports in 
inches ( = 6 inches), b and d the breadth and depth in inches, and W the 
load in pounds, which produces rupture. 

All the above tests will be made by the Bureau of Tests of the State 
Commissionof Highways. 



792 SPECIFICATIONS 

61.4. On grades of 5 per centum or over an approved special form of 
block suitable for steep grades shall be used. 

61.5. The size of the brick shall be sH inches in width by four inches 
in depth by &}i inches in length, and shall not vary from these dimensions 
more than one-eighth inch in width or depth nor more than one-half inch 
in length. Bricks of a given brand shall not vary among themselves more 
than 3'^-inch in depth nor more than 3'^ -inch in width nor more than ^'^-inch 
in length in any one shipment. If the edges are rounded the radius shall 
not be greater than He of an inch. One side shall contain lugs of such 
dimensions that transverse joints will not be less than Me of an inch nor 
more than }i-mch. in width. Each end shall contain a semi-circular groove 
of }i to ^-inch radius, or a bulge or at least He inch. The grooves shall 
be horizontal, and shall match perfectly when the bricks are laid in the fin- 
ished pavement. Bricks in any course shall not vary in width by more 
than ys inch. 

SAND CUSHION 

61.6. Not less than ten days after the concrete foundation has been 
completed, there shall be laid a bed of clean Cushion Sand as described 
under "Materials of Construction," which shall be one and one-half inches 
thick after being rolled with a roller weighing 150 pounds per foot of width. 
Before being rolled this bed of sand shall be brought to the proper elevation 
and crown as shown on plans by a template of a shape and size satisfactory 
to the Engineer. After being rolled all irregularities of the surface shall be 
eliminated and the sand cushion shall be brought to the exact form and sec- 
tion by the use of lutes or hand templates. 

EXPANSION JOINT 

61.7. Longitudinal expansion joints shall be placed alongside each curb 
or edging, and shall be one of the following types: 

Premolded Type, requiring no heating or pouring at the place of insertion. 
These expansion joints shall be of the proper thickness and width, as speci- 
fied, made in convenient lengths ready for use. The joints shall be placed 
as the paving progresses, and shall rest directly on the sand cushion. The 
expansion joints shall be composed entirely of a high grade asphalt, and shall 
pass the following tests: 

Specific gravity . 985 to i . 002 

Melting point 235° to 265° F. 

Loss on heating for 5 hours at 325° F .0% 

Bitumen soluble in carbon disulphide 99 • 5 % to 99 • 9 % 

Bitumen soluble in carbon tetra-chloride 99-4% to 99-8% 

Bitumen soluble in Be. Naphtha to % 

Penetration at 32° F 25 to 35 

Penetration at 77° F 40 to 50 

Penetration at 1 15° F 65 to 75 

Poured Type. — This type shall be provided for by placing alongside each 
curb or edging wooden strips with metal wedge shape pieces dropped over 
the top of the boards and between the board and the curb every three feet 
apart to facilitate the removal of the boards, or, by using two planed wedge- 
shaped strips so cut that when placed together in reverse positions their 
total section shall be rectangular and of a thickness and depth equal to the 
thickness and depth of the required expansion joint. The strip placed next 
to the curb shall be set with the wide edge up. _ These expansion joint forms 
shall be set next to the curb on a true grade with all end joints tight, and 
be pressed into sand so that their tops shall be one-quarter inch below the 
top surface of the pavement blocks before rolling. The two strips compris- 
ing the joint form shall break joints. 

The thickness of longitudinal expansion joints shall be as called for by the 
plan. 

61.8. On the sand cushion prepared as in section 61.6 the blocks shall 
be carefully set on edge with the best edge up, shall be laid straight at and 
right angles to the edging line, except at road intersections, where they shall 
be laid at such angles as directed by the Engineer. All block shall be laid 
with the lugs in the same direction, joints shall be close and at right angles 
to the tops and sides. ^ Each alternate course shall be commenced with a 
half brick. No half bricks or bats shall be used except at the ends of courses. 
All joints shall be broken with a lap of not less than three (3) inches. 



METHODS 793 

All brick shall be clean when placed in the pavement. Brick which in 
the opinion of the Engineer are not satisfactorily clean, shall be washed before 
being placed. 

In no case shall the sand cushion in front of the pavement be disturbed 
or walked on during the laying of the blocks. 

61.9. After a sufficient number of blocks have been laid, all soft, broken 
or badly misshapen blocks shall be marked by the inspector and removed. 
Any blocks slightly spalled or kiln-marked shall be turned over, ,and should 
the opposite face be acceptable, it may be replaced in the pavement, other- 
wise, it must be removed. 

In laying block pavement, the inspector shall keep the blocks culled, and 
the Contractor shall make the necessary changes and replacements so that the 
work shall at all times be ready for grouting within 300 feet from the block- 
laying. 

GROUTING 

61.10. After all objectionable blocks have been removed from the 
pavement and all replacements have been made, the pavement shall be 
swept clean and thoroughly rolled with a self-propelled tandem roller weigh- 
ing not over five tons and not less than three tons. Horse rolling shall not 
be permitted. This rolling shall start along the outside edges and progress 
toward the center. It shall then be rerolled diagonally- both ways until the 
surface is even. After final rolling the pavement shall be tested with a ten- 
foot straight edge laid parallel with the curb, and any depression exceeding 
one-quarter inch shall be corrected and brought to the proper grade. All 
blocks disturbed in making replacements or correcting depressions shall 
be settled into place by ramming or by rerolling. Each section of pavement 
must be acceptable to the Engineer before the grouting on that section may 
be commenced. 

61. 1 1. Grout for filling the joints of brick or block pavements shall be 
composed of one part Portland cement and one part Grout Sand. 

61.12. The box for mixing this grout shall be about four feet eight 
inches long, two feet six inches wide and one foot two inches deep, supported 
on legs of different lengths in order that the mixture shall readily flow to the 
lowest corner, which shall not be more than six inches above the pavement. 
Approved mechanical grout mixers may be used. 

61.13. The mixture, not exceeding one sack of cement together with a 
like amount of sand, shall be placed in the box and mixed dry, until the mass 
assumes a uniform color. Water shall then be added, forming a liquid mix- 
ture of the consistency of thin cream for the first coat and slightly thicker 
for each succeeding coat. From the time the water is applied until the last 
drop is removed and floated into the joints of the pavement the mixture must 
be constantly agitated. 

61.14. The brick shall be wet to the satisfaction of the Engineer before 
any grout is placed. The grout shall be removed from the box to the street 
surface with a scoop shovel and immediately swept into the joints, the mix- 
ture in the box being constantly agitated while this is being done. 

The work of grouting shall proceed for the entire width of the pavement. 
When sufficient time has elapsed for the grout to thoroughly penetrate all the 
joints, but before the cement has attained its initial set, the section treated 
shall be gone over a second time in the same manner, care being taken to 
thoroughly fill all joints from the bottom flush with the top of the block. If 
necessary to secure flush joints, a third, fourth or fifth coat of the grout shall 
be swept in and smoothed off with a suitable squeegee. 

Care shall be taken to so conduct the grouting that no part of any joint 
wiirreceivje an application of the second grout until the first is satisfactorily 
completed, nor of the third until the second is completed, etc. To insure 
this result metal strips 1-16 in. by 6 in. by 3 ft. must be inserted, for the full 
length of the joint, at work intervals; all of the several applications of grout 
must be completed up to this joint before any grouting is begun on the other 
side of it. 

61.15. After the joints 5,re thus filled flush with the top of the blocks and 
sufficient time for hardening has taken place, so that the cover coat will 
not absorb any moisture from the grout, one inch of suitable material shall 
be spread evenly over the entire surface, and be kept moist for a period of at 
least ten days and until the grout has thoroughly set. 

During this period the section grouted must remain absolutely free from 
disturbance or traffic of any kind. After 30 days from the spreading, this 
cover coat shall be completely removed. 



>^94 SPECIFICATIONS 

EXPANSION JOINTS 

61.16. In case the poured type of expansion joint is used, after the grout 
has set but within thirty-six hours after its application the expansion joint 
forms shall be withdrawn and the space thus formed thoroughly cleaned and 

• a bituminous filler having a melting point not less than 120 degrees Fahren- 
heit nor more than 140 degrees Fahrenheit shall be immediately poured into 
place at a temperature not less than 200 degrees Fahrenheit. 

61.17. If required,^ transverse expansion joints shall be constructed 
of the materials and in the manner prescribed by the Engineer. 

61.18. The quantity of pavement to be paid for under this item shall 
be the number of square yards placed in accordance with the plans or direc- 
tions of the Engineer. The price bid per square yard shall include the sand 
cushion, paving block, grout, material for expansion joint, sand covering, 
sprinkling, and all other labor, materials and incidentals necessary to satis- 
factorily complete the work. 

The amount to be estimated under this item shall be computed by multi- 
plying the actual width of pavement, including expansion joints, by the 
total length of pavement measured along the axis of the road and parallel to 
the surface. j 

DUNN WIRE-CUT LUG BRICK COMPANY 
CONNEAUT, OHIO 



SPECIFICATIONS 






SUGGESTIONS FOR THE CONSTRUCTION OF A VITRIFIED BRICK 
WEARING SURFACE ON CEMENT-SAND BED-STREETS 
AND HIGHWAYS 
General. — The durability of a brick pavement depends upon three 
essentials: 

1. Good Design. 

2. Good Material. 

3. Good Construction. 

Design. — The specifications should clearly and concisely cover all the 
integral parts of the work viz. : sub-grade, drainage, foundation, brick wearing 
surface, curbing, etc. 

The specifications for the sub-grade should insure a sub-grade free of 
ground water, unyielding, of uniform density and of proper grade and cross 
sections. The drainage of all underground water should be given careful 
consideration and means specified to remove same from the sub-grade. 

The type of foundation and its thickness depend largely on local conditions 
the nature of the subsoil, the amount of traffic, and the cost of materials. 
The foundation should be designed to carry and distribute the load placed 
upon it and should be no deeper than is necessary to do its work. Its upper 
surface should be smooth, and of uniform distance below the surface of the 
finished pavement. A foundation of 1-3-6 concrete is the best type for use 
under a brick wearing surface. 

A cement-sand bed one inch deep should be considered by the engineer 
as one inch of the foundation; that is: if a five inch foundation is designed, 
the concrete should be only four inches thick, the cement-sand bed constitut- 
ing the other inch. 

The crown of the brick wearing surface should be light. A straight crown 
of one-quarter inch to a foot is recommended. 

Premolded or prepared bituminous strips the depth of the brick should be 
used for longitudinal expansion joints. No transverse expansion joints 
should be used; but a substantial header, either of stone or concrete, should 
be used at the end of the pavement and at all street and alley intersections. 

The use of a combined concrete curb and gutter should be avoided, for it 
brings the longitudinal expansion joint in the way of traffic, causing a rapid 
wearing away of the concrete joint. 

On highway work the use of steel forms to holdthe bricks until the same 
are grouted is recommended. The cement-sand bed will bind the brick 
wearing surface and the concrete foundation together, requiring no flush 
edging, thus saving considerable expense. 

Materials. — The specifications should describe the best materials available, 
and prescribe means for the testing of same. Special care should be used in 
selecting the grouting sand. It should not be too fine but well graded. 



METHODS 795 

The brick for the wearing surface should be standard Wire-Cut Lug brick 
with bulged ends. The specifications should not leave it to the contractor 
to say which style of brick shall be used, but should specify the shape of brick 
which the engineer considers will make the most durable pavement. Wire- 
Cut Lug brick are made by independent, competing companies and are 
marketed at the same price as the repressed brick. Their rough bonding sur- 
faces, theirsquare edges and their uniform lugs have proved their superiority 
under service and engineers are specifying them exclusively, knowing they 
will obtain a high grade paving brick, made on engineering lines. 

Wire-Cut Lug brick are made the standard depth, four inches, but if so 
specified can be made three and one-half inches or three inches in depth. 
These shallow brick are particularly adapted for use on a cement-sand bed 
as their structural features give exceptional strength to the bond, and their 
use insures a considerable saving in material, freight and haulage. 

High grade Portland cement should be specified, especially for the grout 
and cement-sand bed. 

Construction. — All materials should pass a rigid inspection. The paving " 
brick should be tested at the plant where they are made. All Wire- Cut 
Lug brick companies have a standard rattler which is at the service of the 
testing engineer. ^ All cement should be tested. ^ 

Good construction is obtained by close inspection, and the inspector should 
always be on the work. 

The interpretation of the specifications shall be made by the engineer, and 
materials, manner of testing, and equipment for doing the work, should 
meet with his approval. 

In the preparation of the cement-grout filler, the sand should be carefully 
selected, and should be well graded and not too fine. The amount of water 
necessary to obtain the proper consistency should be determined, and so 
regulated as to obtain the same amount for each batch of the filler. ^ Too 
much water will cause separation; too little water will cause a bridging of 
the joints. 

SPECIFICATIONS FOR THE BRICK WEARING SURFACE 

Brick. — The contractor shall submit samples and name the brands of 
brick with prices respectively upon which he submits bids. The brick 
shall be of the quality and size commercially known as wire-cut lug vitrified 
paving brick. They shall be reasonably straight, uniform in size, texture 
and shape and shall be hard, tough, evenly burned and thoroughly annealed. 
When broken, the brick shall show a uniform fracture, free from lime, 
marked laminations and other defects which would tend to depreciate their 
value as a paving material. They shall have square edges and shall have 
one fairly straight face, and one side of the brick shall be provided with four 
(4) projections, which shall not project more than one-fourth (34) of an 
inch or less than one-eighth (3^) of an inch. Each end shall have a bulge 
of at least one-sixteenth (He) of an inch. All brick so distorted as to lay 
unevenly in the pavement shall be rejected. 

The standard size of paving brick shall be three and one-half (3H) inches 
in width, four (*4) inches in depth, and eight and one-half (8^) inches in 
length, and shall not vary from these dimensions more than one-eighth (3^) 
of an inch in width or depth, nor more than one-quarter (34) of an inch in 
length. 

Inspection. — All brick shall be subject to thorough inspection before and 
after laying and rolling. Factory inspection of brick including the rattler 
test shall be made if in the judgment of the engineer it be expedient. 

Test. — The bricks shall not lose of their weight more than 24 per cent, 
after being submitted to the Standard Rattler Test, to be made under the 
specifications, in the manner and method and with a rattler, together with 
records thereof, as adopted by the American Society for Testing Materials 
at their annual meeting in 191 5. 

Cement-sand Bed. — Upon the foundation as prepared there shall be 
spread a bed of cement and sand of uniform density to the depth of one (i) 
inch and in the proportion of one cement and four sand. The cement and 
sand shall be thoroughly mixed dry in a mixer until a uniform color is 
obtained. 

The cement-sand bed shall be carefully shaped to a true cross section, 
parallel with the finished pavement, by means of a template covering at least 
*If local conditions justify, the depth of the brick may be made three and 
one-half (S/'i) or three (3) inches. 



796 SPECIFICATIONS 

one-half (H) of the width of the brick work, and so made as to be easily drawn 
over the curb or guide rails set to the proper elevation. The operation of 
shaping the cement-sand bed for the brick is considered of prime importance 
in securing the desired evenness in the surface of the finished pavement. 

Expansion Joints. — Expansion joints shall be placed parallel with and at 
each curb line and extend across each street and alley intersections. It 
should be one-half (}4) of an inch in width for streets less than twenty (20) 
feet wide; three-fourths (^i) of an inch for streets from twenty (20) to I 
thirty (30) feet wide, and one (i) inch in width for streets wider than thirty 
(30) feet. This joint must extend to the depth of the brick. 

A premolded or prepared bituminous strip which will be unafTected by the 
action of water and will remain pliable at all temperatures to which it may be 
subjected shall be used for this purpose. The material should be made into 
strips of suitable length and of the required depth and thickness and shall 
be placed in the pavement with the ends closely joined as the bricks are being 
laid. 

Delivery of Brick. — Before the grading is finished the brick shall be hauled 
and neatly piled without the curb line in sufficient quantities to complete 
the brick surface. Clamps or conveyors may be used in connection with 
this work, but the brick shall not be dumped from wagons nor shall they be 
thrown from wagons to piles, or from cars to wagons, nor shUl they be piled 
in any location^ where they are likely to become bespattered or covered with 
mud or otherwise injured, unless thoroughly protected. 

In delivering the brick from the piles for placement in the street, no wheel- 
ing in barrows will be allowed on the brick surface. The brick shall be so 
arranged and carried on a pallet, or conveyor, that when delivered to the 
dropper each brick, in the regular operation of placing upon the cement-sand 
bed as prepared, will naturally lie with the projections in the same direction 
and with the best edge uppermost. 

Brick Laying. — Upon the cement-sand bed as prepared^ the brick shall 
be immediately laid with the best edge up, the projections in one direction, 
and with the courses straight and at right angles to the center line of the 
pavement, except in the case of hillside brick which are to be laid parallel 
thereto. All joints must be broken at least three (3) inches; and the courses 
straightened by tapping lightly with a sledge on a four by four inch timber, 
three (3) feet in length, provided for that purpose. Nothing but whole brick 
shall be used except in starting and finishing courses, or in such cases as may 
be directed by the engineer. The cutting and trimming of the brick shall be 
done by experienced men. For closures, nothing less than three (3) inch 
bats shall be used; and the fractured ends laid towards the center of the 
pavement. Broken and chipped brick suitable for batting shall be used so 
far as practical in obtaining the necessary half brick for breaking courses 
and making closures, instead of breaking otherwise whole and sound brick. 
All brick when laid shall be clean and kept clean and entirely free from 
dirt or other foreign matter until the pavement is completed. AH the work 
of brick laying shall be done over the brick already laid. The disturbing of 
the prepared cement-sand bed is prohibited. As soon as any surplus of de- 
livery of brick is ascertained, they shall promptly be moved forward for use. 

After the brick have been laid, the chips shall be swept from the street, all 
soft brick removed, and those badly broken, badly spawled or misshapen 
shall be turned over or removed by the contractor. Brick slightly chipped 
on corners, otherwise good, shall be accepted. All rejected brick, suitable 
for batting in, shall be carried forward and used for that purpose; the 
remainder shall be placed in separate piles along the street. The inspector 
shall keep the brick culled and the contractor shall make the necessary 
changes and replacements so that the work at all times shall be ready for 
the grouting within fifty (50) feet of the brick laying. 

Rolling. — Immediately after the brick in the pavement have been inspected 
and the surface of the pavement swept clean, it shall be rolled with a self- 
propelling tandem roller, weighing approximately three (3) tons, in the 
following manner; the rolling will commence near the curb or edging line, at 
a slow pace and continue back and forth until the center of the pavement is 
reached, then pass to the opposite curb or edging line and repeat in the same 
manner to the center of the street. After the first passage of the roller the 
pace may be quickened. The pavement shall then be rolled transversely 
at an angle of forty-five (45) degrees; repeat the rolling in like manner in the 
opposite direction, then roll parallel with the curb or edging line until the 
surface is smooth, 



I 



METHODS 797 

Before this last rolling takes place all broken or injured brick must be 
taken up and replaced with acceptable ones. Portions of the pavement 
inaccessible to the roller shall be tamped to grade by the use of a hand tamper 
applied upon a two-inch plank. 

After the final rolling the surface shall be tested with a ten (lo) foot straight 
edge laid parallel with the center line of the pavement and any depressions 
exceeding one-quarter (M) of an inch shall be taken out. 

All brick laid shall be rolled ready for grouting at the end of the working 
day. 

Cement Grout Filler. — The cement grout used in filling the joints in the 
brick shall consist of one (i) part of cement and one and one-half (i}^i) parts 
of sand. 

The cement shall meet the requirements of the Standard Specifications for 
Portland Cement of the American Society for Testing Materials, adopted 
August i6th, 1909, with amendments and additions thereto adopted by said 
Society. 

The sand for the cement-sand bed and the grout filler shall be composed 
of clean, sharp, well graded quartz grains and shall not contain more than 
5 per cent, of clay or silt. The grains shall be such size' that all will pass a 
No. 12 sieve and that not more than 40 per cent, will i)ass a No. 50 sieve. 

As soon as the pavement is rolled and before the filler is applied the pave- 
ment shall be thoroughly saturated with water so as to insure the hardening 
of the cement-sand bed. 

The cement and sand for grouting in correct proportions shall be thor- 
oughly mixed dry until the mass assumes a uniform color. From this mix- 
ture a small batch not exceeding two cubic feet shall be placed in a suitable 
box or a machine especially adapted foi» that purpose. Slowly add water and 
thoroughly mix until the mixture is of such a consistency that it will readily 
flow into the joints without separation. Ample time must be taken in pre- 
paring this liquid mixture, first making a plastic mortar, then gradually 
thinning by mixing and slowly adding water; continue the mixing until all 
is removed and applied to the surface in small quantities. The application 
should be continued until the joints appear to be filled. ^ Any surplus material 
remaining on the bricks shall then be swept into the joints. Extreme care 
must be taken that the joints are not cemented over and that the filler extends 
down to the bottom of the brick. 

After the first coat has had a chance to settle and before the initial set 
develops, a second coat shall be applied in a similar manner with a somewhat 
thicker grout. After this application has had time to settle and before the 
initial set takes place, the pavement shall be finished to a smooth surface 
with a squeegee having a rubber edge which shall be worked over the brick 
at an angle with the joints — thus leaving them entirely filled. 

The contractor shall provide thin metal strips one-sixteenth (He) of an 
inch by six (6) inches by three (3) feet long and insert same in the brick 
joints across the street when closing up a stretch of grouting at work, intervals, 
so that the grouting will end in a vertical joint. These strips must be taken 
out when the grout becomes stiff and before the initial set. 

Protection of Filler. — After the surface has been thoroughly inspected 
and if approved, and sufficient time for setting has taken place so that a 
coating of sand or earth will not absorb any moisture from the cement mix- 
ture, the surface shall be covered with one (i) inch or more of sand or earth 
I to prevent too rapid drying of the filler. This shall be kept moist for at least 
four (4) days, and no traffic shall be allowed on the street for a period of at 
'least fifteen (15) days. 

Hillside Brick. — On grades when ordered by the engineer standard Wire- 
Cut Lug hillside brick shall be used. These brick shall in quality and test 
I conform to the requirements of these specifications. 

< The general method of constructing a Wire-Cut Lug hillside pavement shall 
'conform to the standard specifications, except that the bricks shall be laid 
I longitudinally instead of transversely. They shall be grouted in the manner 
ispecified for brick pavements except that all the grout in the surface grooves 
of the Wire-Cut Lug hillside brick shall be broomed out before it shall have 
.time to set up (care toeing taken not to disturb the grout in the longitudinal 
joints). This broommg should be done transversely with a rattan broom. 

Notes. — We strongly advise the use of a small mixer properly equipped 
for applying the grout. This mixer should be used for the first application, 
and a suitable box for the second application.' When boxes are used the 
I'grout shall be removed from same with scoop shovels. 
♦»-•■-•-.• - 



798 



SPECIFICATIONS 



Item 62 — Stone Block Pavement 

62.1. Under this item the Contractor shall furnish and place upon a 
properly prepared foundation Stone Block pavement of the quality specified 
below, where shown upon the plans or directed by the Engineer. 

The item will include the furnishing and placing of all the block, sand 
cushion, grout, expansion joints and all material, labor and other expenses 
incidental thereto but will not include the concrete foundation, edging, 
curbing, manholes, catch basins, etc., which will be paid for under the espe- 
cially designated items therefor. 

62.2. The dimensions of the blocks shall be as follows: Not less than six 
inches nor more than twelve inches long on top, not less than three and one- 
half inches nor more than four and one-half inches wide on top, and not less 
than four inches nor more than five inches deep. They shall be dressed so 
that after laying, no measurement of any joint shall show a width of more 
than one-half inch for a depth of one inch, or a width of more than one inch 
in any part of the joint. The head of the block shall be so cut that it shall 
not have a depression in it more than three-eighths inch deep, and the edges 
and corners must be full unchipped and unbroken. All blocks shall be 
sorted and laid in straight courses of uniform width and depth. 

62.3. The blocks shall be of stone of medium sized grain showing an even 
distribution of constituent material. ^ They shall be of uniform quality and 
texture, without seams, scales or disintegration, and free from an excess of 
mica or feldspar.^ They shall be made from rock which when tested in the 
Deval Rattler will show a "coefficient of wear" of more than 7 and less 
than 14. All blocks for any one contract shall be from the same quarry un- 
less otherwise directed. 

62.4. On the prepared foundation, sufficient clean Cushion Sand as de- 
scribed under "Materials of Construction" on page 719, shall be spread tc 
such a thickness that after the pavement has been thoroughly rammed or 
settled the sand under the block shall be nowhere less than one inch thick. 

On the sand cushion above specified, the blocks shall be set vertically on 
edge in close contact with each other, and in straight rows across the road 
at right angles to the curb, except at intersections, where the angle of the 
rows with the curb shall be varied to meet the conditions. Blocks in adjoin- 
ing rows shall be set to break joints not less than three inches. All blocks 
shall be set so that when thoroughly rammed or settled to a firm, unyielding 
bearing, they will then be true to lines, grades and cross-sections, and have 
no joints greater than the maximum allowable. All depressions or irregu- 
larities in the surface shall be corrected to the satisfaction of the Engineer. 
Only practiced and competent pavers shall be employed in laying the blocks. 

After the blocks are laid, sufficient approved clean gravel shall be sjjxead 
over the surface and swept into the joints so as to fill the latter to a depth 
of about two inches from the bottom. The blocks shall then be thoroughly 
rammed or rolled until firm, even and true to the lines, grades and cross- 
sections. ' _ ^ 

Approved expansion joints shall be provided along the curb as may be 
required and shall be filled with the same quality of filler as is specified for 
expansion joints in brick pavements. Portland cement grout mixed in pro- 
portions of one part cement and one part sand shall then be poured into the 
joints until the grout flushes to the surface of the pavement. The grout 
shall be broomed when required, and the pouring and brooming shall be 
continued until all the joints are thoroughly filled, and the grout is even with 
the highest part of any and all blocks. Sprinkling or otherwise wetting the 
blocks before grouting shall be done when atmospheric or other conditions 
require this precaution to be taken. 

62.5. After grouting shall have been completed and the grout shall have 
sufficiently hardened, a coating of suitable material about one inch deep 
shall be spread over the whole surface of the grouted pavement, and the 
road shall then be sprinkled with water. This covering shall be kept wet, 
and no travel of any kind shall be allowed on the completed pavement for 
at least seven days thereafter, nor until the grout shall have thoroughly set, i 
when the covering shall be completely removed. 

62.6. The quantity to be paid for under this item shall be the number of ■ 
square yards, including expansion joints, of pavement laid in accordance | 
with the plans and as directed by the engineer. 

The price bid shall include the furnishing and placing of all materials, the i 
spreading of sand cushion, and laying, ramming or rolling, grouting, surfac- I 
ing and all labor and incidental expenses necessary to complete the work. 



METHODS 799 

MEDINA SANDSTONE BLOCK PAVEMENT 

(City of Rochester, N. Y., Specifications, 1911) 
The grading, subwork, and curbs having been completed as herein speci- 
fied under the proper headings, the work of laying the concrete foundation 
and paving will then proceed. 

A concrete foundation six (6) inches thick, of Portland cement, as speci- 

, fied in the bidding sheet and shown in plans, will be laid in accordance with 

the specifications herein contained. The surface will be eight (8) inches 

below the finished pavement and parallel thereto, or sevenl(7) inches if a 

•five (5) inch block is specified. 

The surface to be kept wet until covered with sand, and, at least, thirty- 
six (36) hours shall be allowed for the concrete to set before the pavement is 
laid. When connection is to be made with any layer set, or partially set, the 
i edge of such layer must be broken down, shall be free from dust and properly 
i wet, so as to make the joints fresh and close. On this concrete foundation 
. shall be laid a bed of clean, sharp sand, perfectly free from moisture (made so 
c by artificial heat if deemed necessary), not less than one (i) inch thick, to 
; the depth necessary to bring the pavement and crosswalks to the proper 
grade when thoroughly rammed. 

Upon this bed of sand, the stone blocks and crosswalks must be laid. The 
; stone blocks are to be laid in straight courses at right angles with the line 
! of the street, except in intersections of streets, where the courses shall be 
: laid diagonally, and except in special cases, when they shall be laid at such 
= angle, with such crown and at such grade as the city engineer may direct. 

■ Each course of blocks shall be uniform in width and depth, and shall be 
gauged and selected for the pavers on the sidewalks, and so laid that all 

■ longitudinal joints or end joints shall be close joints and shall be broken by a lap 
1 of at least three inches, and that joints between courses shall not be more 
? than one-half inch in width. The blocks shall then be thoroughly rammed 

by courses at least three times by a rammer weighing not less than eighty 
! (80) pounds — no iron of any kind being allowed on its lower face to come in 
1 contact with the paving, and until brought to an unyielding bearing, with 

■ a uniform surface, true to the roadway on the established grade. The sur- 

■ face of the pavement thus completed must be even and smooth throughout 
\ and molded to conform to the wells of the surface sewers, street and alley 
i intersections, drainage details, and the grade lines established by the city 
: engineer. During the final ramming the pavement shall be tested with a 
: straight-edge and templet, and any unevenness must be taken out and made 

true to the required grade, level, and cross-section. 

If a paving pitch filler is used, the joints shall be filled with clean, dry, 
J hot gravel of proper size as herein specified, heated in pans especially pro- 
' vided for that purpose, and poured from cans having small spouts and thor- 
oughly settled in place with wire picks until the level of the gravel is at least 

• two inches below the top of the pavement. 

The gravel used between the blocks shall be of such size as will pass through 
5 a sieve having four meshes per square inch, and be retained on a sieve of 
\ sixty-four meshes per square inch, and must be screened when dry. 
■I There shall be immediately poured into the joints, while the gravel is hot, 
' boiling paving cement as hereinafter described, heated to a temperature of 

* 300° F. until the joints and all interstices of gravel filling are full and will 
: take no more, and are filled flush with the top of the blocks. Dry, hot gravel 
: must then be poured along the joints, filled with paving cement, as above 
j described. 

I The paving cement to be used in filling the joints as herein provided shall 
be a paving pitch of the best quality, of a brand that has been proved by 
)' actual use in pavements known to the city engineer to be best adapted to 
1 the purpose. It shall be delivered on the work in lots at least one week 
5 before using, in order that the necessary analysis and examination may be 
1 made by the city engineer. In addition to this the contractor must furnish 
i the city engineer with the certificate of the manufacturer or refiner that the 
I materials are of the kind specified. 

The city engineer may direct that a Portland cement grout filler may be 
i used in the joints instead of a paving pitch, in which case the pavement shall 
'be thoroughly sprinkled or washed with water before grouting. The grout 
shall be mixed with clean, sharp sand of approved quality, in the proportion 
' of one to one, the cement and sand to be thoroughly mixed together dry, 
j in a box, and then only a sufficient amount of water added to make the grout 
i of the proper fluidity when thoroughly stirred. 



8oo SPECIFICATIONS 

The grout shall be prepared only in small quantities at a time, and shall be 
stirred rapidly and constantly in the box and while being applied to the 
pavement, and no settlings or residue will be allowed to be used. 

The grout shall be transferred to the pavement in such a way as the engi- 
neer may think most advantageous and best for the work, and shall then 
be rapidly swept into the joints of the pavement with proper brooms. The 
stones shall be well wet as directed before the grout is applied, and the pour- 
ing must be continued until the joints remain full. 

All teams and traffic of any kind, except on planks, shall be rigidly pro- 
hibited on the pavement for ten days after the grout is applied, or until, in 
the opinion of the engineer, it has become thoroughly set and hardened, so 
that the bond will not be broken by traffic over the pavement. 

STANDARD SPECIFICATIONS FOR 
HIGHWAY BRIDGE CONSTRUCTION 



Series of 1917 

IOWA STATE HIGHWAY COMMISSION 

AMES, IOWA 

Section Three 

GENERAL CONSTRUCTION AND MATERIAL CLAUSES 

GENERAL INSTRUCTIONS 

1. Location and Alignment — The general location and elevation of the 
structure at the proposed site will be determined by the engineer, but the 
contractor shall assume full responsibility for the alignment, elevations and 
dimensions of each and all parts of the work and their mutual agreement. 

2. Excavation. — The depth of all foundations shall be shown on the 
accompanying drawings and the prices bid shall cover the total cost of foun- 
dations carried to the elevations shown. 

If directed by the engineer, the contractor shall carry the excavation 
deeper and this cost shall be covered as follows: 

For the first two feet or fraction thereof below elevation shown on the 
plans, the cost of excavation shall be included in the price bid per cubic 
yard for additional concrete placed below the elevation of bottom of foot- 
ings. For excavation carried below this depth, i.e., 2 feet below elevation 
of bottom of footings as shown on plans, the contractor shall be allowed actual 
cost plus ten per cent., in addition to the unit price bid for extra concret in 
foundations. 

If rock foundation is secured, the excavation shall be done in such a manner 
as to allow the rock to be exposed and prepared for receiving the concrete. 
All loose and disintegrated rock or thin strata shall be stripped to a clean 
bed acceptable to the engineer. 

3. Additional or* Less Concrete. — Additional concrete placed or concrete 
not placed shall be paid for at the prices stipulated in the form of tender. 
All costs of excavations are included in the price bid on additional concrete 
except as noted in Section 3, Paragraph 2. 

4. Inspection of Excavation Forms and Reinforcing. — After the excava- 
tion is completed the contractor shall notify the engineer who shall make an 
inspection of the depth and character of the foundation. No concrete shall 
be run or masonry placed until after the engineer has approved the depth 
and character of foundation material. 

After the forms are constructed and the reinforcing secured in place and 
before any concrete is run the contractor shall^ notify the engineer who shall . 
make an inspection of the forms and reinforcing. 

The county shall be responsible for all delays caused by the failure to 
make inspection after a twenty-four (24) hour notice has been given by the 
contractor or his authorized agent. 



BRIDGES 8oi 

5. Filling. — The contractor shall do no filling work around completed 
bridges or culverts without the permission of the engineer.^ If any filling 
is contemplated in this contract it shall be specifically provided for in the 
proposal. Specifications governing the manner of placing the filling around 
bridges and culverts will be found under the detailed specifications for that 
type of structure. 

It shall be the duty of the county engineer to report to the board of super- 
visors the actual cost of filling over or around bridges and culverts on the 
township road system. 

6. Removal of Present Structure.— Prices bid for each structure shall 
include the cost of removing any existing structure, but it is understood 
that the contractor may use during construction any material in such old 
structure that is not needed by the county for building a temporary crossing. 
Usable material shall not be cut or otherwise destroyed, and on completion 
of the work, the contractor shall pile this material in an accessible location 
as directed by the engineer. 

Concrete Masonry 

7. Concrete Measuring and Proportioning. — The proportions of the differ- 
ent classes of concrete shall be carefully secured by some method of measur- 
ing satisfactory to the engineer, the cement being measured as packed by the 
manufacturers and the aggregate loose. The use of bottomless boxes and 
square wheelbarrows of uniform size designed for this purpose, will be ac- 
cepted as satisfactory methods. 

8. Concrete Mixing and Placing. — All C9ncrete used under these specifica- 
tions shall be thoroughly mixed in a machine mixer of the batch type. The 
concrete shall be mixed continuously for a minimum of twelve (12) revolu- 
tions in a mixer having an approximate speed of 12 revolutions per minute. 
The plant shall be equipped and arranged to mix and place the concrete 
quickly and uniformly. Care shall be taken not to bulge the forms in placing 
concrete and all exposed faces shall be worked in some manner to bring a 
thick layer of mortar in contact with the forms. The consistency of the 
concrete shall be such that water will thoroughly flush the surface under 
tamping. 

All top surfaces of walls, abutments, girders, floors, copings and hand- 
railing shall be carefully tamped and trowelled to a smooth, even surface, 
and shall be protected while setting from the direct rays of the sun. 

Note. — One of the most important factors of good concrete is proper mixing 
and no deviation from the above requirements will be permitted except by 
written orders of the engineer. 

9. Hydrated Lime. — Where a dense or impervious concrete is desired 
the engineer may specify the use of not to exceed eight per cent (8%) (by 
weight of cement) of hydrated lime. The hydrated lime used shall conform 
to the requirements of the standard specifications of the American Society 
for Testing Materials. 

If hydrated lime is to be used the engineer shall specify in the instructions 
to bidders the portions of the work to which the hydrated lime is to be added. 

10. Concrete in Freezing Weather. — No concrete shall be laid in freezing 
weather without the permission of the engineer. For placing concrete 
during freezing weather, a suitable plant shall be established by the con- 
tractor subject to the approval of the engineer. The water, sand, gravel 
and crushed stone shall be heated and the concrete masonry protected as 
directed by the engineer. 

11. Curing Cement. — Careful attention shall be given by the contractor 
to the proper curing of the concrete. Handrails, floors, and trowelled 
surfaces shall be protected from the sun, and in dry, hot weather, the whole 
structure shall be kept damp for a period of one week. The floors on con- 
crete and steel bridges shall be covered with damp sand or other suitable 
material as soon as the concrete has taken its initial. set. Other precautions 
to insure thorough curing of the concrete shall be taken by the contractor as 
directed by the engineer. 

MATERIALS 

Concrete Materials 

12. Cement. — The cement shall be a standard Portland Cement of a 
brand approved by the engineer and shall conform to the standard specifica- 
tions of the American Society for Testing Materials, effective January i, 
191 7. If car load shipments are made, the engineer shall have at least 



8o2 



SPECIFICATIONS 



ten (lo) days after the cement is delivered to the work to make such tests as I 
he may think desirable before it is used. If the cement fails to pass the 1 
accelerated test for soundness, it may be held for the 28-day test. Care 
must be exercised in the storing and protection of the cement on the work, 
and any cement damaged by moisture or which fails to meet any of the above 
requirements, shall be rejected. 

13. Water. — Water used in concrete shall be fresh, clean and free from 
dirt and sewage or alkali and shall be used in such quantities as the engineer 
directs. 

14. Sand. — The sand shall consist of clean, siliceous grains uniformly 
graded in size, from finest particles up to a diameter passing a }''i" screen. It 
shall contain not more than two and one-half per cent. {2}i%) of clay by 
actual dry weight. 

Note. — If tested with water in a graduate the apparent clay content after 
one hour settlement shall not exceed seven (7 %) per cent. 

15. Screened Gravel. — Screened gravel shall be uniformly graded in size 
from grains rejected by a }i'' screen to those passing a iW screen for Class 
"A" and Class "C" concrete, and to those passing a 2>^" screen for Class 
"B" concrete. Any material containing shale, lumps, disintegrated or 
rotten boulders or clay exceeding two and one-half per cent. (2>^%) dry 
weight, shall be rejected, unless by washing a clean product can be produced. 

16. Unscreened Gravel. — Unscreened or pit-run gravel shall conform to 
the above requirements for sand and gravel as to size, cleanness, and quality. 
The engineer may permit the use of unscreened or pit-run gravel subject 
to frequent tests to determine the relative proportions of sand and pebbles. 
If unscreened gravel is used the proportions shall conform strictly to the 
requirements of each class of concrete specified. 

17. Crushed Stone. — All crushed stone shall be clean and hard showing a 
fine compact grain. The quality of crushed stone required will be met by , 
trap, quartzite or limestone, having a French coefficient of wear of not less | 
than 6. Stone dust or dirt appearing as a film covering the individual 
pieces, will cause rejection unless the stone is cleaned by washing. The 
crushed stone when delivered at the site shall be placed on planks or other 
suitable material to prevent its being mixed with dirt or other injuri9us 
substances. The crushed stone shall be placed in separate storage piles 
from the fine aggregate. 

Concrete Classes for Screened and Graded Aggregate 

18. Class "A'* Concrete. — i part cement; 2 parts sand; 4 parts crushed 
stone or screened pebbles passing i>^'' screen. 

19. Class "B'* Concrete. — i part cement; 2}4 parts sand; 5 parts crushed 
stone or screened pebbles passing a 2>^'' screen. . 

20. Class "C* or Thin Section Concrete. — i part cement; 2 parts sand; 
SH parts crushed stone or screened pebbles passing a ^i" screen. 

21. Hand Rail Concrete. — i part cement; 2}4 parts screened sand; or 
I part cement; iK parts sand; i^ parts crushed quartzite passmg a W 
screen. 

Quantities For One Yard Of Concrete Using Screened Material 

22. Approximate Quantities. — For ordinary materials, sand screened 
through a K^L screen and aggregate of size as specified in the various classes, 
the following are approximate quantities required per cubic yard of concrete: 



Kind 



Class "A". 



Class "B". 



Class "C" 



Hand Rail. 



Cement 



1.46 bbl. 



1.68 



2.84 " 



Sand 



0.44 cu. yd. 



0.46 



0.47 " 



Broken Stone 



0.89 cu. yd. 



0.83 " 



Note. — It shall be permissible for the engineer to slightly vary the above 
proportions of sand and aggregate for the different classes to secure a denser 
concrete with materials used. 



BRIDGES 



803 



Proportions and Quantities for Unscreened or Pit-run Gravel 
23. Proportion and Quantities for Unscreened Gravel. — If the engineer 
permits the use of unscreened or pit-run gravel frequent determination shall 
be made of the amount of sand passing 3. yi" screen and the concrete shall 
be proportioned by the following tables for the various classes of concrete 
as specified: 

Class "A" Concrete Pit-run Gravel. — 



24. 



CLASS A 



Sand Passing 
yi " Screen 


Proportions 


No. Barrels Cement per 
Cu. Yd. of Concrete 


Cement Pit-run Gravel 


42% 


I sk. to 4.50 cu. ft. 


1.50 bbl. 


45" I .. .. ^ QQ .. .. 


1.68 •♦ 


55" I .. .. 3 50 .. - 


1.90 " 


65" I " " 3 00 '• •' 


2.25 " 



(Not to exceed 65 % sand passing }ri" screen.) 
25. Class "B'* Concrete Pit-run Gravel. — 
CLASS B 



Sand Passing 
yi" Screen 


Proportions 


No. Barrels Cement per 
Cu. Yd. of Concrete 


Cement Pit-run Gravel 


42% 


I sk. to 5-5 cu. ft. 


1.22 bbl. 


45" 


I " " 50 •♦ " 


1.35 '* 


55" 


I •: '• 4.5" " 


1.50 " 


65" 


I " *' 4.0 " " 


1.68 " 



(Not to exceed 65 % sand passing yi," screen.) 
CLASS C 

26. Class "C" Concrete Pit-run Gravel. — Same as Class "A" for Un- 
screened Aggregate. 

27. Hand Stone. — In piers, _ abutments and bases of wing and retaining 
walls with sections two feet thick and over, it will be permissible to use hand 
stone. If used, the individual pieces shall be carefully placed not less than 
their own thickness apart nor less than 6" from any face of the concrete. 

28. Mortars. — All mortars shall be specified by classes, the same letters 
indicating the same proportion of sand to cement as in the classes of concrete. 
Par. 18 to Par, 21, Sec. three. 

Reinforcement Steel 

29. Reinforcement Steel. — All reinforcement steel required shall have 
net sectional areas, distribution and sizes as shown on the plans, and shall 
have a deformed section to provide a mechanical bond at frequent intervals 
between steel and concrete. ^ The steel shall meet the requirements of the 
standard specifications for billet steel concrete reinforcement bars adopted 
by the American Society for Testing Materials, 191 1, revised 1914, with the 
limitations that all steel shall be made by the open hearth process and all 



8o4 



SPECIFICATIONS 



bars shall be rolled from new billets of the structural steel or hard grade. 
Any form of bar will be approved for use under the specifications that pro- 
vides a net section equivalent to the net section of a plain, square bar of the 
size indicated on the drawing. 

All bars shall be free from rust, dirt, paint or grease, and shall present a 
clean, fresh surface when placed in the structure. Each bar shall be held 
rigidly to position by blocking to the forms and wiring to the bars at contact 
points,- In general, all reinforcement steel shall be placed securely in posi- 
tion before the concrete is run. 

In splicing bars a minimum lap of 24 diameters shall be used. 

Note. — Shop bent reinforcement shall preferably be used for slab and 
girder bridges. 

30. Structural Steel in Concrete. — All structural steel used for concrete 
reinforcement shall be designed to meet the requirements of Section eight. 

Forms 

31. Forms. — All forms and centerings shall be built of material sufficient 
in thickness and strength to hold the concrete without bulging between 
supports. Additional requirements for each particular class of work are 
specified under that class. 

Square corners shall be filleted and for all projections of the concrete the 
containing forms shall be given a bevel of \" per foot. Beveled forms shall 
be so framed as to increase the thickness of any such projections at their 
base, and to maintain as the minimum the dimensions shown on the plans. 

Piling 

32. Timber Foundation Piling. — Timber piling used in the foundation 
shall be cut from sound trees, shall be close-grained and solid and free from 
defects, such as injurious ring shakes, large, unsound or loose knots and 
decay, or other defects which will materially impair their strength or 
durability. 

Timber piling for foundations shall be of white, willow, burr or post oak, 
red cedar, western or white cedar, cypress, chestnut, tamarack, Douglas fir, 
long leaf southern pine, Norway pine, or any other wood that will satisfac- 
torily resist the blow of the hammer and is durable. 

Timber piles must be cut above the ground swell and have a uniform 
taper. A line drawn from the center of the butt to the center of the tip 
shall lie within the body of the pile. All knots must be trimmed close to the 
body of the pile, and all bark removed soon after cutting. 

For round piles the minimum diameter at the tip shall be 8" for all lengths. 
The minimum butt diameter for any pile shall be 10". All piling ordered 
by the engineer shall be in multiples of 2 foot lengths. 

Where used the piling shall be designed to carry the full load. To carry 
the safe load per pile the following formula shall be used: 

Safe load in lb. = ■ in which w = weight of hammer in pounds, 

h = fall in feet and s = average penetration in inches for the last three 
blows of the hammer. 

After driving the piling the tops shall be trimmed of all broomed wood. 
The minimum projection into the concrete shall be 12'' and the maximum 
projection 18". 

The price paid for piling shall be paid for the full length of the pile in the 
leads as ordered by the engineer or shown on the plans, and all piles required 
shall be ordered, number and length to be specified, within ten days after 
the contract is signed. 

Piling delivered to the site and not driven shall be taken over by the county 
at cost to the contractor, as shown by the original material and freight bills. 
This cost shall include the actual cost of the piling delivered to the bridge 
site plus any actual expense incurred by the contractor in delivering pile 
driving equipment to the bridge site. 

The total lineal feet of piling which is expected to be used with each 
bridge shall be used in comparing bids received. The right is reserved to 
make specific conditions for the furnishing and driving of piling for any 
particular bridge. 

The price bid for piling includes driving the piling to place in the founda- 
tion and no extras will be allowed above the price bid. The piling shall be 
driven to a *'good refusal" and to the satisfaction of the engineer. 



BRTDOES 805 

Section Four 
TYPES OF BRIDGES AND LOADINGS 

CLASSIFICATION 

These specifications outline the minimum requirements for ordinary per- 
manent highway bridges, such as are necessary generally outside the limits 
of the larger cities. One class only, Class A, is recognized throughout with 
the single exception of the Class B loading for wood floors on permanent 
steel bridges. 

If any structures are to be built under these specifications to provide for 
heavy city traffic, street car or interurban loadings, the standard loadings 
as set forth herein are not applicable, and special specifications will be sup- 
plied by the Commission to meet these requirements on application of the 
board or engineer. 

Bridges erected over drainage ditches shall, where necessary, be so con- 
structed as to allow the superstructure to be removed for cleaning said 
ditches with as little damage to the removal and_ permanent parts of said 
bridge as practicable. The county engineer shall in all cases determine the 
necessity of making provision for such construction. 

Types of Bridges 

I. Steel Bridges. — These standard specifications have reference to the 
following types of bridges: 

Steel I-beams Spans up to 32 ft. in length. 

Plate Girder Spans, 20 ft. to 80 ft. 

Pony Truss Spans, riveted, 30 ft. to 100 ft. 

High Truss Spans, 100 ft. and over, riveted up to 140 ft. 

a. Reinforced Concrete Bridges and Culverts. — 

Box Culverts up to 16 ft. span. 

Slab Bridges from 14 ft. to 25 ft. span. 

Arch Bridges and Culverts, 6 ft. span and over. 

Girder Bridges from 24 ft. to 40 ft. spans. 

3. Other Types of Culverts. — These specifications do not apply to various 
types of small culverts such as circular concrete culverts, vitrified pipe tile, 
corrugated iron, boiler iron or reinforced concrete pipe. Detailed specifica- 
tions are prepared for each of these types. 

4. Standard Plans. — Standard plans of the State Highway Commission 
are drawn in accordance with these standard specifications and are designed 
to interpret the minimum requirements herein stipulated. ^ These plans will 
be supplied to all county engineers and special and detailed plans will be 
supplied by the Commission on request of county engineers and county 
supervisors without cost to the county. 

Loadings 

5. Dead Loadings. — Plans submitted under these specifications shall pro- 
vide for the following loadings: 

Dead Loadings: 

The dead loading includes the weight of structure, floor and filling, 
using the following unit weights: 

Earth filling 120 lb. per cu. ft. 

Concrete 150 " 

Brick 150 " " " '* 

Timber — Untreated sH " " ft. B. M. 

Timber — Treated 5 ' " '* 

6. Loadings for Steel Trusses. — Uniform Live Load: 

Not less than 100 lb. per sq. ft. for spans up to 50' 

90 " " " '* " " 50' " " 100' 

80 " " " " " " , 100' *' " 150' 

70 " " '■ * * " 150' " " 200' 

60 " " •' " " " 200' •' '* 250' 

Note. — Decrease 0.2 lb. for each increase of i ft. in length down to mini- 
mum of 50 lb. per sq. ft. 

Uniform Live Load for Sidewalks: 50 lb. per sq. ft. 



8o6 SPECIFICATIONS 

Class "A'* Floors and Sidewalks 

7. Loadings for Floors on Steel Bridges. — Uniform Live Load: 100 lb. per 
sq. ft. 

Concentrated Live Load: For Class "A" floors the minimum concen- 
trated live load shall be a fifteen ton traction engine distributed as follows: 

10,000 lb. on front wheels. 

20,000 lb. on back wheels. 

Distance between front and rear axle, 11' o''. 

Distance center to center of back wheels, 6' o''. 

Width of back wheels, 22". 

For concrete floors on steel bridges without joists the above wheel loading 
is to be distributed 4' longitudinally and 4' transversely. 

For concrete floors on steel bridges with joists }ri of a wheel loading as 
above is to be distributed to each joist. 

The above loadings shall be so placed as to produce maximum stresses in 
joists and floor beams. Diagrams for distribution of this loading are shown 
on the standard plans of the High way Commission for truss spans. 

Uniform live load for sidewalks, stringers and brackets 75 lb. per square 
foot. 

Class "B'* Floors 

Uniform Live Load: 100 lb. per square foot. 

Concentrated Live Load: The minimum concentrated live load for Class 
"B" floors shall be a ten ton traction engine having the distribution of 
loadings directly proportionate to that specified for the 15 ton engine loading. 
This loading is to be applied only to the floors of steel bridges and may be 
used only on the township road system, or for temporary use with wood 
joists and wood flooring on steel trusses for the county road system. The 
distribution of each wheel load on the joists shall be 50% to the joist directly 
under the wheel and 25 % to the joists on either side. 

8. Wind Loadings. — Wind and lateral forces on steel spans shall be as- 
sumed as 150 lb. per lineal foot of span on the unloaded chord and 300 lb. 
per lineal foot of span on the loaded chord, all loads to be considered as 
moving. For the towers of steel viaducts the wind and lateral forces shall 
be assumed as follows: 30 lb. per square foot on one and one-half times the 
vertical projection of the girders, 100 lb. per foot of vertical height of bent, 
and a load of 100 lb. per lineal foot of span applied 4' 6" above grade. 

9. Loadings for Concrete Girders, Slabs and Floors. — Dead Loading: As 
specified in Paragraph five. 

Uniform Live Load: 100 lb. per square foot of roadway and sidewalk 
surface. 

Concentrated Live Load: Minimum concentrated load consisting of a 15 
ton traction engine. For heavy slabs the distribution is to be as follows: 

20,000 lb. on rear wheels. 

10,000 lb. on front wheels. 

11' o" between axles. 

6' o" center to center of back wheels. 

Width of wheels, 22". 

Each back wheel load is assumed to be distributed 6' 0'' transversely and 
5' o" longitudinally. For thin slabs on girders the same wheel load is 
assumed to be distributed 4' o" longitudinally and 4' 0'' transversely. 

Typical detail drawings of concrete floors, slabs and girders will be supplied 
by the Commission to indicate the requirements of these specifications. 

10. Loadings for Concrete Arches. — Dead Loading: As specified in para- 
graph 5. 

Uniform Live Load: 100 lb. per square foot over roadways and sidewalk 
surfaces. 

Concentrated Live Load: Fifteen ton traction engine so placed as to iDro- 
duce in combination with the dead load stresses maximum stresses in the 
arch rings. 

Allowance for temperature: Concrete arch bridges shall be designed to 
provide for stresses induced by a temperature range of 80 degrees F. 

Contractor's Plans 

11. Contractor's Plans. — All plans submitted under these specifications 
shall be in sufficient detail to show amount, kind, sizes and quality of mate- 
rial and type of construction to be used. They shall specify the amount of 
waterways and depth of foundation below low water. 



BRIDGES 



807 



Note. — For all bridges for which plans are prepared by the contractor the 
engineer shall supply as a basis for the design a profile of the steam crossing, 
showing foundation soundings, grade line of finished roadway, waterway 
required, and such other information as necessary to define accurately the 
structure required. 

Section Five 
BOX CULVERTS, SLAB AND GIRDER BRIDGES 

1. Standard PJans. — Standard plans for concrete box culverts, slab 
and girder bridges will be furnished by the Commission to the county 
boards and engineers to supplement and interpret requirements of these 
specifications. 

2. Roadways — County Road System. — For bridges of the above types 
ample roadway should be provided. The following table gives the recom- 
mended minimum width of roadway for average conditions of traffic, but 
these widths shotild be increased inside of corporations or where traffic is 
unusually heavy. The minimum legal width of roadway is also specified. 
These widths refer to the minimum width of finished roadway. ^ 

Side slopes are to be figured at one vertical to i^ horizontal in determin- 
ing the length of culverts and bridges under fills. The width of roadway 
for each specified structure shall be as specified on the plans. 

Roadways for County Road Systems 



Type 


Span 


Recommended 

Minimum Width 

of Roadway 


Minimum 
Legal Width 
of Roadway 


Box culverts 


2' to 16'' 


24'-0" 


2o'-o'' 




Slab bridges 


16' to 25" 


20'-0" 


i6'-o'' 




Girder bridges 


16' to do" 


2o'-o" ' i6'-o" 1 








1 



3. Roadways — Township Road System. — For roadways of culverts and 
bridges of above type on township road system, the recommended minimum 
width is shown in the following table, also the minimum legal width. For 
roads which are at present included in the township road system but which 
will later be included in the county road system, and which now carry large 
traffic, the width of roadways given under the county road system should 
apply. 

Roadways for Township Road Systems 



Type 


Span 


Recommended 

Minimum Width 

of Roadway 


Minimum 
Legal Width 
of Roadway 


Box culverts 


2' to 16" 


2o'-o''' 


20'-0" 




Slab bridges 


Over 16' 


i8'-o" 


i6'-o" 




Girder bridges 


All spans 


l8'-0" tA' r^K 1 









4. Design and Loadings. — In general the dimensions shown on the stand- 
ard plans of the Commission are minimum for each size and type of struc- 
ture. The loadings shall be as specified in Section Four. 

5.' Permissible Stresses. — The stresses used in -designing slab and girder 
bridges shall not exceed the following; 



8o8 SPECIFICATTONS 

Concrete in compression 600 lb. per sq. in. 

Concrete in tension ^ \\ '* ** \[ 

Concrete in shear 1 00 ' 

(Diagonal tension, reinforced members) 

Steel in tension 16,000 lb. per sq. in. 

Steel in compression 15 times the surrounding concrete. 

6. Footings. — Footings shall be carried down below the stream bed a 
minimum distance of 4 feet to a stiff clay or harder foundation, except for 
spans under ,16 feet which may be built without footings but with a heavily 
reinforced floor distributing the pressure on the foundatien. The floor or 
footings of slab culverts under heavy fills, shall be designed to distribute the 
pressure the full length of the foundations by longitudinal reinforcing. The 
foundation pressure for ordinary soils shall not exceed two (2) tons per square 

Depth of footings shown on the standard plans of the Commission should 
be increased or decreased to reach a firm foundation satisfactory to the 
engineer. For drainage ditches on very flat grades which will fill, the top 
of the footings may be made level with the grade line of the ditch. Curtain 
walls should be used at each end of the floor, and in streams having a swift 
current or subject to heavy floods the floors should be continued to the end 
of the wings on the down'stream side and a curtain wall placed across the 
end of this paving. ... , 1, , -i- j • o x- 

Compensation for extra depth of footings shall be as specified m bection 

' After the excavation is completed no concrete shall be run in the footings 
of abutments or piers until the engineer has approved the depth of excava- 
tion and the character of the foundation. . ^ , r ■ 

7. Piling. — If a suitable foundation is not found for the footings 4 feet 
below the dry weather surface of the stream, piling shall be used, driven 3 
feet centers. The top of the piles shall project not less than 12 inches nor 
more than 18 inches into the concrete after all damaged wood has been cut 
off. Where piling are used they shall carry the full load. 

Safe load on piling shall be figured as specified m Section 3, Paragraph 32. 

For all concrete bridges 25-foot span and above for which rock foundation 
is not available the use of wood piling under the footings is recommended 
to insure permanency. ^ , , n . 1 j x 1 xi. 

8. Reinforcement. — The reinforcing steel shall be placed not less than 
one (i) inch from any outside surface and shall be held m place, as shown in 
the plans, by blocking from the forms and wiring to other reinforcement at 
contact points. For the bending required in either slab or girder reinforce- 
ment, shop bending is preferable. The contractor shall be held responsible 
for accurately placing the steel in the position and true to the shape required 
on the plans. All the reinforcing in slabs and girders shall be placed, spaced 
and secured in position before the concrete is run. All slabs shall be well 
reinforced transversely as well as longitudinally. Stirrups shall be used in 
girder bridges to carry the shear. For material see Section 3. Paragraph 29. 

9. Concrete in Slab Bridges. — The following classes of concrete shall be 
used in slab bridges: .. a »♦ 

Abutments, wingwalls and slabs — Class A. 

Hand rail — hand rail concrete. .... , 

Concrete shall be placed in the abutments m uniform layers across the 
length of each abutment, care being taken to secure a good bond between 
the' footings and the abutment wall. A full longitudinal section of the 
floor slab shall be run continuously, any unavoidable joints being made m 
a longitudinal direction. ^, . „ . , - x v n 

10. Concrete in Girder Bndges. — The following classes of concrete shall 
be used in girder bridges: ^^ 

Abutments, wingwalls, girders and floor — Class A. 

Hand rail — ^hand rail concrete. , . , x 

Each girder shall be concreted in a continuous operation, the concrete 
being placed in layers along the length of the girders. The contractor shall 
provide adequate equipment to insure the completion of each superstructure 
within ten hours after the first concrete is placed 

1 1. Forms. — Forms for girders and slabs shall be built tight to allow the 
use of a wet mixture. Water in excess shall not be used. The forms for all 
exposed faces of the concrete shall be dressed smoothly and evenly. 



BRIDGES 809 

In general piling shall be driven to support the forms for all girder bridges 
rigidly in position while the concrete is being poured. If appreciable 
settlement occurs in the forms, the engineer shall stop the work and require 
a thorough remodeling to insure without question a completed product 
true to line and grade as shown on the plans. 

To insure a first-class finish, the forms shall be painted with linseed oil 
or some other means taken to prevent the concrete from adhering to the 
lumber, and all form lumber used the second time shall be cleaned, and 
warped or bulged surfaces resized. The sharp angles in the forms shall 
be filled to prevent thin or sharp comers in the concrete. 

12. Hand Railing. — The prices bid shall be on the form shown on the 
plans, but the contractor may submit alternate designs and bids. 

13. Expansion Joints. — Expansion joints shall be left between the abut- 
ments and floor slabs or girders. The details of these expansion joints shall 
be as shown on the standard plans of the commission for each type. 

14. Name Plate. — On important bridges the contractor shall furnish and 
set a name plate of design acceptable to the engineer. 

15. Camber. — All single span girder and slab bridges shall be given a 
permanent camber equal to J^o iT^ch per foot of clear span. Bridges of two 
or more spans shall be given a camber at the center not less than ^^0 i^ch 
per foot of structure. 

16. Finishing and Curing. — The tops of all accessible surfaces shall be 
trowelled to a smooth finish using a richer mortar for this purpose if necessary 
to produce a smooth finish. All fresh concrete shall be protected from the 
direct rays of the sun, and shall be kept damp for at least one week following 
placing. The contractor shall follow the directions of the engineer, and 
shall provide such means as he directs to insure a thoroughly cured product. 

17. Removal of Forms. — The forms under box culverts 8' X 8' and larger 
slabs, and girders shall remain in place in warm weather not less than three 
weeks and in cold weather at the discretion of the engineer. On box culverts 
having a clear span of less than 8 feet the forms shall remain in place for a 
period of ten days after the concrete in the top slab is poured. 

As soon as forms are removed all rough places or holes _ shall be filled 
with mortar of the same grade as the concrete used, and if necessary to 
insure its uniform appearance of smoothness a fresh coat of i to i mortar 
shall be applied to the entire outside surface of the structure. _ This shall 
be done by the contractor at the direction of the engineer, without extra 
compensation, as it is the intent^ of these specifications to provide for 
material and workmanship that will produce a first-class quality of con- 
crete and a smooth neat appearance, and every precaution shall be taken by 
the contractor to insure such. 

18. Drainage of Floors. — Floors on slab and girder bridges shall be drained 
where necessary by tile drains and the top sloped toward these drains. The 
drainage from floors shall preferably be carried off through drain pipes in 
the floors. 

19. Sidewalks. — Sidewalks where built shall conform to the requirements 
; of the incorporation in which they are built. Dimensions and details shall 
' be shown on the plans. 

20. Filling. — Unless specifically provided in the contract it is understood 
that the contractor will do no filling over structures of the above type. The 
earth fill shall be placed under direction of the engineer, and shall be carried 

; against all walls in horizontal layers avoiding wedge-shaped sections of 
\ earth against side walls or wings. The fill shall not exceed the depth speci- 
fied on the plans, and shall not be placed over box culverts until the concrete 
has been in place ten days. 

Fop the floor of deck and through girders and slab bridges which carry a 
light fill, a bituminous floor covering is recommended, as specified in Section 
8, Paragraph 82. If used, specific provision shall be made for such floors 
in the contract. 

21. Wearing Surface. — All concrete floors on slabs and girders not covered 
'with a bituminous surface shall be finished with a one-half inch (3^'0 wearing 

surface of i to i mortar. ^ Immediately after the concrete floor has been 
poured to the required thickness and before the concrete has reached its 
initial set the entire top surface of the floor shall be covered with a i to i 
wearing surface of sand and cement. This mortar coat shall be rubbed in 
and finished with a heavy wood float in such a manner as to provide a 
smooth even wearing surface. 



8io 



SPECIFICATIONS 



Section Six 
CONCRETE ARCHES 

I. Roadways — County Road System. — For bridges of the above types 
ample roadway should be provided. The following table gives the recom- 
mended minimum width of roadway for average conditions of traffic, but 
this width should be increased inside of corporations or where traffic is 
unusually heavy. The minimum legal width of roadway is also specified. 
These widths refer to the minimum width of finished roadway. 

Side slopes are to be figured at i vertical to i3^ horizontal in determining 
the length of culverts and bridges under fills. The width of roadway for 
each specified structure shall be as specified on the plans. 





Roadways for 


County Road Systems 


Type 


Span 


Recommended 
Minimum Width 


Minimum Legal 
Width 


Arch culverts 

Bridges 


Up to i6' 
Above 1 6' 


24'-o" 

20'-0'' 


20'-0" 

i6'-o" 







2. Roadways — Township Road System. — For roadways of culverts and 
bridges of above type on township road system, the recommended minimum 
width is shown in the following table, also the minimum legal width. For 
roads which are at present included in the township road system but which 
will later be included in the county road system, and which now carry large 
traffic, the width of roadways given under the county road system should 
apply. 

Roadways for Township Road Systems 



Type 


Span 


Recommended 
Minimum Width 


Minimum Legal 
Width 


Arch culverts 

Bridges 


Up to 1 6' 
Above i6' 


2o'-o" 
i8'-o'' 


20'-0" 

i6'-o'' 





In general, specific plans in accordance with these specifications will be 
furnished for arch designs by the Commission on request of the engineer 
or board. 

3. Design and Loadings. — In all designs the dimensions of concrete and 
areas of steel at each point shall be proportioned to carry the loadings in- 
cluding the temperature stresses as specified in Paragraph lo, Section 4. 

4. Permissible Stresses. — The materials used shall not be stressed above 
the following units: 

Concrete in compression — 600 lb. per sq. in. 
Concrete in tension — o lb. per sq. in. 
Steel in tension — 16,000 lb. per sq. in. 
Steel in compression — 15 times surrounding concrete. 

For arch rings, with temperature stresses included, the following units 
may be used: 

Concrete in compression — 750 lb. per sq. in. 
Steel in tension — 20,000 lb. per sq. in. 

5. Piling.- — If a suitable foundation is not found for the footings 5 feet 
below the bed of the stream, piling may be used. The top of the piles shall 
project not less than 12 inches or more than 18 inches into the concrete after 
all damaged wood has been cut off. 

Piling if used, shall take the full load, spacing to be determined by the 
formula in Section 3, Paragraph 32. In no case shall the maximum load on 
any single pile exceed twenty tons. 

Foundations on piling shall preferably be enclosed by permanent water- 
tight sheet piling with the tops sawed off about i foot below low water. 

If the engineer orders sheet piling to be left in place, the contractor 
shall be compensated at the unit prices bid for sheet piling placed per- 
manently. If sheet piling is to be left in place permanently bids shall be | 



BRIDGES 8il 

taken on the estimated number of square feet of such piling required, and 
settlement made on this basis. 

Footings for arch culverts under 1 6-foot span may be carried down to solid 
foundation or may be reinforced slab floor with curtain walls at one or 
both ends. Abutments for arch bridge over 1 6-foot span shall be carried 
down a minimum depth of 4 feet below bed of stream at its lowest point. 
Tiers shall be carried a minimum depth of 6 feet below the bed of the stream. 

6. Abutments and Footings. — Allowable pressure under piers and abut- 
ments shall not exceed the following units: 

Clay, sandy clay — 2 tons per sq. ft. 

Sand or gravel, confined — 2 tons per sq. ft. 

Cemented gravel — 5 tons per sq. ft. 

Rock cleaned to solid bed — up to 25 tons per sq. ft. 

The floors of arch culverts shall be protected by curtain walls at either 
end and in streams having a swift current, or subject to heavy floods, the 
paving shall be carried to the end of the wing walls at the downstream 
side and protected with a curtain wall at the extreme end. 

Extra depth of excavation shall be paid for as specified in Section 3, Para- 
graph 2. After the excavation is completed no concrete shall be run in the 
footings of abutments or piers until the engineer has approved the depth of 
excavation and the character of the foundation. 

7. Concrete in Arch Bridges. — The following classes of concrete shall be 
used in arch bridges: 

For arch ring^Class "A" concrete. 
For spandrel walls — Class "A" concrete. 

For abutments and piers below springing — Class "A" concrete. 
For hand rails including all concrete placed above spandrels — hand 
rail concrete. 

Hand stone may be used in abutments, piers and gravity sections. 

8. Steel Reinforcement. — Steel reinforcement shall be of the quality 
required in Section 3, Paragraph 29, and shall conform to the detailed 
requirements of the plans as to size, net areas, bending and position. 

Each rod shall be :placed and secured in position before the concrete is 
run. Preferably small concrete blocks ^ shall be used under the steel to 
block from forms. The concrete covering shall not be less than i inch. 
The area of metal at the crown shall not be less than ^i of i % . 

Arch reinforcement shall be of the double and preferably of the sym- 
metrical type and there shall be at each point in the arch ring a sufficient 
area of steel to take all the tension, on the assumption that the concrete 
takes no tension. 

9. Forms. — Forms for arch bridges shall be built tight and surfaces of all 
exposed faces dressed smoothly and evenly. Some adequate means shall be 
taken to insure non-adhesion of the concrete. Lumber used the second 
time shall be cleaned and resized, if necessary, to insure plane surfaces. 
Square comers shall be filled. 

The contractor shall obtain the approval of the Commission on his cen- 
tering plans before the work is started. 

10. Removal of Forms.^ — The forms under arches shall be left in place a 
minimum of three weeks in warm weather and in cold weather for a length 
of time as directed by the engineer. The hand rail shall be built after the 
forms have been lowered sufficiently to allow the arch ring to take the 
dead load. 

11. Expansion Joints. — Expansion joints shall be left in the spandrels and 
hand rail including the base. The minimum number of expansion joints 
for spandrels shall be three (3) for arches under 50 ft. span and five (s) for 
arches above 50 ft. in span. Unless otherwise provided, these shall consist 
of tongue and groove joints thoroughly waterproofed. 

12. Drainage and Waterproofing. — The top of the arch ring and lower 
six inches of the inside surface of the spandrel walls shall be brought to a 
reasonably smooth surface with a coating of rich cement _ mortar, then 
thoroughly covered with a neat cement grout or hot bituminous coating. 
The method and materials shall be subject to the approval of the en^neer. 
Drainage shall be provided for the back of the arch at each pier and abut- 
ment by pipe drains. 

13. Paving and Aprons. — Paving if used in the bed of the stream, shall 
be not less than nine (9) inches in thickness and the bottom shall be at least 
two (2) feet below the bed of the stream. Nine (9) inch aprons shall extend 
two (2) feet below the top of pavement on both upper and lower sides. 



8l2 SPECIFICATIONS 

14. Hand Rail. — The prices bid shall be of the form and dimensions shown 
on the plans submitted but the contractor may submit alternate bids and 
designs. 

15. Name Plate. — For the large bridges a name plate of design approved 
by the engineer shall be furnished and set by the contractor. 

16. Sidewalks and Lighting. — Sidewalks where built shall conform to the 
requirements of the incorporation in which they are built. Dimensions 
and details shall be shown on the plans. Details of lighting and wiring 
shall be clearly specified on the plans and in the instructions to bidders. 

17. Filling. — Unless otherwise specified in the contract, the board will 
do the filling. Care should be taken not to fill against green concrete and 
to load the arch or arches at each end simultaneously. The filling shall be 
done in horizontal layers, avoiding wedge shaped sections of loose earth or 
other material against spandrels, wings, and abutments. 

Section Seven 
SUBSTRUCTURES AND FOUNDATIONS 

CONCRETE PIERS AND ABUTMENTS 

Standard plans will be furnished by the Commission showing in detail the 
minimum requirements of the various types of abutments here specified. 

1. Standard Plans and Design. — The design may be of either the rein- 
forced cantilever, counterforted or gravity section capable of resisting the 
over- turning action of the earth and the impact of ice jams or floating dibris. 
In either design steel shall be used at all points where tension may be de- 
veloped. Full dimensions and details shall be shown on accompanying 
drawings. The clearance shall be at least 2 inches between the parapet 
wall and the edge of the shoes or bearing plates. 

2. Special Designs. — Special designs or those calling for the use of steel 
piling, pedestals, or other constructions not included in the above types 
or not approved under these specifications will be approved by the Com- 
mission only for special cases for which the detailed plans are submitted. 

3. Permissible Stresses. — Steel in tension — 16,000 lb. per sq. in. 
Concrete in compression — 500 lb. per sq. ft. 

Bearing on masonry bridge seats — 400 lb. per sq in. 

4. Piling. — Where foundations acceptable to the board and engineer can 
not be obtained 4 feet below the bed of the stream, piling may be used. 
The number and spacing of the piling shall be determined by the formula in 
Section 3, Paragraph 32. In general the spacing shall not exceed 3' o" 
center to center. If piling can be driven, its use is recommended under all 
important structures. 

After driving the tops shall be trimmed of all broomed wood. The mini- 
mum projection into the concrete shall be 12 inches but the tops of the 
piling may be left at varying elevations from 12 to 18 inches. 

5. Footings. — The footings shall extend a rninimum distance of 4 feet 
below the bed of the stream and shall be carried to a firm foundation or 
placed on piling. 

For excavation carried below the elevations as shown on the plans the 
contractor shall be compensated as provided in Section 3, Paragraph 2. 

Before any concrete is placed in footings of piers or abutments, the engineer 
shall approve the depth of excavation and character of foundations. 

6. Reinforcement. — In cantilevered, counterforted or other reinforced 
abutments, the reinforcement shall be placed and secured in position before 
the concrete is run. Care shall be taken to secure thoroughly ends of all 
rods as shown on plans. 

All reinforcement steel used shall conform to the requirements of Section 
3, Paragraph 29. 

7. Concrete in Reinforced Abutments and Wing "Walls. — For reinforced 
abutments and wings, Class "A" concrete shall be used throughout. The 
concrete shall be carried up in horizontal layers full length of abutments 
and wings. 

8. Concrete in Gravity Abutments and Piers. — For gravity sections 
the following classes shall be used: 

Body of piers and abutments — Class "B." 
Coping — Class "A." 

Hand stone may be used and concrete must be carried up in horizontal 
layers. 



BRIDGES 813 

9. Joints. — If the forms are not entirely filled before the cement sets 
and there are no reinforcing rods projecting, hand stone shall be one-half 
imbedded to form a bond for the new concrete. The stones shall be carefully- 
placed with their beds parallel to flow of stream. 

10. Cofferdam. — Pumping will not be permitted from the inside of 
foundation forms while concrete is being placed, and if necessary to prevent 
flooding, a seal of concrete shall be placed through a closed chute and allowed 
to set. Concrete shall not he placed in running water and shall only be 
placed in still water with suitable appliances and under the direction of the 
engineer. 

The inside dimensions of the cofferdam shall be sufficiently large to give 
easy access to all parts of the foundation forms. For underwater work a 
suitable cofferdam shall be provided. 

11. Forms. — Forms for all exposed faces shall be preferably of T & G 
lumber, sized and carefully fitted by competent workmen. 

Thickness of lumber, spacing of studding, bolting, wiring and external 
braces shall be sufficiently strong to produce plane- surfaces on all exposed 
faces and to protect green concrete from the sudden rising of the stream. 

12. Pier Anchorage. — Where rock foundations are secured for piers the 
footings shall be carried not less than 6 inches into solid rock to secure 
anchorage or anchor rods not less than 2 inches in diameter and 6 feet long 
shall be set as shown on accompanying plans. 

13. Ice Breaker. — On piers built in streams carrying heavy ice, an ice 
breaker with 'not less than an 8" X 8" X K" angle or a Tee rail embedded 
for cutting edge, shall be provided. 

14. Protection Railing. — The contractor for the sub-structure shall 
furnish and install the 2-inch gas pipe protection railing placed on the wings 
of abutments for steel truss bridges. 

15. Drainage. — Adequate drainage for the backs of abutments and wings 
shall be provided by tile or pipe drains through the face of the abutments 
at the ground line. 

16. Setting Bed Plates. — Bed plates shall be accurately set to position 
and elevation in Class "A" mortar, which shall be allowed not less than 
forty-eight hours in which to harden. 

17. Placing of Superstructure. — The weight of the superstructure shall 
not be placed on concrete piers or abutments until, within the judgment of 
the engineer, the concrete shall be sufficiently set to receive the super- 
structure without injury to the concrete. 

18. Filling. — Unless otherwise provided in the contract, all of the filling 
back of abutments shall be done by the board. The concrete shall be 
allowed reasonable time to set and the fill shall be carried up in horizontal 
layers, well tamped. The slope of the old surface back of the abutments 
shall be destroyed by steppings. All p9ssible care shall be taken to prevent 
a saturated wedge of the earth fill settling against abutments or wings. 

19. Special Designs and Details. — Special designs and details shall be 
clearly shown on general and detailed drawings. The depth and kind of 
foundations shall be specified. 

Tubular Steel Piers 

20. Tubular Steel Piers. — The minimum diameter of steel tubes used for 
piers shall be 30 inches and minimum thickness of material shall be ^ inch. 
Each pair of tubes shall be rigidly connected by a web extending from the 
top to within two feet of low water and braced by pairs of angles, at the 
top and bottom of the web and intermediate splices. 

Tubular piers shall not be used for abutments, and shall not be used in 
any case without consent and approval of the engineer. 

Class "B" concrete shall be used for filling. The size, weight, depth of 
foundation and number of piling must be shown on the drawings. 

Section Eight 

STEEL SUPERSTRUCTURES 

General Design 
I. Types and Loadings. — The types of bridges and loadings shall be as 
specified in Section 4. 

■ 2. Dimensions. — In these specifications, the following dimensions obtain: 
• Span of Girders, distance center to center of bearings. 



8i4 



SPECIFICATIONS 



Span of Trusses, distance center- to center of pedestals, or end pins. 
Span of Floor Beams, distance center to center of girders or trusses. 
Span of J oists, distance center to center of floor beams (one panel length.) 
Depth of Girders, distance between centers of gravity of flanges. 
Depth of Trusses, distance between center of gravity of chords or between 
pin centers. 

3. Masonry Layout. — The masonry layout shall be provided by the con- 
tractor for the superstructure within fifteen days after the contract becomes 
effective. This shall be in sufficient detail to show the position and elevation 
of all bed plates and anchor bolts. 

4. Clearance. — On a straight line, the clear height of through bridges shall 
- not be less than 15 feet above the floor for a distance of s^r^ feet on each side 

of center line of roadway. The clear width between trusses for a height 
of 10 feet above the floor shall be not less than the nominal roadway which 
in no case is to be less than 16 feet. 

5. Permissible Stresses in Metal. — All parts of the structure shall be so 
proportioned that the sum of the maximum stress shall not exceed the 
following amounts in pounds per square inch except as modified in Para- 
graphs 8 to II. 

For Steel 
Axial tension on net section — 16,000. 
Axial compression on gross section — 16,000 — 70 — 

Where "1" is the unsupported length of the member in inches and "r" is 
the least radius of gyration in inches. 

Bending: on extreme fibers of rolled shapes, built sections and girders; 
net sections — 16,000. 

On extreme fibers of pins, rivets and bolts — 25,000. 

Shearing: on pins and shop driven rivets — 12,000. 

On field driven rivets and turned bolts — 9,000. 

On plate girder web; gross section — 10,000. 

Bearing on pins and shop driven rivets — 24,000. 

On field driven rivets and turned bolts — 18,000. 

On masonry — 400. 

On expansion rollers or rockers where "d" is the diameter of the rocker 
or roller in inches, per linear inch — 6ood. 

On pin bearing on rockers — 12,000. 

For Cast Steel 

Tension — ^16,000. 
Compression — 16,000. 
Shear — 10,000. 

For Concrete 

6. Permissible Stresses in Concrete.— Compression — 600. 
Tension — o. 

For Douglas Fir, White Oak and Long Leaf Yellow Pine Timber 

7. Permissible Stresses in Timber. — Bending extreme fiber — 1500. 
Tension with grain — 1500. 

Compression with grain — 1500. 
Shearing across grain — 600. 
Shearing along grain stresses — 200. 

8. Alternate Stresses. — Members subject to alternate stress of tension and 
compression shall be proportioned for the stress giving the largest section. 
If the alternate stresses occur in succession during the passage of one load, 
each stress shall be increased by fifty per cent. (50%) of the other. The 
connections shall in all cases be proportioned for the sum of the stresses.^ 

9. Counter Stresses. — Wherever live and dead load stresses are of opposite 
character, only 70 per cent, of the dead load stress shall be considered as 
effective in counteracting the live load stress. 

10. Axial and Bending Stresses Combined. — Members subject to both 
axial and bending stresses shall be proportioned so that the combined fiber 
stresses will not exceed the allowed axial stress. 

11. Lateral and Other Stresses Combined. — For stresses produced by 
lateral or wind forces combined with those from live and dead load forces, 
the unit stress may be increased 30 per cent, over those given above; but 
the section shall not be less than required if the lateral or wind forces be 
neglected. 



BRIDGES 815 

12. Tension Members. — Net sections must be used in all cases in calcula- 
ting tension members, deducting the area of rivet holes one-eighth inch 
(>^") in diameter larger than the nominal size of rivet. The net sections 
at pin holes shall be twenty-five per cent. (25 %) in excess of the net section 
through the body of the main member. The net section back of the pin 
hole, parallel to the axis of the member shall be not less than that through 
the body of the main member. Main tension members shall be composed 
of sections symmetrically placed about the central plane through the truss. 

13. Limiting Length of Compression Members. — The length of main 
compression members shall not exceed 125 times their least radius of 
gyration. 

14. Proportioning Plate Girders.— Plate girders shall be proportioned 
either by the moment of inertia of their net section or by assuming that the 
flanges are concentrated at their centers of gravity; in which case one-eighth 
of the gross section of the web, if properly spliced, may be used as flange area. 

15. Compression Flange. — The gross section of the compression flanges 
of plate girders shall not be less than the gross section of the tension flange 
and the unsupported length of the compression flange shall not be greater 
than 15 times its width. 

16. Depth Ratios. — Trusses shall preferably have a depth of not less than 
one-tenth of the span and plate girders a depth of not less than one-twelfth 
of the span. If shallower trusses or girders are used, the section shall be 
increased so that the maximum deflection will not be greater than if the 
above limiting ratios had not been 'exceeded. 

DETAILS OF DESIGN 

General'Requirements 

'17. Open Section and Water Pockets. — Structures shall be so designed 

that all parts will be accessible for inspection, cleaning and painting. Any 

pockets or depression likely to hold water shall be provided with drains 

or be filled with water-proof material. 

18. Symmetrical Sections. — Unsymmetrical sections, such as top chords 
and end posts composed of two rolled or built up channels and a cover 
plate, shall be proportioned to bring the center of gravity as near as pos- 
sible to the center of the web. 

The neutral axis of the main members around the joints shall intersect 
at a common point. 

19. Splices. — All joints in riveted work, whether the stress be tension or 
compression, shall be spliced to develop the full stress in the members. 

20. Minimum Thickness. — No material shall be used less than one-quarter 
inch (3'i'O in thickness except for lining or filling vacant spaces and in webs 
of rolled channels. 

21. Pitch of Rivets. — The minimum pitch shall be not less than three 
diameters of the rivet and perferably not less than the following: 

For J-^ in. rivets, minimum pitch — 3 in. 
" ^1 " " " " —23^ in. 

" % " " •* '• — 2Km. 

•• M •• •• " " — i^in. 

The pitch of rivets in the direction of the strain shall not exceed six mches 
(6") or sixteen times the thinnest outside plate. For angles with two gage 
lines and rivets staggered the maximum shall be 9 inches in each line. 

22. Edge Distance. — The minimum distance from the center of any 
rivet hole to a sheared edge shall be; 

i>^ in. for % in. rivets. 

I " 3^2 " 

For rolled edges, except flanges of I-beams and channels: 
i^'i in. for J^i in. rivets. 

I " " ys " " 

14 " " y2 " " - . 

The maximum distance from any edge shall be eight times the thickness 
of the outside plate, but shall not exceed five inches (s'O* 

23. Compression Members. — In compression members the metal shall be 
concentrated as much as possible in the webs and flanges. Cover plates shall 

', have a thickness of not less than one-fortieth of the distance between rivet 
lines. 



8 1 6 SPECIFICATIONS 

24. Tie Plates. — The open sides of compression members shall be latticed 
and shall have tie plates at the ends and at intermediate points where 
the lattice is interrupted. These plates shall have a length equal to the width 
of the main members on the connected side and a thickness not less than one- 
fiftieth iyio) of the distance between the rivets connecting them to the 
member. The minimum thickness shall be one-fourth inch (^'0» 

25. Lattice Bars. — The minimum width of lattice bars shall be as follows. 
2M inches for %'^ rivets. 

2K ♦' •• ^'' " 

iH " , •• >^'' " . . . , 

Single lattice bars shall have an inclination of approximately 60 degrees 
with the axis of the main member and shall have a minimum thickness of 
one-fortieth Oio) of the distance between rivets connecting them to the 
member. When the distance between rivet lines exceeds fifteen inches (15") 
double lattice bars with an inclination of approximately 45 degrees shall be 
used. The minimum thickness shall be one-sixtieth (Ko) of the distance 
between the rivets connecting them to the member and they shall be riveted 
at the intersections. 

26. Pin Plates. — All pin holes shall be reinforced by plates if necessary 
These reinforcing plates shall contain sufficient rivets to transfer the propor- 
tion of pressure which comes upon them and at least one plate on each side 
of the member shall extend not less than six inches (6") beyond the tie plate. 

27. Pins. — Pins shall be long enough to insure a full bearing of all parts 
connected upon the turned body of the pin. They shall be secured by cham- 
bered nuts. The screw ends shall be long enough to admit of burring the 
threads. 

28. Pin Packing. — Members shall be symmetrically packed on pins using 
filler rings if necessary to prevent any lateral movement. 

29- Provision for Temperature Changes. — Provision for the free expan- 
sion and contraction to the extent of one-eighth of an inch for each 10 ft. of 
length shall be made for all bridges. Spans of 65 feet and less shall have one 
end free to move on planed surfaces. Above these length, all steel bridges 
shall be provided with rocker shoes of approved design. 

30. Shoes, Bed Plates and Anchor Bolts. — Spans over 65 feet in length 
shall have pin bearing shoes. Details of shoes shall conform to the standard 
details shown on plans of the Commission. 

Cast bed plates shall be planed on top, the cut of the tool paralleling the 
direction of expansion. All bed plates shall be grouted true to position. 

The setting of all anchor bolts for the steel work shall be included as part 
of the contract for the superstructure. Unless otherwise specified, the 
bolts shall have a minimum diameter of one and one-fourth inches (i 3^") 
and shall extend eighteen inches (18") into the masonry and be set in neat 
Portland cement mortar. 

31. Field Connections. — The field connections of spans under 70 feet in 
length may be bolted or riveted at the discretion of the engineer. If field 
connections for spans of this length are to be riveted, this fact must be speci- 
fically stated in the Instructions to Bidders or Form of Tender. The holes 
in floorbeam connections and joist connections (where the joist connects 
directly to the web of the floorbeams) must, if bolted, be sub-punched and 
reamed to iron templates and the open holes in the main splices of trusses 
must be sub-punched and reamed to size at the shop while the trusses are 
assembled. The bolts used shall have hex heads and hex nuts and ^ inch 
washers, and must fit the holes tightly.^ The bolts shall be threaded to 
such a length that the thread will end inside the washer and not extend 
into the effective grip of the bolt. The use of square-headed or button- 
headed bolts, or square-nuts will not be allowed. 

All field connections of all spans 70 feet or more in length erected on per- 
manent abutments shall be riveted except handrail connections as noted 
below. Handrail connections shall in all cases be bolted. 

Floor Systems 

32. Floor Beams. — Floor beams shall be arranged perpendicularly to the 
girder or truss at the panel points and in through bridges, shall be riveted 
to the verticals. Rolled shapes such as floor beams and joists shall be pro- 
portioned by their moments of inertia. 



BRIDGES 817 



33. Joists. — Steel joists shall preferably be riveted to the webs of floor 
beams. Rolled beams used as joists shall be spaced not to exceed 2' 6" 
centers under wood floors. 

34. Beam Bridges. — Rolled shapes for beam bridges shall be spaced and 
proportioned as previously specified. The separate lines shall be held truly 
to position by struts or spreaders. The two outside lines at least shall be 
rigidly connected by angle or channel struts at intervals of about 8 feet. 

Note. — In all concrete floor construction over steel shapes, plates or cor- 
rugated arches shall not be used over or between the joists or beams. 

Bracing 

3 5. Rigid Bracing.— All lateral, longitudinal and transverse bracing 
shall be composed gf rigid members. 

36. Through Truss Spans. — Through truss spans shall have riveted 
portals rigidly connected to the top chord and end posts. They shall be as 
deep as the clearance will allow. _ 

Transverse struts shall be provided at all intermediate posts. 

The struts in the top lateral system shall be as deep as the chord section 
and shall be riveted to each flange of the top chord. The section shall 
preferably be of four angles connected by latticing. 

37. Pony Trusses. — The top chord of pony trusses shall be securely held 
to position at the panel points by gusset plates, knee braces or wide-webbed, 
vertical posts rigidly connected to the floor beams. 

38. Deck Truss. — Deck truss spans shall be provided with sway bearing at 
each panel point, sufficient to resist all lateral stresses. Such braces to have 
riveted connection with the main members. 

39. Steel Trestles. — Each trestle bent shall be composed of two columns 
braced together. The majority of bents shall be united in pairs forming 
a tower which shall be rigidly braced on the four sides and shall have longi- 
tudinal and transverse struts at the bases. 

Plate Girders 

40. Top Flange — Through plate girders shall preferably have their upper 
corners neatly rounded and if flange plates are used one plate of the upper 
flange shall extend over the comers to the bottom of the girder. 

41. Web Splices. — The web plates of girders shall be spliced at all joints 
by a plate on each side, capable of transmitting the full stress through splice 
rivets. At least two rows of rivets on each side of splice must be used. 

42.^ Stiflfener Angles. — Stiffener angles shall be placed at points of bearing, 
at points of concentrated loading and at points required by the formula: 

d = — (12,000 — s) 
40 

Where d = the clear distance between stiff eners or flange angles; t = the 
thickness of web; s = the shear per square inch on the web. 

The stiffeners at ends and at points of concentrated loads shall be deter- 
mined by the formula: 
L 
p = 16,000 — 70- 
r 
In which p = the allowable unit stress; L = H the depth of the girder in 
inches; r = the radius of gyration of angles neglecting fillers and web. 

Trusses 

43. Working Lines. — In general the following working lines shall be used: 
For channels with cover plates used for top chords and end posts, working 

lines shall be taken as near as practicable to the center of gravity of the 
section. For two angle chord and diagonal sections the working line may 
be taken as gage line nearest the back of the angle. For symmetrical sec- 
tions the working line shall be taken at center of gravity of the section. 

44. Camber. — All truss spans shall be given a proper camber by increasing 
the length of the top chords. For spans carrying wood floors, an increase of 
one-eighth inch (H'O for each ten feet of length and for spans carrying con- 



8i8 SPECIFICATIONS 

Crete floors, an increase of "three-sixteenths inches (Me") for each ten feet 
of length shall be used. 

45. Rigid Members. — Hip verticals and the two end panels of the bot- 
tom chord in pin connected trusses shall be rigid members. 

46. Eye-Bars. — Eye-bars shall be placed as nearly parallel to the central 
plane of the truss as possible, the maximum inclination of any bar being one 
inch (I'O in sixteen feet. Adjustable eye-bars used as counters shall have 
the screw ends upset. 

Workmanship 

47. Punching. — All rivet work must be punched accurately with holes 
one-sixteenth inch (He'O larger than the size of rivet used and when the 
pieces forming one member are put together, the holes must be truly oppo- 
site. No drifting to distort metal will be allowed. If necessary to admit the 
rivets, the holes shall be enlarged by reaming. 

48. Rivets. — Rivet heads must be of approved hemispherical shape and of 
uniform size for the same size of rivet throughout the work. They must be 
full, neatly finished and concentric wi h the rivet hole. All rivets shall 
preferably be machine driven by direct acting machines. 

49. Eye-Bars. — The heads of eye-bars shall be not less in strength than 
the body of the bar and shall be of an approved make. The head shall be 
made by upsetting, rolling or forging into shape. Welding in the body of 
the bar shall not be allowed . 

50. Boring Eye-Bars. — Eye-bars which are to be placed side by side in the 
structure shall be bored at the same temperature and at one operation. 
They shall be of such equal length that upon being piled, the pins shall 
pass through the holes at both ends simultaneously without driving. 

51. Annealing. — All eye-bars must be annealed. 

52. Play in Pin Holes. — The clearance between any pin and pinhole shall 
be 3'^ of 3-11 inch up to four inches (4") in diameter and for pins above four 
inches (4") not more than }^i2 of an inch. 

53. Pins. — Pins shall be accurately turned to gages and shall be straight 
and smooth and entirely free from flaws. 

54. Driving and Pilot Nuts. — All pins shall be supplied with steel driving 
and pilot nuts for use during erection. 

Structural Material 

55. Grades of Material. — The superstructure shall be fabricated from 
the following materials: 

Rivet steel, structural steel, cast iron, or cast steel. 

56. Manufacture. — All steel and steel castings shall conform in detail 
to the standard specifications of the American Society for Testing Materials, 
for Strucutral Steel for Bridges, adopted August 16, 1909. 

57. Structural Steel. — Structural steel shall be used in all parts of the 
structure except for rivets, shoes, rockers or pedestals. 

58. Rivet Steel. — All rivets shall be made of rivet steel. 

59. Cast Steel and Cast Iron.— Shoes, rockers and pedestals shall be 
made of either cast steel or cast iron. If of cast iron, test bars one inch 
square, loaded in middle between supports of twelve inches (i2'0 apart shall 
bear 2500 pounds or over and deflect 0.15 of an inch before rupture. 

60. Name Plate. — A suitable name plate inscribed as directed by the 
engineer shall be provided and securely attached. 

61. Hand Rail. — A steel hand rail of the design shown on the plans shall 
be provided and accurately lined to position. If material other than steel 
is desired, the plans shall show the material and construction in detail. 

62. Shop Drawings. — The contractor s all furnish the engineer two sets 
of shop drawings. These drawings shall in general be checked by the Com- 
mission, and three corrected sets of shop drawings shall be furnished the 
engineer, one set for his use, one set to be forwarded to the Commission, and 
one set to be filed as a part of the contract with the county auditor. 

Test and Inspection 

63. Tests and Inspection. — The purchaser under these specifications shall 
be furnished by the manufacturer with every facility for complete inspection 
and test and shall on request be supplied with copies of the full orders, 
shipping invoices and weights. 



BRIDGES 819 



SPECIFICATIONS FOR PAINT 

64. Metal Must be Clean Before Shop Coat is Put On. — One shop or 
prime coat and one field coat of paint shall be applied in conformity with 
the following requirements. 

All metal work (including railings) shall be cleaned from all rust, scale, 
dirt or grease before the shop coat of paint is applied. If rust, which in 
the opinion of the inspector can not be removed is found on any piece, that 
piece shall be rejected. All parts which come in contact shall be painted 
before they are riveted together. After assembling and riveting, the metal 
work thoroughly clean and dry, and before leaving the shop, shall be 
painted carefully with one coat of one of the hereinafter specified prime 
coat paints. Parts not ^ accessible after erection shall^ be painted two 
coats. While metal work is being erected in place all abrasions of the original 
paint and all rivet and bolt heads and location marks must be cleaned and 
painted, preparatory to the second coat. 

65. Protecting Machined Surfaces. — Machined surfaces shall be coated 
with white lead and tallow before shipment or before being placed in the open. 

66._ Paint for Shop Coat. — The pigment of the paint to be used as the shop 
or prime coat shall be one of the following according to the final tint or color 
required by the engineer: 

1. Pure Red Lead. 

2. Pure Sublimed Blue Lead. 

3. Pure Sublimated Sulfate of Lead. 

4. Basic Lead or Zinc Chromate. 

5. Pure Iron Oxide mixed with not less than 10% Basic Lead or Zinc 

Chromate. 

6. Pure Natural Graphite mixed with not less than 20 % Basic Lead or 

Zinc Chromate. 

The word "pure" in the above shall be interpreted as meaning without 
the addition of any substances foreign to the various pigments such as 
silica, silicates, and other inert materials or impurities. 

No shop painting shall be done in wet or freezing weather unless such 
painting is done under cover where the conditions are such that no moisture 
will condense on the surface of the steel and where the temperature of the 
atmosphere will be above 45 degrees for at least 10 hours per day. 

67 . One Coat of Field Paint After Erection. — After the structure is com- 
plete in place, touched up as described above and cleaned of dirt, grease, or 
oil that may have accumulated during erection, one coat of one of the herein- 
after specified field coat paints shall be applied to all accessible parts. 

No field painting shall be done in wet weather or when the temperature 
of the atmosphere is not above 45 degrees F. for at least 10 hours per day. 

68. Paints for Field Coat. — The paints for field coats shall contain any of 
the following pigments: 

I. Red Lead. 
I 2. Sublimed Blue Lead. 
I 3. Sublimed Sulfate of Lead. 

4. Iron Oxide. 
j 5. Pure Graphite (natural). 
I , 6.^ Pure Carbon. 

Pigments other than graphite or carbon may contain not more than 25 % 
'of inert material such as silica, china clay, or asbestine. 

1 Lampblack, Prussian Blue and Chrome Yellow shall be used for obtaining 
ithe proper tints. 

The pigment of graphite or carbon paints shall not contain less than 70% 
'total graphitic carbon or carbon. 

' No paint pigment shall contain more than 5 % of either Calcium Carbon- 
■ate or Calcium Sulfate. 

1 No red lead paint shall be used as a field coat without the addition of 
^ome tinting pigment in sufficient quantity to eliminate the fading effect of 
!a straight red lead paint. 

1 69- Paint Vehicle. — The paint vehicle in every case shall be pure boiled 
linseed oil or China wood oil with the necessary amount of Japan dryer to 
produce a good drying coefficient and shall in no case contain moisture to 
exceed 0.5%. The amount of volatile vehicle shall not exceed 10% of the 
vehicle. 

A paint containing coal tar or asphaltic products shall not be used. 



820 SPECIFICATIONS 

70. Percentage of Pigment in Shop Coat. — The percentage of pigment in 
the different shop or prime coat paints shall approximate the following: 

Red Lead Paints — not less than 65 %. 

Sublimed Blue Lead Paints — not less than 60%. 

Sublimed Lead Sulfate — not less than 60 %. 

Basic Lead and Zinc Chromate Paint — not less than 60%. 

Iron Oxide Paints — not less than 55 %. 

Graphite Paints — not less than 35%. 

71- Percentage of Pigment in Field Coat. — The percentage of pigments 
in the various field coat paints shall approximate the following: 

Red Lead Paints — not less than 55 %• 

Sublimed Blue Lead Paints — not less than 50%. 

Sublimed Lead Sulfate Paints — not less than 55%. 

Iron Oxide — not less than 50%. 

Pure Graphite — not less than 25%. 

Pure Carbon — not less than 25 %. 

The Red Lead of any pigment shall not contain more than 10% of Lith- 
arge (PbO) nor more than i.o % of materials other than Oxide or Carbonate 
of Lead. 

The Sublimed Blue Lead of any pigment shall be a mixture of Lead Sulfate, 
Sulfite and Sulfid and Lead Oxide and Zinc Oxide and shall contain not less 
than 30 % of uncombined Lead Oxide (PbO). 

The Sublimed Lead Sulfate of any pigment shall be a mixture of Lead 
Sulfate, Basic Lead Carbonate, or Lead Oxide and Zinc Qxide and shall not 
contain less than 15% of uncombined Lead Oxide (PbO) or the equivalent 
of Basic Lead Carbonate. 

72. Samples for Testing. — Before ordering the paint, a sample of at least 
one quart shall be furnished the engineer, which sample, if approved, will 
be used in determining the merits of the paint furnished on the work, All 
paint used must equal the sample in quality. 

Samples of the paint delivered at the shop and in the field shall be fur- 
nished the engineer by the contractor. These samples shall be tested at the 
laboratory of the Iowa Highway Commission before any paint is applied. 

73. Manufacturers* Guarantee. — The contractor should therefore secure 
the necessary paint in ample time so that no delay to the work will be caused 
by the time necessarily used in testing for which ten days should be allowed 
from the time the sample is collected by the inspector. 

In order to facilitate contracting and prevent the necessary delays in col- 
lecting and testing samples, the contractor may submit to the Highway 
Commission a certificate of guarantee from the paint manufacturer stating 
that the paint which said manufacturer intends to supply for a particular 
job has been tested and accepted by the Highway Commission and that the 
paint to be furnished is guaranteed to conform in every respect to the 
sample submitted to the Highway Commission for testing. The following 
form shall be used by the paint manufacturers: 

74- Form of Guarantee. — 

We do hereby represent aad guarantee that the 

paint which we have furnished 

for painting or other steel 

structures conforms in every respect to the sample submitted to the Iowa 
State Highway Commission for the purpose of testing and accepted by 

them under Laboratory No 

(Signed) 

Note. — The attention of manufacturers is directed to the requirements of 
Chapters iiA and iiB, Title 12, Supplement to the Code, 1913. relative 
to the manufacture and sale of paint and linseed oil. 

Floors 

75. Floors. — The floors shall be included as a part of the contract price 
of the superstructure. 

76. Timber Floors. — Timber floors shall consist of one thickness of three 
inch (3") northern fir, yellow pine or white oak laid at right angles to the li 
length of the bridge. The timber used shall be sawed true, of even thickness ' 
and free from all defects impairing its strength or durability. Connections, 
wheel guards and nailing places shall be as shown on the detailed plans. |j 

77- Concrete Floors. — Concrete floors shall be built of Class "C" concrete. ( 
The thickness of concrete, sizes and placing of reinforcing steel shall conform '^ 
to the detailed drawings. No concrete shall be run until the reinforcing 
steel has been placed, spaced and secured in position. 



BRIDGES 821 

78. Wearing Stirface. — All concrete floors not covered with a bituminous 
surface shall be finished with a one-half inch (3^'0 wearing surface of i to i 
mortar. Immediately after the concrete floor has been poured to the re- 
quired thickness and before the concrete has reached its initial set the entire 
top surface of the floor shall be covered with a i to i wearing surface of sand 
and cement. This mortar coat shall be rubbed in and finished with a 
heavy wood float in such a manner as to provide a smooth, even wearing 
surface. 

79. Expansion J9ints. — Concreting over each span shall be completed in a 
continuous operation. Expansion shall be provided between spans, and 
under each end of floors, resting on the abutments. These joints shall be 
filled with tar or asphalt or tarred paper as shown on the drawings. 

80. Protecting Expansion Joints. — At expansion joints the edges of the 
concrete shall be protected by steel plates approved by the engineer and the 
joints shall be filled with an asphaltic felt. 

The centering under the steel trusses shall be lowered and the trusses 
swung free on their own bearing before the concrete is run for the floor. 

On long spans unless provision is made for reversal of stresses in the trusses, 
concreting of the floors shall be carried on from each end simultaneously. 

81. Protection During Curing. — The exposed surfaces of all concrete 
placed in floors shall be protected from the direct rays of the sun by canvas, 
or other method of covering approved by the engineer. All concrete shall 
be kept moist for a minimum of one week. Adequate water supply shall be 
provided by the contractor, and the curing of the conrecte shall be carried 
on in detail as directed by the engineer. 

82. Bituminous Floor Coating. — A tar or asphalt of quality acceptable to 
the engineer and Commission shall be applied hot to the concrete at the 
rate of one-third gallon per square yard. Over this coating while hot shall 
be sifted, hot, clean, dry sand, screened through a ^i-inch mesh. The 
sand shall be placed in excess and rolled with a hand roller. All joints 
and comers shall be thoroughly filled with the asphalt or tar. 

The county reserves the right to specify the tar or asphalt to be used, and 
the method of application and temperatures shall be in strict accor.dance 
with the written directions furnished the contractor by the engineer. All 
concrete surfaces to be covered with the bituminous coating shall be cleaned 
with steel brooms and blown free of all loose particles of any character. 

If such coating is desired, it shall be specified in the instruction to bidders. 

83. Drainage Pipes. — On all truss spans provision for floor drainage shall 
be made by providing and placing 4-inch cast iron drain pipes with per- 
forated cast iron covers. On pony truss spans without joists one drain 
pipe shall be located in each end panel and in each alternate intermediate 
panel on both sides of the bridge. On truss spans with joists one drain 
pipe shall be located in each panel on both sides of the bridge. 

84. Reinforcement Steel. — All reinforcement steel used in concrete 
floors shall meet the requirements of Section 3, Paragraph 29. 

85. Sidewalks. — Sidewalks where built shall conform to the requirements 
of the incorporation in which they are built. Dimensions and details shall 
be shown on the plans. 

86. Creosote Wood Floors. — Creosote wood block floors may be laid over a 
creosote sub-plank or concrete base, but in either case all creosoted material 
used shall conform to the following requirements: 

Timber 

87. Creosoted Material. — All timber used in wood block bridge floor 
construction shall be creosoted. This includes sub-plank, sheathing, re- 
taining pieces, scupper blocks, felloe guards, spiking pieces and paving blocks. 

88. Quality. — The paving blocks shall be cut from Dense Southern Yellow 
Pine conforming to the density rules as adopted by the American Society for 
Testing Materials, August, I9i5. 

The lumber shall be cut from Southern Yellow Pine of the same quality 
as specified above for the paving blocks, or from Douglas Fir. 

The material for the lumber and blocks shall be well manufactured, 
square-edged, and free from bark, shakes, large, loose or rotten knots, or 
other defects which may be detrimental to its strength or durability. 

89. Dimensions. — The lumber shall be of the standard commercial 
j dimensions corresponding to the nominal dimensions shown on the plans or 



822 SPECIFICATIONS 

noted in these specifications. Felloe guards, scupper blocks, and retaining 
pieces shall be surfaced one side and one edge. 

The paving blocks shall have a minimum length of 6 inches and a maxi- 
mum length of 10 inches. They shall be 4 inches wide and 3 inches deep, 
surfaced one side and one edge, and shall not vary in width more than }i 
inch or in thickness more than j^i q inch. 

Wherever possible all material including scupper blocks shall be cut to 
size before being treated. The ends of all material sawed in the field shall 
be dipped in hot creosote oil before being put in place. 

Treatment 

90. Treatment of Lumber and Blocks. — The timber shall be placed in an 
air-tight cylinder where, by means of steam and a vacuum pump, the sap 
will be vaporized and the moisture removed. During the process of steam- 
ing which shall last at least three hours, a vent shall be kept open in the 
cylinder to permit the escape of water, air and condensed steam from the 
cylinder. After the heating or steaming period, the drain or vent in the 
bottom of the cylinder shall be opened and all moisture removed from the 
cylinder. During the vacuum period the temperature in the cylinder must 
be above the boiling point of water under existing vacuum. When the 
cylinder is thoroughly drained a vacuum of not less than twenty inches of 
mercury shall be maintained. 

When the timber is thoroughly dry the cylinder shall be filled with oil 
following a vacuum of not less than twenty inches of mercury and pressure 
shall then be applied and increased gradually to not more than two hun- 
dred (200) pounds per square inch and maintained until sufiicient oil is 
forced into the timber to insure that it is thoroughly impregnated and that 
the amount retained per cubic foot of timber shall be not less than 16 pounds 
for the paving blocks and not less than 12 pounds for the dimension lumber. 

The pressure period on the oil shall be continuous and of a duration of 
not less than three (3) hours. After the surrounding oil has been removed, 
the timber shall remain in the closed cylinder for a period of thirty (30) 
minutes to allow the excess oil on the surface of the timber to drain off. 
The oil thus drained off shall be forced back into the treating tank in order 
to determine the amount of impregnation. 

The temperature of the oil after entering the cylinder shall be not lower 
than one hundred and sixty-five degrees Fahrenheit. _ The _ cylinder shall 
be provided with sufficient steam coils to fully maintain this temperature 
throughout injection. 

The oil tanks and cylinder in which the timber is treated shall be equipped 
with the necessary gauges, thermometers, and drawcocks in order to facilitate 
a thorough inspection of the materials and treatments. 

The plant shall be provided with proper means for obtaining the absolute 
measurement and weight of all oils entering the cylinder and the amount 
of oil retained by the timber. 

91. Notification of Treatment. — The creosoting company shall notify 
the State Highway Commission a sufficient length of time before the material 
is to be treated so that an inspector may be furnished at the plant to inspect 
the material and check the treatment. 

92. Plant Inspection Waived. — Should the creosoting company be notified 
in writing that plant inspection will be waived, the creosoting company will 
be required to furnish a certified staternent, signed by proper officers of 
the company, which statement shall indicate the amount of creosoted oil 
injected and remaining in the timber, and the results of analysis of the oil, 
which analysis shall be made in accordance with the methods described in 
these specifications. 

93. Failure to Give Notice of Treatment.— Should the creosoting company 
fail to notify the State Highway Commission of the date the material is 
to be treated, as heretofore provided, then field determination of the quantity 
of creosote contained in the lumber or blocks may be made in such manner 
as the Highway Commission may desire, and if in their opinion the timber 
contains less creosote oil than required by the specifications, it shall be 
rejected. 

Creosote Oil 

94. General Character. — The oil shall be a distillate obtained wholy 
from coal tar without the admixture of any other material. 



BRIDGES 823 

The oil shall contain not more than one per cent, (i %) of matter insoluble 
in hot benzol or chloroform. 

95. Distilling Test. — The oil shall be subject to a distilling test as follows: 
The apparatus for distilling the creosote must consist of a stoppered glass 

retort having a capacity, as nearly as can be obtained, of eight ounces up to 
the bend of the neck, when the bottom of the retort and the mouth of the 
takeoff are in the same plane. ^ The btilb of the thermometer shall be placed 
one-half 00 inch above the liquid in the retort at the beginning of the dis- 
tillation, and this position must be maintained through the operation. The 
condensing tube shal. be attached to the retort by a tight cork joint. The 
distance between the thermometer and the end of the condensing tube shall 
be twenty-two (22) inches, and during the process of the distillation the tube 
may be heated to prevent the congealing of the distillates. The bulb of the 
retort and at least two (2) inches of the neck must be covered with a shield 
of heavy asbestos paper during the entire process of distillation, so as to 
prevent heat radiation, and between the bottom of the retort and the flame 
of the lamp or burner two sheets of wire gauze each twenty (20) mesh fine 
and at least six (6) inches square must be placed. The flame must be pro- 
tected against air currents. 

The distillation shall be continuous and uniform, the heat being applied 
gradually. It shall be at a rate approximately one (i) drop per second, 
and shall take from thirty (30) to forty (40) minutes after the first drop 
of distillate passes into the receiving vessel. One hundred grams of the oil 
shall be taken for distillation. The distillates shall be collected in weighed 
bottles and all percentages determined by weight in comparison with dry oil. 

96. Oil for Paving Blocks and Dimension Lumber. — The specific gravity 
of the oil at 38 degrees Centigrade shall be not less than 1.03 and not more 
than 1.08. 

When subjected to the distilling test described above the amount of dis- 
tillate shall not exceed the following: 

Up to 200 degrees C, no distillate. 

Up to 210 degrees C, not to exceed 5 %. 

Up to 23s degrees C, not to exceed 25%. 

The residue at 355 degrees C. if it exceeds 5 % shall be soft. The oil shall 
be a pure distillate of coke-oven tar or coal-gas tar without the admixture 
of any other material. It shall be completely liquid at 38 degrees C, 
shall contain no suspended matter and shall contain not to exceed 3 % of 
water. 

Asphalt Filler 

The asphalt used for block filler and expansion joints shall conform to 
the following requirements, the various properties to be determined by the 
methods proposed by the American Society for Testing Materials. 

97. Specific Gravity. — The asphalt shall have a specific gravity at 25 
degrees C. of not less than 0.97 nor more than 1.06. 

98. Total Bitumen. — The asphalt shall be soluble in cold carbon disulphide 
to the extent of at least 98 %. 

99. Naphtha Insoluble Bitumen. — Of the total bitumen, not less than 
twenty (20) per cent, nor more than thirty (30) per cent, shall be insoluble 
in 86 degrees B. naphtha. 

100. Loss on £yai)oration. — jWhen 20 grams (in a tin dish 2^^ inches in 
diameter and ^^4 inch deep with vertical sides) are maintained at a tem- 
perature of 163 degrees C. for s hours in a N. Y. testing laboratory oven, 
the evaporation loss shall not exceed 2 % and the penetration shall not have 
been decreased more than 35 %• 

10 1. Fixed Carbon. — The fixed carbon shall not exceed 16 % by weight. 

102. Penetration. — The penetration as determined with the Dow machine 
using a No. 2 needle, 100 gm. weight, 5 seconds time, and a temperature of 
25 degrees C. shall not be less than 3.0 mm. nor more than 5.0 mm. 

103. ParaflSne. — The asphalt shall not contain to exceed 4 % by weight 
of parafline scale. 

Construction 

104. Spiking Pieces. — The spiking pieces shall be of the sizes shown on 
the plans and shall be securely bolted to the channels or I-beams as indicated. 

195. Sub-planks. — The sub-planks shall be 2" X 12" and shall be laid 
at right angles to the roadway with tight joints. 



824 



SPECIFICATIONS 



Each plank shall be securely double spiked to each longitudinal spiking 
piece. 

1 06. Sheathing. — On top of the sub-plank 1" sheathing shall be laid 
at an angle of 45 degrees with the axis of the bridge. It shall be laid with 
tight joints and securely nailed to the sub-plank. 

107. Retaining Pieces. — The side retaining pieces shall be spiked and 
bolted in position as shown on the plans. The end retaining pieces shall be 
securely spiked in place. 

108. Scupper Blocks. — The scupper blocks shall be securely fastened to 
the retaining pieces by means of spikes in addition to the bolts shown on 
the plans. 

109. Felloe Guards. — The felloe guards shall be fastened on top of the 
scupper blocks by means of 3,^ inch bolts at each end of each piece and at 
each intermediate scupper block. These bolts shall extend through the 
felloe guard, scupper block, retaining piece, as shown on the plans. 

110. Washers. — Standard size cast or wrought iron Ogee washers shall 
be used under all bolt heads or nuts which would otherwise come in contact 
with wood. 

111. Laying the Blocks.— The blocks shall be thoroughly sprinkled the night 
before they are laid. Noiie but whole blocks shall be used except at the 
ends of the rows. After the sub-plank, sheathing, retaining pieces, etc., 
are in place all irregularities in the surface of the floor shall be removed. 
The floor shall then be covered with a thin layer of asphalt filler as specified 
above and the creosoted blocks immediately laid thereon before the asphalt 
has had time to cool. To insure that the asphalt will be hot when the 
blocks are set it shall be spread on the floor for only a short distance in 
front of the block laying. 

^ The block shall be laid with the grain vertical and in regular courses at 
right angles to the center line of roadway. They shall be laid with \i inch 
joints all around them and the blocks in adjacent rows shall break joints by 
at least 3 inches. The M inch transverse joints between the rows of blocks 
shall be secured by the use of a '^i inch steel plate or template which shall 
extend the full width of the roadway. Immediately after the blocks are 
laid they shall be tarnped until firmly bedded in the asphalt. 

112. Expansion Joints. — An expansion joint one inch wide shall be pro- 
vided along each retaining piece and shall be kept free from obstruction 
during construction by a wood strip one inch thick extending down to the 
sheathing. 

113. Filling Joints. — After the blocks have been laid and tamped the 
wood strips shall be removed from the expansion joints and all joints over 
the entire surface of the roadway shall then be filled with the asphalt filler 
which shall be applied at a temperature of not less than 400° F. After the 
filler has been applied the entire surface shall be covered with a light coating 
of clean, coarse, dry sand. 



PART IV 



Linear Units 



GENERAL TABLES AND FORMULAE 

Conversion Table 68 

Old Surveyors^ Units 
I link =7.92 in. 
100 links = I chain = 66 ft. 
2$ links = I rod =16.5 ft. 





Ordinary Measure 




12 


1 in. = I ft. 




3 


1 ft. = I yd. 




5280 ft. = I mile 


Square Units 








I sq. ft. = 


= 144 sq. in. 




I sq. yd. = 


= 9 sq. ft. 
= 1296 sq. in. 




I acre 


= 43,560 sq. ft. 
= 4840 sq. yds. 




I sq. mile = 


= 27,878,400 sq. ft. 
= 3,097,600 sq. yds. 
= 640 acres 


Volume Units 






I 


cu. ft. 


= 1728 cu. in. 

= 7.4805 ordinary gal. 

= 6.232 Imperial gal. 


I 


cu. yd. 


= 27 cu. ft. 

= 46,656 cu. in. 


I 


ordinary gal. 


= 231 cu. in. 


I 


Imperial gal. 


= 277 cu. in. 


I 


barrel 


= 31-5 gal. 
= 4.21 cu. ft. 


Weight Units 








I pound 


= 16 ounces 




I ordinary 


ton = 2000 pounds 




I long ton 


= 2240 pounds 


Temperature Units 




Freezing point ^ 


of water 


= 32° Fahrenheit 
= 0° Centigrade 


Boiling point of water at normal air 


pressure 




= 212 lahrenher 



I degree Fahrenheit 
I degree Centigrade 



= 100" Centigrade 

= 0.5556 degree Centigrade 

= 1.8 degrees Fahrenheit 



825 



826 



GENERAL TABLES AND FORMULAE 



Table 69 

Equivalents of Inches and Fractions of Inches in Decimals 
OF a Foot 



In. 


In. 


I In. 


2 In. 


3 In. 


4 In. 


5 In. 






.0833 


.1667 


.2500 


•3333 


.4167 


A 


.0026 


.0859 


.1693 


.2526 


•3359 


•4193 


iz 


.0052 


.0885 


.1719 


•2552 


.3385 


.4219 


A 


.0078 


.0911 


•1745 


.2578 


.3411 


.4245 


I 


.0104 


.0938 


.1771 


.2604 


.3438 


.4271 


^7 


.0130 


.0964 


.1797 


.2630 


•3464 


•4297 


A 


.0156 


.0990 


.1823 


.2656 


.3490 


•4323 


T% 


.0182 


.1016 


.1849 


.2682 


•3516 


.4349 


i 


.0208 


.1042 


.1875 


.2708 


•3542 


•4375 


1^ 


.0234 


.1068 


.1901 


.2734 


.3568 


.4401 


A 


.0260 


.1094 


.1927 


.2760 


•3594 


.4427 


a 


.0286 


.1120 


•1953 


.2786 


.3620 


•4453 


f 


•0313 


.1146 


.1979 


.2813 


.3646 


•4479 


i! 


•0339 


.1172 


.2005 


.2839 


.3672 


•4505- 


l\ 


•0365 


.1198 


.2031 


.2865 


.3698 


•4531 


il 


.0391 


.1224 


.2057 


.2891 


•3724 


•4557 


i 


.0417 


•1253 


.2083 


.2917 


•3750 


.4583 


U 


•0443 


.1276 


.2091 


.2943 


•3776 


.4609 


t\ 


.0469 


.1302 


•2135 


.2969 


.3802 


•4635 


if 


.0495 


.1328 


.2161 


•2995 


.3828 


.4661 


f 


.0521 


•1354 


.2188 


.3021 


.3854 


.4688 


U 


•0547 


.1380 


.2214 


•3047 


.3880 


.4714 


■i 


•0573 


.1406 


.2240 


•3073 


.3906 


.4740 


■ f 


•0599 


.1432 


.2266 


•3099 


•3932 


.4766 


f 


.0625 


.1458 


.2292 


•3125 


.3958 


.4792 


11 


.0651 


.1484 


.2318 


•3151 


.3984 


.4818 


-H 


.0677 


.1510 


.2344 


'3^77 


.4010 


.4844 


*l 


.0703 


•1536 


.2370 


•3203 


.4036 


.4870 


i- 


.0729 


•1563 


.2396 


.3229 


.4063 


.4896 


^1 


.0755 


.1589 


.2422 


•3255 


.4089 


.4922 


"f 


.0781 


.1615 


.2448 


.3281 


.4115 


.4948 


rf 


.0807 


.1641 


.2474 


^3307 


.4141 


.4974 



EQUIVALENTS OF DECIMALS OF A FOOT 827 

Equivalents of Inches and Fractions of Inches in Decimals 
OF A Foot 



In. 


6 In. 


7 In. 


8 In. 


9 In. 


10 In. 


11 In. 




.5000 


•5833 


.6667 


.7500 


.8333 


.9167 


A 


.5026 


.5859 


.6693 


.7526 


.8359 


•9193 




•5052 


.5885 


.6719 


•7552 


•8385 


•9219 


^ 


.5078 


•5911 


•6745 


.7578 


.8411 


•9245 


i 


.5104 


.5938 


.6771 


.7604 


.8438 


.9271 


A 


'5^3<^ 


.5964 


.6797 


.7630 


.8464 


.9297 


A 


•5156 


•5990 


.6823 


.7656 


.8490 


.9323 


A 


.5182 


.6016 


.6849 


.7682 


.8516 


•9349 


i 


.5208 


.6042 


.6875 


.7708 


.8542 


•9375 


i\ 


•5234 


.6068 


.6901 


•7734 


.8568 


.9401 


A 


.5260 


.6094 


.6927 


.7760 


•8594 


•9427 


H 


.5286 


.6120 


•6953 


•7786 


.8620 


•9453 


i 


•5313 


.6146 


.6979 


.7813 


.8646 


•9479 


*J 


•5339 


.6172 


.7005 


.7839 


.8672 


•9505 


A 


.5365 * 


.6198 


•7031 


.7865 


.8698 


•9531 


it 


•5391 


.6224 


•7057 


.7891 


.8724 


•9557 


i 


•5417 


.6250 


.7083 


.7917 


.8750 


•9583 


H 


•5443 


.6276 


.7109 


•7943 


.8776 


.9609 




.5469 


.6302 


•7135 


.7969 


.8802 


•9635 


if 


•5495 


.6328 


.7161 


•7995 


.8828 


.9661 


f 


.5521 


.6354 


.7188 


.8021 


.8854 


.9688 


«- 


•5547 


.6380 


.7214 


.8047 


.8880 


.9714 


i^ 


•5573 


.6406 


.7240 


•8073 


.8906 


.9740 


h 


•5599 


.6432 


.7266 


.8099 


.8932 


.9766 


1 


•5625 


.6458 


.7292 


.8125 


.8958 


.9792 


7i 


•5651 


.6484 


.7318 


.8151 


.8984 


.9818 


il 


.5677 


.6510 


•7344 


•8177 


.9010 


.9844 


ji 


•5703 


.6536 


•7370 


.8203 


.9036 


.9870 


1 


•5729 


.6563 


.7396 


.8229 


.9063 


.9896 


■ 2 


.5755 


.6589 


.7422 


^255 


.9089 


.9922 


"6 


•5781 


.6615 


.7448 


.8281 


•9115 


.9948 


"* 


.5807 


.6641 


•7474 


.8307 


.9141 


.9974 



828 



Areas 



GENERAL TABLES AND FORMULA 
Table 70. Areas and Volumes 



^-b-> 


h 


<.-.-.b--> 



£ 



hz^^. 



71f 

h 



Squares^ Rectangles, and Parallelograms. Area = hh 




>^-b">{ 



•b M 



nsmy 



•\3-M 



\fr'h'M 



Triangles Area = ^ hh 



Trapezoids Area = h 



Area 



Circles 
r R^ = 



n D^ 



K 


^^ 


/ Circumference of Circle =2 n R = tr D 
Commonly used value of n = 3.1416 






'"^ Sector of Circle 

J Area =.7?^^^, 



^■'"S\ Segment of a Circle 

"^'^tj Area = ( . ;j.-g) - ( (i^ sin ±) (R cos f ) ) 

Volumes 

Cubes, Rectangular Prisms, ParallelopipedSy Cylinders, etc. All 
solids having parallel bases and a constant cross-section. 

Volume = area of base X perpendicular height between the 
planes of the bases. 



<F 






Wedges, Having parallel ends. 
Volume = area of base X | the height perpendic- 
X \ ular to the plane of the base. 



AREAS AND VOLUMES 



829 



Cones and Pyramids, whether right or oblique, regular or irreg- 
ular. 

Volume = \ area of the base X height perpendicular to the 
plane of the base 




Frustums of Pyramids or Cones, whether right or oblique, reg- 
ular or irregular provided the base and top are parallel. 




Volume = i perpendicular 
height between base and top 
or by the prismoidal formula 
Volume / 



f area 
\top 



, area , [area ^ 
■^ base "^ 'V top ^ 



area \ 
base / 



vuiumc ^area area 4 X area of section par-\ 

= i perpendicular height X L 4-|3^ggH-allel to and midway 1 
between base and top \ ^ between base and top ^ 

Prismoidal Formula 

Trautwine defines a prismoid as a solid having for its ends 
two parallel plane figures connected by other plane figures on 
which and through every point of which a straight line may be 
drawn from one of the two parallel ends to the other. These 
connecting planes may be parallelograms or not and parallel to 
each other or not. This includes cubes, all parallelopipeds, 
prisms, cylinders, pyramids, cones, and their frustums, provided 
the top and base are parallel and wedges. 

The prismoidal formula applies to all these solids either alone 
or to any form that can be separated into units of the above 
forms. 
Prismoidal formulce 



Volume = ^ X 



A +a + 4M 
6 



h = perpendicular distance between the parallel ends 
A = area of one of the parallel ends 
a = area of the other parallel end 
M = area of a cross-section midway between and parallel to 
the two parallel ends 
Sphere 

Volume = t TT R^ == 4.1888 R^ 

= i,r 2^3 ==0.5236 D^ 

In which R = radius of sphere 

D = diameter of sphere 



830 



GENERAL TABLES AND FORMULAE 



Table 71 

Squares, Cubes, Square Roots,' Cube Roots, Circumferences 
AND Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 




Circum. 


Area 


I 


I 


I 


1. 0000 


1 .0000 


3.142 


0.7854 


2 


4 


8 


I.4142 


1-2599 


6.283 


3.1416 


3. 


9 


27 


I.7321 


1.4422 


9-425 


7.0686 


4 


16 


64 


2.0000 


1.5874 


12.566 


12.5664 


5 


25 


125 


2.2361 


1.7100 


15.708 


19.6350 


6 


36 


216 


2.4495 


1.8171 


18.850 


• 28.2743 


7 


49 


343 


2.6458 


1. 91 29 


21.991 


38.4845 


8 


64 


512 


2.8284 


2 .0000 


25-133 


50.2655 


9 


81 


729 


3.0000 


2.0801 


28.274 


63.6173 


10 


100 


1000 


3.1623 


2.1544 


31.416 


78.5398 


II 


121 


1331 


3.3166 


2.2240 


34.558 


95-033 


12 


144 


1728 


3.4641 


2.2894 


37-699 


113.097 


13 


169 


2197 


3.6056 


2.3513 


40.841 


132.732 


14 


196 


2744 


3-7417 


2.4IOI 


43.982 


153-938 


15 


225 


3375 


3-8730 


2.4662 


47.124 


176.715 


16 


256 


4096 


4.0000 


2.5198 


50.265 


201.062 


17 


289 


4913 


4.1231 


2.5713 


53-407 


226.980 


18 


324 


5832 


4.2426 


2.6207 


56.549 


254.469 


19 


361 


6859 


4.3589 


2.6684 


59-690 


283.529 


20 


400 


8000 


4.4721 


2.7144 


62.832 


314.159 


21 


441 


9261 


4.5826 


2.7589 


65.973 


346.361 


22 


484 


10648 


4.6904 


2.8020 


69.115 


380.133 


^3 


529 


12167 


4.7958 


2.8439 


72.257 


415.476 


24 


576 


13824 


4.8990 


2.8845 


75-398 


452.389 


25 


625 


15625 


5.0000 


2.9240 


78.540 


490.874 


26 


676 


17576 


5.0990 


2.9625 


81.681 


530.929 


27 


729 


19683 


5.1962 


3.0000 


84.823 


572.555 


28 


784 


21952 


5-2915 


3-0366 


87-965 


615.752 


29 


841 


24389 


5-3852 


3-0723 


91.106 


660.520 


30 


900 


27000 


5-4772 


3.1072 


94.248 


706.858 


31 


961 


29791 


.5.5678 


3-I414 


90.389 


754.768 


32 


1024 


32768 


5-6569 


3-1748 


100.531 


804.248 


ZZ 


1089 


35937 


5-7446 


3-2075 


103.673 


855.299 


34 


1156 


39304 


5-8310 


3.2396 


106.814 


907.920 


35 


1225 


42875 


5.9161 


3.271I 


109.956 


962.113 


36 


1296 


46656 


6.0000 


3-3019 


113.097 


1017.88 ' 


37 


1369 


50653 


6.0828 


3-3322 


116.239 


1075.21 


38 


1444 


54872 


6.1644 


3.3620 


119.381 


li34.II 


39 


1521 


59319 


6.2450 


3-3912 


122.522 


1194.59 


40 


1600 


64000 


6.3246 


3.4200 


125.660 


1256.64. 



SQUARES, CUBES, ETC. 



831 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 




AND Circular Areas of Nos. from i to 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


41 


1681 


68921 


6.4031 


3-4482 


128.81 


1320.25 


42 


1764 


74088 


6.4807 


3-4760 


131.95 


1385.44 


43 


1849 


79507 


6.5574 


3-5034 


135.09 


1452.20 


44 


1936 


85184 


6.6332 


3-5303 


138.23 


1520.53 


45 


2025 


91125 


6.7082 


3.5569 


141.37 


1590.43 


46 


2116 


9n?>^ 


6.7823 


?>-S^ZO 


144.51 


1661.90 


47 


2209 


103823 


6.8557 


3.6088 


147.65 


1734.94 


48 


2304 


I 10592 


6.9282 


3.6342 


150.80 


1809.56 


49 


2401 


I I 7649 


7.0000 


3.6593 


153.94 


1835.74 


50 


2500 


125000 


7.0711 


3.6840 


157.08 


1963.50 


51 


2601 


132651 


7.1414 


3-7084 


160.22 


2042.82 


52 


2704 


140608 


7.2111 


3-7325 


163.36 


2123.72 


53 


2809 


148877 


7.2801 


3.7563 


166.50 


2206.18 


54 


2916 


157464 


7-3485 


d>'n9^ 


169.65 


2290.22 


55 


3025 


166375 


7.4162 


3.8030 


172.79 


2375.83- 


56 


Z-^?,^ 


175616 


7.4833 


3.8259 


175.93 


2463.01 


57 


3249 


185193 


7.5498 


3.8485 


179.07 


2551.76 


58 


3364 


195112 


7.6158 


3.8709 


182.21 


2642.08 


59 


3481 


205379 


7.681 1 


3.8930 


185.35 


2733.97 


60 


3600 


216000 


7.7460 


3.9149 


188.50 


2827.43 


61 


3721 


226981 


7.8102 


3.9365 


191.64 


2922.47 


62 


3844 


238328 


7.8740 


3.9579 


194.78 


3019.07 


63 


3969 


250047 


7-9373 


3.9791 


197.92 


3117.25 


64 


4096 


262144 


8.0000 


4.0000 


201.06 


3216.99 


65 


4225 


274625 


8.0623 


4.0207 


204.20 


3318.31 


66 


4356 


287496 


8.1240 


4.0412 


207.35 


3421.19 


67 


4489 


300763 


8.1854 


4.0615 


210.49 


3525.65 


68 


4624 


314432 


8.2462 


4.0817 


213.63 


3631.68 


69 


4761 


328509 


8.3066 


4.1016 


216.77 


3739.28 


70 


4900 


343000 


8.3666 


4.1213 


219.91 


3848.45 


71 


5041 


357911 


8.4261 


4.1408 


223.05 


3959.19 


72 


5184 


373248 


8.4853 


4.1602 


226.19 


4071.50 


73 


5329 


389017 


8.5440 


4.1793 


229.34 


4185.39 


74 


5476 


405224 


8.6023 


4.1983 


232.48 


4300.84 


75 


5625 


421875 


8.6603 


4.2172 


235.62 


4417.86 


76 


5776 


438976 


8.7178 


4.2358 


238.76 


4536.46 


77 


5929 


456533 


8.7750 


4.2543 


241.90 


4656.63 


78 


6084 


474552 


8.8318 


4.2727 


245.04 


4778.36 


P 


6241 


493039 


8.8882 


4.2908 


248.19 


4901.67 


80 




6400 


512000 


8.9443 


4.3089 


251.33 


5026.55 

















832 



GENERAL TABLES AND FORMULA- 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 




AND Circular Areas of Nos. from i to 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


8i 


6561 


531441 


9.0000 


4.3267 


254.47 


5153.00 


82 


6724 


551368 


9-0554 


4.3445 


257.61 


5281.02 


83 


6889 


571787 


9.IIO4 


4.3621 


260.75 


5410.61 


84 


7056 


592704 


9.1652 


4-3795 


263.89 


5541.77 


85 


7225 


614125 


9.2195 


4.3968 


267.04 


5674.50 


86 


7396 


636056 


9.2736 


4.4140 


270.18 


5808.80 


87 


7569 


658503 


9-3274 


4.4310 


273.32 


5944.68 


88 


7744 


681472 


9.3808 


4.4480 


276.46 


6082.12 


89 


7921 


704969 


9-4340 


4.4647 


279.60 


6221.14 


90 


8100 


729000 


9.4868 


4.4814 


282.74 


6361.73 


91 


8281 


753571 


9-5394 


4.4979 


285.88 


6503.88 


92 


8464 


778688 


9-5917 


4-5144 


289.03 


6647.61 


93 


8649 


804357 


9-6437 


4.5307 


292.17 


6792.91 


94 


8836 


830584 


9-6954 


4.5468 


295.31 


6939.78 


95 


9025 


857375 


9.7468 


4.5629 


298.45 


7088.22 


96 


9216 


884736 


9.7980 


4.5789 


301.59 


7238.23 


97 


9409 


912673 


9.8489 


4.5947 


304.73 


7389.81 


98 


9604 


941192 


9.8995 


4.6104 


307.88 


7542.96 


99 


9801 


970299 


9.9499 


4.6261 


311.02 


7697.69 


100 


1 0000 


I 000000 


10.0000 


4.6416 


314.16 


7853-98 


lOI 


10201 


1030301 


10.0499 


4.6570 


317.30 


8011.85 


102 


10404 


1061208 


10.0995 


4.6723 


320.44 


8171.28 


103 


10609 


1092727 


10.1489 


4.6875 


323-58 


8332.29 


104 


10816 


I I 24864 


10.1980 


4.7027 


326.73 


8494.87 


105 


11025 


I157625 


10.2470 


4.7177 


329.87 


8659.01 


106 


11236 


I191016 


10.2956 


4.7326 


333.01 


8824.73 


107 


II 449 


1225043 


10.3441 


4.7475 


336.15 


8992.02 


108 


1 1 664 


1259712 


10.3923 


4.7622 


339.29 


9160.88 


109 


11881 


1295029 


10.4403 


4.7769 


342.43 


9331-32 


no 


1 2 100 


1331000 


10.4881 


4.7914 


345.58 


9503-32 


III 


12321 


1367631 


10.5357 


4.8059 


348.72 


9676.89 


112 


12544 


1404928 


10.5830 


4.8203 


351.86 


9852.03 


113 


12769 


1442897 


10.6301 


4.8346 


355.00 


10028.7 


114 


12996 


1481544 


10.6771 


4.8488 


358.14 


10207.0 


115 


13225 


1520875 


10.7238 


4.8629 


361.28 


10386.9 


116 


13456 


1560896 


10.7703 


4.8770 


364.42 


10568.3 


117 


13689 


1601613 


10.8167 


4.8910 


367.57 


10751-3 


118 


13924 


1643032 


10.8628 


4.9049 


370.71 


10935-9 


119 


14161 


1 685 1 59 


10.9087 


4.9187 


373.85 


11122.0 


120 


14400 


1728000 


10.9545 


4.9324 


376.99 


II309.7 



SQUARES, CUBES, ETC. 



833 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
AND Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


121 


1 4641 


I7;?i56i 


11.0000 


4.9461 


380.13 


1 1499.0 


122 


14884 


1815848 


11.0454 


4.9597 


383.27 


II 689 .9 


123 


15129 


1860867 


11.0905 


4.9732 


386.42 


1 1882 .3 


124 


15376 


1906624 


II.1355 


4.9866 


389.56 


12076.3 


125 


15625 


1953125 


11-1803 


5.0000 


392.70 


12271.8 


126 


15876 


2000376 


11.2250 


5.0133 


395.84 


12469.0 


127 


16129 


2048383 


11.2694 


5.0265 


398.98 


12667.7 


128 


16384 


2097152 


II.3137 


5.0397 


402.12 


12868.0 


129 


1 6641 


2146689 


11.3578 


5.0528 


405.27 


13069.8 


130 


16900 


2197000 


1 1. 401 8 


5.0658 


408.41 


13273.2 


X3I 


17161 


2248091 


11.4455 


5.0788 


411.55 


13478.2 


132 


17424 


2299968 


1 1. 489 1 


5.0916 


414.69 


13684.8 


^33 


17689 


2352637 


11.5326 


5.1045 


417.83 


13892.9 


134 


17956 


2406104 


11.5758 


5.1172 


420.97 


14102.6 


135 


18225 


2460375 


1 1. 6190 


5.1299 


424.12 


14313.9 


136 


18496 


2515456 


1 1. 6619 


5.1426 


427.26 


14526.7 


137 


18769 


2571353 


11.7047 


5.1551 


430.40 


14741.I 


138 


19044 


2628072 


11.7473 


5.1676 


433.54 


14957.I 


139 


19321 


2685619 


11.7898 


5.1801 


436.68 


15174.7 


140 


19600 


2744000 


11.8322 


5.1925 


439.82 


15393.8 


141 


19881 


2803221 


11.8743 


5.2048 


442.96 


15614.5 


142 


20164 


2863288 


1 1. 9164 


5.2171 


446.11 


15836.8 


143 


20449 


2924207 


11.9583 


5.2293 


449.25 


16060.6 


144 


20736 


2985984 


12.0000 


5.2415 


452.39 


16286.0 


145 


21025 


3048625 


12.0416 


5.2536 


455.53 


16513.O 


146 


21316 


3112136 


12.0830 


5.2656 


458.67 


16741.5 


147 


21609 


3176523 


12.1244 


5.2776 


461.81 


16971.7 


148 


21904 


3241792 


12.1655 


5.2896 


464.96 


17203.4 


149 


22201 


3307949 


12.2066 


5.3015 


468.10 


17436.6 


150 


22500 


3375000 


12.2474 


5.3133 


471.24 


17671.5 


151 


22801 


3442951 


12.2882 


5.3251 


474.38 


17907.9 


152 


23104 


35 II 808 


12.3288 


5.3368 


477.52 


18145.8 


153 


23409 


3581577 


12.3693 


5.3485 


480.66 


18385.4 


154 


23716 


3652264 


12.4097 


5.3601 


483.81 


18626.5 


155 


24025 


3723875 


12.4499 


5.3717 


486.95 


18869.2 


156 


24336 


3796416 


12.4900 


5.3832 


490.09 


19II34 


157 


24649 


3869893 


12.5300 


5.3947 


493.23 


19359.3 


158 


24964 


3944312 


12.5698 


5.4061 


496.37 


19606.7 


159 


25281 


4019679 


12.6095 


5.4175 


499.51 


19855-7 


160 


25600 


4096000 


12.6491 


5.4288 


502.65 


20106.2 



834 



GENERAL TABLES AND FORMULA 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
AND Circular Areas of Nos. from i to 520 



TSIrk 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


INO. 


Circum. 


Area 


161 


25921 


4173281 


12.6886 


5.4401 


505.80 


20358.3 


162 


26244 


4251528 


12.7279 


5-4514 


508.94 


20612.0 


163 


26569 


4330747 


12.7671 


5.4626 


512.08 


20867.2 


164 


26896 


4410944 


12.8062 


5-4737 


515.22 


21124.I 


165 


27225 


4492125 


12,8452 


5.4848 


518.36 


21382.5 


166 


27556 


4574296 


12.8841 


5-4959 


521.50 


21642.4 


167 


27889 


4657463 


12.9228 


5-5069 


524.65 


21904.0 


168 


28224 


4741632 


12.9615 


5-5178 


527.79 


22167. 1 


169 


28561 


4826809 


13.0000 


5-5288 


530.93 


22431.8 


170 


28900 


4913000 


13.0384 


5-5397 


534.07 


22698.0 


171 


29241 


50002 II 


13.0767 


5-5505 


537-21 


22965.8 


172 


29584 


5088448 


13.1149 


5-5613 


540.35 


23235.2 . 


173 


29929 


5177717 


13-1529 


5-5721 


543-50 


23506.2 


174 


30276 


5268024 


13.1909 


5-5828 


546.64 


23778.7 


175' 


30625 


5359375 


13.2288 


5-5934 


549.78 


24052.8 


176 


30976 


5451776 


13.2665 


5-6041 


552.92 


24328.5 


177 


31329 


5545233 


13-3041 


5-6147 


556.06 


24605.7 


178 


31684 


5639752 


13-3417 


5-6252 


559.20 


24884.6 


179 


32041 


5735339 


13-3791 


5-6357 


562.35 


25164.9 


180 


32400 


5832000 


13.4164 


5.6462 


565.49 


25446.9 


181 


32761 


5929741 


13-4536 


5-6567 


568.63 


25730.4 


182 


33124 


6028568 


13.4907 


5-6671 


571-77 


26015.5 


183 


33489 


6128487 


13-5277 


5-6774 


574.91 


26302.2 


184 


33856 


6229504 


13-5647 


5-6877 


578.05 


26590.4 


185 


34225 


6331625 


13.6015 


5.6980 


581.19 


26880.3 


186 


34596 


6434856 


13.6382 


5-7083 


584.34 


27171.6 


187 


34969 


6539203 


13.6748 


5.7185 


587.48 


27464.6 


188 


35344 


6644672 


13-7113 


5.7287 


590.62 


27759.1 


189 


35721 


6751269 


13-7477 


5-7388 


593.76 


28055.2 


190 


36100 


6859000 


15.7840 


5.7489 


596.90 


28352.9 


191 


36481 


6967871 


13.8203 


5.7590 


600.04 


28652.1 


192 


36864 


7077888 


13.8564 


5-7690 


603.19 


28952.9 


193 


37249 


7189057 


13.8924 


5-7790 


606.33 


29255-3 


194 


37636 


7301384 


13.9284 


5.7890 


609.47 


29559.2 


195 


38025 


7414875 


13.9642 


5.7989 


612.61 


29864.8 


196 


38416 


7529536 


14.0000 


5.8088 


615.75 


30171.9 


197 


38809 


7645373 


14.0357 


5.8186 


618.89 


30480.5 


198 


39204 


7762392 


14.0712 


5.8285 


622.04 


30790.7 


199 


39601 


7880599 


14.1067 


5.8383 


625.18 


31102.6 


200 


40000 


8000000 


14.1421 


5.8480 


628.32 


31415.9 



SQUARES, CUBES, ETC. 



83s 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 




AND Circular Areas of 


NOS. FROM I TO 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


201 


40401 


8120601 


14.1774 


5.8578 


631.46 


31730.9 


202 


40804 


8242408 


14.2127 


5.8675 


634.60 


32047.4 


203 


41209 


8365427 


14.2478 


5.8771 


637.74 


32365.5 


204 


41616 


8489664 


14.2829 


5.8868 


640.89 


32685.1 


205 


42025 


8615125 


14.3178 


5.8964 


644.03 


33006.4 


206 


42436 


8741816 


14.3527 


5.9059 


647.17 


33329.2 


207 


42849 


8869743 


14.3875 


5.9155 


650.31 


33653-5 


208 


43264 


8998912 


14.4222 


5.9250 


653.45 


33979.5 


209 


43681 


9129329 


14.4568 


5.9345 


656.59 


34307.0 


210 


44100 


9261000 


14.4914 


5.9439 


659.73 


34636.1 


211 


44521 


9393931 


14.5258 


5.9533 


662.88 


34966.7 


212 


44944 


9528128 


14.5602 


5.9627 


666.02 


35298.9 


213 


45369 


9663597 


14.5945 


5.9721 


669.16 


35632.7 


214 


45796 


9800344 


14.6287 


5.9814 


672.30 


35968.1 


215 


46225 


9938375 


14.6629 


5.9907 


675.44 


36305-0 


216 


46656 


10077696 


14.6969 


6.0000 


678.58 


36643.5 


217 


47089 


10218313 


14.7309 


6.0092 


681.73 


36983.6 


218 


47524 


10360232 


14.7648 


6.0185 


684.87 


37325.3 


219 


47961 


10503459 


14.7986 


6.0277 


688.01 


37668.5 


220 


48400 


10648000 


14.8324 


6.0368 


691.15 


38013.3 


221 


48841 


10793861 


14.8661 


6.0459 


694.29 


38359.6 


222 


49284 


10941048 


14.8997 


6.0550 


697.43 


38707.6 


223 


49729 


I 1089567 


14.9332 


6.0641 


700.58 


39057.1 


224 


50176 


11239424 


14.9666 


6.0732 


703.72 


39408.1 


225 


50625 


I 1390625 


15.0000 


6.0822 


706.86 


39760.8 


226 


51076 


11543176 


15-0333 


6.0912 


710.00 


401 15.0 


227 


51529 


I 1697083 


15.0665 


6.1002 


713.14 


40470.8 


228 


51984 


11852352 


15.0997 


6.IO91 


716.28 


40828.1 


229 


52441 


12008989 


15.1327 


6.I180 


719.42 


41187.1 


230 


52900 


I 2 167000 


15.1658 


6.1269 


722.57 


41547.6 


231 


53361 


12326391 


15.1987 


6.1358 


725.71 


41909.6 


232 


53824 


12487168 


15.2315 


6.1446 


728.85 


42273.3 


^?>2> 


54289 


12649337 


15.2643 


6.1534 


731.99 


42638.5 


234 


54756 


12812904 


15.2971 


6.1622 


735.13 


43005.3 


235 


55225 


12977875 


15.3297 


6.1710 


738.27 


43373.6 


236 


55696 


13144256 


15.3623 


6.1797 


741.42 


43743.5 


237 


56169 


13312053 


15.3948 


6.1885 


744.56 


441 15.0 


238 


56644 


13481272 


15.4272 


6.1972 


747.70 


44488.1 


239 


57121 


13651919 


15.4596 


6.2058 


750.84 


44862.7 


240 


57600 


13824000 


15.4919 


6.2145 


753.98 


45238.9 



836 



GENERAL TABLES AND FORMULAE 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 




AND Circular Areas of Nos. from i to 520 


"NTn 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


INO. 


Circum. 


Area 


241 


58081 


13997521 


15.5242 


6.2231 


757.12 


45616.7 


242 


58564 


14172488 


15.5563 


6.2317 


760.27 


45996.1 


243 


59049 


14348907 


15.5885 


6.2403 


763.41 


46377.0 


244 


59536 


14526784 


15.6205 


6.2488 


766.55 


46759.5 


245 


60025 


14706125 


15.6525 


6.2573 


769.69 


47143.5 


246 


60516 


14886936 


15.6844 


6.2658 


772.83 


47529.2 


247 


61009 


15069223 


15.7162 


6.2743 


775.97 


47916.4 


248 


61504 


15252992 


15.7480 


6.2828 


779.12 


48305.1 


249 


62001 


15438249 


15.7797 


6.2912 


782.26 


48695.5 


250 


62500 


15625000 


15,8114 


6.2996 


785.40 


49087.4 


251 


63001 


15813251 


15.8430 


6.3080 


788.54 


49480.9 


252 


63504 


16003008 


15.8745 


6.3164 


791.68 


49875.9 


253 


64009 


16194277 


15.9060 


6.3247 


794.82 


50272.6 


254 


64516 


16387064 


15.9374 


^-3330 


797.96 


50670.7 


255 


65025 


16581375 


15.9687 


6.3413 


8oi.li 


51070.5 


256 


65536 


16777216 


16.0000 


6.3496 


804.25 


51471.9 


257 


66049 


16974593 


16.0312 


6.3579 


807.39 


51874.8 


258 


66564 


17173512 


16.0624 


6.3661 


810.53 


52279.2 


259 


67081 


17373979 


16.0935 


6.3743 


813.67 


52685.3 


260 


67600 


17576000 


16.1245 


6.3825 


816.81 


53092.9 


261 


68121 


17779581 


16.1555 


6.3907 


819.96 


53502.1 


262 


68644 


17984728 


16.1864 


6.3988 


823.10 


53912.9 


263 


69169 


18191447 


16.2173 


6.4070 


826.24 


54325.2 


264 


69696 


18399744 


16.2481 


6.4151 


829.38 


54739.1 ; 


265 


70225 


18609625 


16.2788 


6.4232 


832.52 


55154.6 


266 


70756 


18821096 


16.3095 


6.4312 


835.66 


55571.6 


267 


71289 


19034163 


16.3401 


6.4393 


838.81 


55990.3 


268 


71824 


19248832 


16.3707 


6.4473 


841.95 


56410.4 


269 


72361 


19465 109 


16.4012 


6.4553 


845.09 


56832.2 


270 


72900 


19683000 


16.4317 


6.4633 


848.23 


57255.5 


271 


73441 


199025 II 


16.4621 


6.4713 


851.37 


57680.4 


272 


73984 


20123648 


16.4924 


6.4792 


854.51 


58106.9 


273 


74529 


20346417 


16.5227 


6.4872 


857.66 


58534.9 


274 


75076 


20570824 


16.5529 


6.4951 


860.80 


58964.6 


275 


75625 


20796875 


16.5831 


6.5030 


863.94 


59395.7 


276 


76176 


21024576 


16.6132 


6.5108 


867.08 


59828.5 


277 


76729 


21253933 


16.6433 


6.5187 


870.22 


60262.8 


278 


77284 


21484952 


16.6733 


6.5265 


873.36 


60698.7 


279 


77841 


21717639 


16.7033 


6.5343 


876.50 


61136.2 


280 


78400 


21952000 


. 16.7332 


6.5421 


879.65 


61575.2 1 

















SQUARES, CUBES, ETC. 



837 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
AND Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


281 
282 
283 
284 
285 


78961 

79524 
80089 
80656 
81225 


22188041 
22425768 
22665187 
22906304 
23149125 


16.7631 
16.7929 
16.8226 
16.8523 
16.8819 


6.5499 

6.5577 
6.5654 
6.5731 
6.5808 


882.79 

885.93 
889.07 
892.21 
895-35 


62015.8 
62458.0 
62901.8 

63347.1 
63794.0 


286 
287 
288 
289 
290 


81796 
82369 
82944 

83521 
84100 


23393656 

23639903 
23887872 

24137569 
24389000 


16.9115 
16.9411 
16.9706 
17.0000 
17.0294 


6.5885 
6.5962 
6.6039 
6.6115 
6.6191 


898.50 
901.64 
904.78 
907.92 
911.06 


64242.4 
64692.5 
65144.1 

65597-2 
66052.0 


291 
292 

293 
294 

295 


84681 
85264 
85849 
86436 
87025 


24642171 
24897088 

25153757 
25412184 

25672375 


17.0587 
17.0880 
17.1172 
17.1464 
17.1756 


6.6267 

6.6343 
6.6419 
6.6494 
6.6569 


914.20 

917-35 
920.49 
923.63 
926.77 


66508.3 
66966.2 
67425.6 
67886.7 

68349.3 


296 
297 
298 
299 
300 


87616 
88209 
88804 
89401 
90000 


25934336 
26198073 
26463592 
26730899 
27000000 


17.2047 

17-2337 
17.2627 
17.2916 
17-3205 


6.6644 
6.6719 
6.6794 
6.6869 
6.6943 


929.91 

933-05 
936.19 

939-34 
942.48 


68813.5 
69279.2 

69746.5 
70215.4 
70685.8 


301 


90601 
91204 
91809 
92416 
93025 


27270901 
27543608 
27818127 
28094464 
28372625 


17-3494 


6.7018 


945-62 
948.76 
951.90 

955-04 
958.19 


71157.9 


302 

304 
305 


17.3781 
17.4069 
17-4356 
17.4642 


6.7092 
6.7166 
6.7240 
6.7313 


71631.5 
72106.6 

72583.4 
73061.7 


306 
307 

308 

309 
310 


93636 

94249 

. 94864 

' 95481 

96100 


286*52616 

28934443 
29218112 
29503629 
29791000 


17.4929 
17-5214 
17-5499 
17-5784 
17.6068 


6.7387 
6.7460 

6.7533 
6.7606 
6.7679 


961.33 
964-47 
967.61 

970.75 
973-89 


73541.5 
74023.0 
74506.0 
74990.6 
75476.8 


311 
312 

313 
314 
315 


96721 

97344 
97969 
98596 
99225 


30080231 
30371328 
30664297 
30959144 
31255875 


17.6352 
17.6635 
17.6918 
17.7200 
17.7482 


6.7752 
6.7824 

6.7897 
6.7969 
6.8041 


977-04 
980.18 

983.32 
986.46 
989.60 


75964.5 
76453.8 
76944.7 

77437.1 
77931.I 


316 
317 

318 

319 
320 


99856 
100489 
101124 
101761 
102400 


31554496 
31855013 
32157432 
32461759 
32768000 


17.7764 
17.8045 
17.8326 
17.8606 
17.8885 


6.8113 
6.8185 
6.8256 
6.8328 
6.8399 


992.74 
995.88 

999-03 
1002.20 
1005.30 


78426.7 

78923.9 
79422.6 
79922.9 
80424.8 



838 



GENERAL TABLES AND FORMULA 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
AND Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


321 


103041 


33076161 


17.9165 


6.8470 


1008.5 


80928.2 


322 


103684 


33386248 


17.9444 


6.8541 


1011.6 


81433-2 


323 


104329 


33698267 


17.9722 


6.8612 


1014.7 


81939-8 


324 


104976 


34012224 


18.0000 


6.8683 


1017.9 


82448.0 


325 


105625 


34328125 


18.0278 


6-^753 


1021.0 


82957-7 


326 


106276 


34645976 


18.0555 


6.8824 


1024.2 


83469.0 


327 


106929 


34965783 


18.0831 


6.8894 


1027.3 


83981.8 


328 


107584 


35287552 


18.II08 


6.8964 


1030.4 


84496.3 


329 


108241 


35611289 


18.1384 


6.9034 


1033.6 


85012.3 


330 


108900 


35937000 


18.1659 


6.9104 


1036.7 


85529-9 


33^ 


109561 


36264691 


18.1934 


6.9174 


1039.9 


86049.0 


332 


IIO224 


36594368 


18.2209 


6.9244 


1043.0 


86569.7 


333 


I 10889 


36926037 


18.2483 


6.9313 


1046.2 


87092.0 


334 


II1556 


37259704 


18.2757 


6.9382 


1049.3 


87615.9 


335 


I12225 


37595375 


18.3030 


6.9451 


1052.4 


88141.3 


336 


I12896 


37933056 


18.3303 


6.9521 


1055-6 


88668.3 


337 


II3569 


38272753 


18.3576 


6.9589 


1058.7 


89196.9 


33^ 


I14244 


38614472 


18.3848 


6.9658 


1061.9 


89727.0 


339 


I14921 


38958219 


18.4120 


6.9727 


1065.0 


90258.7 


340 


I I 5600 


39304000 


18.4391 


6.9795 


1068.1 


90792.0 


341 


I16281 


39651821 


18.4662 


6.9864 


1071.3 


91326.9 


342 


I 16964 


40001688 


18.4932 


6.9932 


1074.4 


91863.3 


343 


1 1 7649 


40353607 


18.5203 


7.0000 


1077.6 


92401.3 


344 


I18336 


40707584 


18.5472 


7.0068 


1080.7 


92940.9 


345 


I19025 


41063625 


18.5742 


7.0136 


1083.8 


93482.0 


346 


I19716 


41421736 


18.601 1 


7.0203 


'1087.0 


94024.7 


347 


120409 


41781923 


18.6279 


7.0271 


1090. 1 


94569.0 


348 


121104 


42144192 


18.6548 


7-0338 


1093-3 


95114.9 


349 


121801 


42508549 


18.6815 


7 .0406 


1096.4 


95662.3 


350 


122500 


42875000 


18.7083 


7 -0473 


1099.6 


962 1 1. 3 


351 


123201 


43243551 


18.7350 


7.0540 


1102.7 


96761.8 


352 


123904 


43614208 


18.7617 


7.0607 


1 105.8 


97314.0 


353 


124609 


43986977 


18.7883 


7.0674 


1 109.0 


97867.7 


354 


125316 


44361864 


18.8149 


7.0740 


1112.1 


98423.0 


355 


126025 


44738875 


18.8414 


7.0807 


III5-3 


98979.8 


356 


126736 


45118016 


18.8680 


7.0873 


1118.4 


99538.2 


357 


127449 


45499293 


18.8944 


7.0940 


I 12 I. 5 


100098 


358 


128164 


45882712 


18.9209 


7.1006 


1124.7 


100660 


359 


128881 


46268279 


18.9473 


7.1072 


1127.8 


IO1223 


360 


129600 


46656000 


18.9737 


7.1138 


1131.0 


101788 



SQUARES, CUBES, ETC. 



839 



Squares, Cubes, Square Roots, Cube Roots, Circumferences 
AND Circular Areas of Nos. from i to 520 













Cmrrv 


No. 


Square 


Cube 


Sq. Root 


Cube Root 






Circum. 


Area 


361 


130321 


47045881 


19.0000 


7.1204 


IT34.I 


102354 


362 


131044 


47437928 


19.0263 


7.1269 


^^37-3 


102922 


363 


131769 


47832147 


19.0526 


7-1335 


1 1 40 .4 


103491 


364 


132496 


48228544 


19.0788 


7.1400 


1143-5 


104062 


365 


133225 


48627125 


19.1050 


7.1466 


1146.7 


104635 


366 


133956 


49027896 


19.1311 


7-1531 


1 149.8 


105209 


367 


134689 


49430863 


19.1572 


7-1596 


1153-0 


105785 


368 


135424 


49836032 


19-1833 


7.1661 


1156.1 


106362 


369 


136161 


50243409 


19.2094 


7.1726 


1159.2 


106941 


310 


136900 


50653000 


19-2354 


7.1791 


1 162 .4 


107521 


37^ 


137641 


51064811 


19.2614 


7-1855 


1165.5 


108103 


372 


138384 


51478848 


19.2873 


7.1920 


1 1 68.7 


108687 


373 


139129 


51895117 


19.3132 


7.1984 


1171.8 


109272 


374 


139876 


52313624 


19-3391 


7.2048 


1175.0 


109858 


375 


140625 


52734375 


19.3649 


7.2112 


1178.1 


I 10447 


376 


141376 


53157376 


19.3907 


7.2177 


1181.2 


IIIO36 


377 


142129 


53582633 


19.4165 


7.2240 


1 184.4 


II1628 


378 


142884 


54010152 


19.4422 


7.2304 


1187.5 


II222I 


379 


143641 


54439939 


19.4679 


7-2368 


1190.7 


II2815 


380 


144400 


54872000 


19.4936 


7.2432 


1193.8 


II34II 


^^0' 


145161 


55306341 


19.5192 


7-2495 


1196.9 


I 14009 


382 


145924 


55742968 


19.5448 


7-2558 


1200.1 


I 14608 


3^3 


146689 


56181887 


19.5704 


7.2622 


1203.2 


II5209 


384 


147456 


56623104 


19-5959 


7.2685 


1206.4 


II5812 


3^5 


148225 


57066625 


19.6214 


7.2748 


1209.5 


I16416 


386 


148996 


57512456 


19.6469 


7.2811 


1212.7 


II702I 


^^ol 


149769 


57960603 


19.6723 


7.2874 


1215.8 


1 1 7628 


388 


150544 


58411072 


19.6977 


7-2936 


1218.9 


I18237 


i 389 


151321 


58863869 


19.7231 


7.2999 


1222. 1 


I 18847 


390 


152100 


59319000 


19.7484 


7.3061 


1225.2 


I 19459 


391 


152881 


59776471 


19-7737 


7-3124 


1228.4 


120072 


392 


153664 


60236288 


19.7990 


7.3186 


1231-5 


120687 


' 393 


154449 


60698457 


19.8242 


7-3248 


1234.6 


I21304 


, 394 


155236 


61 162984 


19.8494 


7-3310 


1237.8 


I21922 


i 395 


156025 


61629875 


19.87^46 


7.3372 


1240.9 


122542 


; 396 


156816 


62099136 


19.8997 


7.3434 


1244.1 


I23163 


1 397 


157609 


62570773 


19.9249 


7.3496 


1247.2 


123786 


• 398 


158404 


63044792 


19.9499 


7.3558 


1250.4 


I244IO 


399 


159201 


63521199 


19.9750 


7.3619 


1253.5 


125036 


: 400 


160000 


64000000 


20.0000 


7.3684 


1256.6 


125664 


' 















840 



GENERAL TABLES AND FORMULA 



Squares, Cubes, Square Roots, Cube Roots. Circumferences, 
AND Circular Areas of Nos. from i to 520 



No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


401 


I 6080 I 


64481 201 


20.0250 


7-3742 


1259.8 


126293 


402 


I 61 604 


64964808 


20.0499 


7.3803 


1262.9 


126923 


403 


162409 


65450827 


20.0749 


7.3864 


1266. 1 


127556 


404 


163216 


65939264 


20.0998 


7.3925 


1269.2 


128190 


405 


164025 


66430125 


20.1246 


7.3986 


1272.3 


128825 


406 


164836 


66923416 


20.1494 


7.4047 


1275.5 


129462 


407 


165649 


67419143 


20.1742 


7.4108 


1278.6 


130100 


408 


I 66464 


67917312 


20.1990 


7.4169 


1281.8 


130741 


409 


167281 


68417929 


20.2237 


7.4229 


1284.9 


131382 


410 


168100 


68921000 


20.2485 


7.4290 


1288.1 


132025 


411 


I 6892 I 


69426531 


20.2731 


7.4350 


1291.2 


132670 


412 


169744 


69934528 


20.2978 


7.4410 


1294.3 


133317 


413 


170569 


70444997 


20.3224 


7.4470 


1297.5 


133965 


414 


171396 


70957944 


20.3470 


7.4530 


1300.6 


134614 


415 


172225 


71473375 


20.3715 


7.4590 


1303.8 


135265 


416 


173056 


71991296 


20.3961 


7.4650 


1306.9 


135918 


^'^ 


173889 


72511713 


20.4206 


7.4710 


1310.O 


136572 


418 


174724 


73034632 


20.4450 


7.4770 


1313.2 


137228 


419 


175561 


73560059 


20.4695 


7.4829 


1316.3 


137885 


420 


176400 


74088000 


20.4939 


7.4889 


1319.5 


138544 


421 


177241 


74618461 


20.5183 


7.4948 


1322.6 


139205 


422 


178084 


75151448 


20.5426 


7.5007 


1325.8 


139867 


423 


178929 


75686967 


20.5670 


7.5067 


1328.9 


140531 


424 


179776 


76225024 


20.5913 


7.5126 


1332.0 


141196 


425 


180625 


76765625 


20.6155 


7.5185 


1335.2 


141863 


426 


181476 


77308776 


20.6398 


7.5244 


1338.3 


I42531 


427 


182329 


77854483 


20.6640 


7.5302 


1341.5 


143201 


428 


183184 


78402752 


20.6882 


7.5361 


1344.6 


143872 


429 


I 8404 I 


78953589 


20.7123 


7.5420 


1347.7 


144545 , 


430 


184900 


79507000 


20.7364 


7.5478 


1350.9 


145220 


431 


185761 


80062991 


20.7605 


7.5537 


1354.0 


145896 


432 


186624 


80621568 


20.7846 


7.5595 


1357.2 


146574 ' 


433 


187489 


81182737 


20.8087 


7.5654 


1360.3 


147254 


434 


188356 


81746504 


20.8327 


7.5712 


1363-5 


147934 


435 


189225 


82312875 


20.8567 


7.5770 


1366.6 


148617 


436 


190096 


82881856 


20.8806 


7.5828 


1369.7 


149301 


437 


190969 


83453453 


20.9045 


7.5886 


1372.9 


149987 


438 


191844 


84027672 


20.9284 


7.5944 


1376.0 


150674 


439 


192721 


84604519 


20.9523 


7.6001 


1379.2 


151363 j 


440 


193600 


85184000 


20.9762 


7.6059 


1382.3 


152053 1 



SQUARES, CUBES, ETC. 



841 



Squares, Cubes 


;, Square Roots, Cube Roots, Circumferences 




AND Circular Areas of Nos. from i to 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. l 


Area 


441 


194481 


85766121 


2 1 .0000 


7.6117 


1385-4 


152745 


442 


195364 


86350888 


21.0238 


7.6174 


1388.6 


153439 


443 


196249 


86938307 


21.0476 


7.6232 


1391-7 


154134 


444 


197136 


87528384 


21.0713 


7.6289 


1394.9 


154830 


445 


198025 


88121125 


21.0950 


7.6346 


1398.0 


155528 


446 


198916 


88716536 


21.I187 


7.6403 


1401.2 


156228 


447 


199809 


89314623 


21.1424 


7.6460 


1404.3 


156930 


448 


200704 


89915392 


21.1660 


7-6517 


1407.4 


157633 


449 


201601 


90518849 


21.1896 


7.6574 


1410.6 


158337 


450 


202500 


91125000 


21.2132 


7.6631 


1413.7 


159043 


451 


203401 


91733851 


21.2368 


7.6688 


1416.9 


159751 


452 


204304 


92345408 


21.2603 


7.6744 


1420.0 


160460 


453 


205209 


92959677 


21.2838 


7.6801 


1423.I 


161171 


454 


206116 


93576664 


21.3073 


7.6857 


1426.3 


161883 


455 


207025 


94196375 


21.3307 


7.6914 


1429.4 


162597 


456 


207936 


94818816 


21.3542 


7.6970 


1432.6 


163313 


, 457 


208849 


95443993 


21.3776 


7.7026 


1435-7 


164030 


' 458 


209764 


96071912 


2 1 .4009 


7.7082 


1438.9 


164748 


459 


210681 


96702579 


21.4243 


7.7138 


1442.0 


165468 


460 


2xi6oo 


97336000 


21.4476 


7-7194 


1445-I 


166190 


461 


2I252I 


97972181 


21.4709 


7.7250 


1448.3 


166914 


\ 462 


213444 


98611128 


21.494^2 


7.7306 


145 1 -4 


167639 


463 


214369 


99252847 


21.5174 


7.7362 


1454-6 


168365 


, 464 


215296 


99897344 


21.5407 


7.7418 


1457.7 


169093 


' 465 


216225 


100544625 


21.5639 


7-7473 


1460.8 


169823 


1 466 


2I7I56 


loi 194696 


21.5870 


7.7529 


1464.0 


170554 


467 


218089 


101847563 


21.6102 


7-7584 


1467.1 


171287 


s 468 


219024 


102503232 


21.6333 


7.7639 


1470.3 


172021 


i 469 


2I996I 


103161709 


21.6564 


7.7695 


1473.4 


172757 


i 470 


220900 


103823000 


21.6795 


7-7750 


1476.5 


173494 


\ 471 


22I84I 


104487111 


21.7025 


7-7805 


1479.7 


174234 


( 472 


222784 


105 I 54048 


21.7256 


7.7860 


1482.8 


174974 


i 473 


223729 


105823817 


21.7486 


7.7915 


1486.0 


175716 


^; 474 


224676 


106496424 


21.7715 


7-7970 


1489. 1 


176460 


\ 475 


225625 


107171875 


21.7945 


7-8025 


1492.3 


177205 


i 476 


226576 


107850176 


21.8174 


7.8079 


1495.4 


177952 


•J 477 


227529 


108531333 


21.8403 


7.8134 


1498.5 


178701 


1 478 


228484 


109215352 


21.8632 


7.8188 


1501.7 


179451 


1 479 


229441 


109902239 


21.8861 


7.8243 


1504.8 


180203 


1 480 


230400 


I 10592000 


21.9089 


7.8297 


1508.0 


180956 



842 


GENERAL TABLES AND FORMULA 




Squares, Cubes, Square 


Roots, Cube Roots, Circumferences 




AND Circular Areas of Nos. from i to 520 


No. 


Square 


Cube 


Sq. Root 


Cube Root 


Circle 


Circum. 


Area 


481 


231361 


II1284641 


21.9317 


7.8352 


1511.I 


181711 


482 


232324 


II1980168 


21.9545 


7.8406 


1514.3 


182467 


483 


233289 


I12678587 


21.9773 


7.8460 


1517.4 


183225 


484 


234256 


I 13379904 


22.0000 


7-8514 


1520.5 


183984 


485 


235225 


I14084125 


22.0227 - 


7.8568 


1523.7 


184745 


486 


236196 


I14791256 


22.0454 


7.8622 


1526.8 


185508 


487 


237169 


115501303 


22.0681 


7.8676 


1530.0 


186272 


488 


238144 


I16214272 


22.0907 


7.8730 . 


1533.I 


187038 


489 


239121 


I16930169 


22.1133 


7.8784 


1536.2 


187805 


490 


240100 


1 1 7649000 


22.1359 


7.8837 


1539.4 


188574 


491 


241081 


I18370771 


22.1585 


7.8891 


1542.5 


1-89345 


492 


242064 


I 19095488 


22.1811 


7.8944 


1545.7 


190117 


493 


243049 


I19823157 


22.2036 


7.8998 


1548.8 


190890 


494 


244036 


120553784 


22.2261 


7.9051 


1551.9 


19 I 665 


495 


245025 


121287375 


22.2486 


7.9105 


I555-I 


192442 


496 


246016 


122023936 


22.2711 


7.9158 


1558.2 


193221 


497 


247009 


122763473 


22.2935 


7.9211 


1561.4 


194000 


498 


248004 


123505992 


22.3159 


7.9264 


1564.5 


194782 


499 


249001 


124251499 


22.3383 


7.9317 


1567.7 


195565 


500 


250000 


125000000 


22.3607 


7.9370 


1570.8 


. 196350 


501 


251001 


125751501 


22.3830 


7.9423 


1573.9 


197136 


502 


252004 


126506008 


22.4054 


7.9476 


1577.1 


197923 


503 


253009 


127263527 


22.4277 


7.9528 


1580.2 


198713 


504 


254016 


128024064 


22.4499 


7.9581 


1583.4 


199504 


505 


255025 


128787625 


22.4722 


7.9634 


1586.5 


200296 


506 


256036 


129554216 


22.4944 


7.9686 


1589.7 


201090 


507 


257049 


130323843 


22.5167 


7.9739 


1592.8 


201886 


508 


258064 


131096512 


22.5389 


7.9791 


1595.9 


202683 


509 


259081 


131872229 


22.5610 


7.9843 


1599.1 


203482 


510 


260100 


132651000 


22.5832 


7.9896 


1602.2 


204282 


511 


261121 


13343 283 I 


22.6053 


7.9948 


1605.4 


205084 


512 


262144 


134217728 


22.6274 


8.0000 


1608.5 


205887 


513 


263169 


135005697 


22.6495 


8.0052 


1611.6 


206692 


514 


264196 


135796744 


22.6716 


8.0104 


1614.8 


207499 


515 


265225 


136590875 


22.6936 


8.0156 


1617.9 


208307 


516 


266256 


137388096 


22.7156 


8.0208 


1621.1 


209117 


517 


267289 


138188413 


22.7376 


8.0260 


1624.2 


209928 


518 


268324 


138991832 


22.7596 


8.03 1 1 


1627.3 


210741 


519 


269361 


139798359 


22.7816 


8.0363 


1630.5 


211556 


520 


270400 


140608000 


22.8035 


8.0415 


1633.6 


212372 














1 



TRIGONOMETRIC FORMULA 



843 



Table 72. Trigonometric Functions and the Solution of 

Triangles 



In the accompanying figure the trig- 
onometric functions of the angle A 
between the lines B A and A C are 
as follows; 



sin A 


= BC 


cos A 


= AC 


tan A 


= EF 


cot A 


= G H 


sec A 


= AE 


cosec A 


= A H 


ex-sec A 


= B E 




In the right-angled triangle ABC 
let a equal the side B C opposite the 

angle A; let b equal the side A C opposite the angle B; let c 
equal A B, the side opposite the angle C 

Let C = 90° 

The following formulae apply to right-angled triangles: 



Angles. A+B+C = 180° 
A + B = 90° 

A = 90°- B 
B = 90° — ^ 



Sides, 



sin A — 


a 

C ' 

h 


Area 


cos A — 








c 


ah 
area = — 




d 


2 


tSiuA = 


T 





a = c sin ^ =5 tan A 

^ = V (c + 6) {c- h) 

b = c COS. A 



tan A 



b = \/ {c -\- a) (c — a) 

_ CL _ b 
sin A cos A 



= V ^2 + ^ 



Oblique Triangles. 

Note. Where an angle is 
more than 90° its sine, cosine, 
and tangent are equal to that 
of the angle (180° — the angle 
in question); that is, if the sine 
of 120° is desired take the sine 
of (180° - 120°) = 60°. 






\a 



^/ LetK=^rea ^ 




844 


GENERAL TABLES AND FORMULA 




Given 


Desired 


Formulae 




A,B,a 


C,b 


C — T^n. . ( i I RV h cin 7? 




sin A 






c, K 


^ • / ^ 1 r>\ r^ ^^ sin 5 sin C 




sin^ ^'"'" i --/»" 2 sin^ 


1 


A, a, b 


B,C 


sin B= ^^ b; C = i8o°- {A + B) 






c 


c = -; — r sin C 
sin ^ 

Two solutions are possible with B' as an acute angle 


i 
! 






and B as an obtuse angle 




C,a,b 


h{A+B) 


^{A+B) =90° - iC 


i 




h{A-B) 


tan J {A -B) = ^-^ tan \ {A + B) 
a -f- 






AB 


B = \{A+B)-\{A-B) 






c 


sin H^ + 5) 






K 


K == \ ab ^m. C 




a, b,c 


B 


In the following formula s = ^ (^ + ^ + c) 
sinM =i/(^-^H^-c) 






K 


V ac 




. „ 2 V ^ (-^ - ^) (^ - ^) (^ - c) 

sm 3 = 

ac 




K = V s{s -a) (s - b) {s - c) 





NATURAL TANGENTS AND CO-TANGENTS 845 











Table 73 


















P 1 


2° 1 


3 







t 


Tan. 


Co-tan. 


Tan. ] 


Co-tan. 


Tan. 


Co -TAN. 


Tan. 


Co-tan. 


/ 





.00000 


Infinite. 


.01746 


57.2900 


.03492 


28.6363 


.05241 


19.0811 


60 


I 


.00029 


3437.750 


.01775 


56.3506 


.03521 


28.3994 


.05270 


18.9755 


59 


2 


.00058 


1718.870 


.01804 


55.4415 


.03550 


28.1664 


.05299 


18.8711 


58 


3 


.00087 


1145.920 


.01833 


54-5613 


.03579 


27.9372 


.05328 


18.7678 


57 


4 


.00116 


859.436 


.01862 


53-7086 


.03609 


27.7117 


.05357 


18.6656 


56 


5 


.00145 


687.549 


.01891 


52.8821 


.03638 


27.4899 


•05387 


18.5645 


55 


6 


.00175 


572.957 


.01920 


52.0807 


.03667 


27.2715 


.05416 


18.464s 


54 


7 


.00204 


491.106 


.01949 


51.3032 


.03696 


27.0566 


.05445 


18.3655 


53 


8 


.00233 


429.718 


.01978 


50.5485 


.03725 


26.8450 


.05474 


18.2677 


52 


9 


.00262 


381.971 


.02007 


49.8157 


.03754 


26.6367 


.05503 


18.1708 


51 


10 


.00291 


343-774 


.02036 


49.1039 


.03783 


26.4316 


.05533 


18.0750 


50 


II 


.00320 


312.521 


.02066 


48.4121 


.03812 


26.2296 


•05562 


17.9802 


49 


12 


.00349 


286.478 


.02095 


47-7395 


.03842 


26.0307 


.05591 


17.8863 


48 


13 


.00378 


264.441 


.02124 


47-0853 


.03871 


25.8348 


.05620 


17-7934 


47 


14 


.00407 


245-552 


.02153 


46.4489 


.03900 


25.6418 


.05649 


17.7015 


46 


15 


.00436 


229.182 


.02182 


45-8294 


.03929 


25.4517 


.05678 


17.6106 


45 


16 


.00465 


214.858 


.02211 


45.2261 


.03958 


25.2644 


.05708 


17.5205 


44 


17 


.00495 


202.219 


.02240 


44-6386 


.03987 


25.0798 


.05737 


17.4314 


43 


18 


.00524 


190.984 


.02269 


44.0661 


.04016 


24-8978 


.05766 


17-3432 


42 


19 


.00553 


180.932 


.02298 


43-5081 


.04046 


24.7185 


.05795 


17-2558 


41 


20 


.00582 


171.885 


.02328 


42.9641 


.04075 


24.5418 


.05824 


17.1693 


40 


21 


.00611 


163.700 


.02357 


42-4335 


.04104 


24-3675 


.05854 


17.0837 


39 


22 


.00640 


156.259 


.02386 


41-9158 


.04133 


24.1957 


.05883 


16.9990 


38 


23 


.00669 


149.465 


.02415 


41.4106 


.04162 


24.0263 


.05912 


16.9150 


37 


24 


.00698 


143-237 


.02444 


40.9174 


.04191 


23-8593 


.05941 


16.8319 


36 


25 


.00727 


137-507 


.02473 


40-4358 


.04220 


23-6945 


.05970 


16.7496 


35 


26 


.00756 


132.219 


.02502 


39-9655 


.04250 


23-5321 


.05999 


16.6681 


34 


27 


.00785 


127.321 


•02531 


39.5059 


.04279 


23-3718 


.06029 


16.5874 


33 


28 


.00814 


122.774 


.02560 


39.0568 


.04308 


23-2137 


.06058 


16.5075 


32 


29 


.00844 


118.540 


.02589 


38-6177 


•04337 


23-0577 


.06087 


16.4283 


31 


30 


.00873 


114-589 


.02619 


38-1885 


.04366 


22.9038 


.06116 


16.3499 


30 


31 


.00902 


110.892 


.02648 


37^7686 


.04395 


22.7519 


.06145 


16.2722 


29 


32 


.00931 


107.426 


.02677 


37-3579 


.04424 


22.6020 


.06175 


16.1952 


28 


33 


.00960 


104.171 


.02706 


36.9560 


.04454 


22.4541 


.06204 


16.1190 


27 


34 


.00989 


101.107 


.02735 


36.5627 


.04483 


22.3081 


.06233 


16.0435 


26 


35 


.01018 


98.2179 


.02764 


36.1776 


.04512 


22.1640 


.06262 


15-9687 


25 


36 


.01047 


95-4895 


.02793 


35.8006 


.04541 


22.0217 


.06291 


15-8945 


24 


37 


.01076 


92.9085 


.02822 


35-4313 


•04570 


21.8813 


.06321 


15.8211 


23 


38 


.01105 


90.4633 


.02851 


35-0695 


.04599 


21.7426 


.06350 


15-7483 


22 


39 


.01135 


88.1436 


.02881 


34-7151 


.04628 


21.6056 


.06379 


15.6762 


21 


40 


.01164 


85-9398 


.02910 


34.3678 


.04658 


21.4704 


.06408 


15.6048 


20 


41 


.01193 


83-8435 


.02939 


34-0273 


.04687 


21.3369 


.06437 


15-5340 


19 


42 


.01222 


81.8470 


.02968 


33-6935 


.04716 


21.2049 


.06467 


15-4638 


18 


43 


.01251 


79-9434 


.02997 


33.3662 


.04745 


21.0747 


.06496 


15-3943 


17 


44 


.01280 


78.1263 


.03026 


33-0452 


•04774 


20.9460 


.06525 


15-3254 


16 


45 


.01309 


76.3900 


.03055 


32^7303 


.04803 


20.8188 


.06554 


15-2571 


15 


46 


.01338 


74.7292 


.03084 


32.4213 


.04832 


20.6932 


.06584 


15-1893 


14 


47 


.01367 


73-1390 


.03114 


32.1181 


.04862 


20.5691 


.06613 


15.1222 


13 


48 


.01396 


71-6151 


-03143 


31.8205 


.04891 


20.4465 


.06642 


^^'°V>1 


12 


49 


.01425 


70.1533 


.03172 


31.5284 


.04920 


20.3253 


.06671 


14.9898 


II 


50 


.01455 


68.7501 


.03201 


31.2416 


•04949 


20.2056 


.06700 


14.9244 


10 


51 


.01484 


67.4019 


.03230 


30.9599 


.04978 


20.0872 


.06730 


14-8596 


9 


52 


.01513 


66.1055 


.03259 


30.6833 


•05007 


19.9702 


.06759 


14-7954 


8 


53 


.01542 


64.8580 


.03288 


30.4116 


•05037 


19-8546 


.06788 


14.7317 


7 


54 


.01571 


63-6567 


•03317 


30.1446 


.05066 


19.7403 


.06817 


14.6685 


6 


55 


.01600 


62.4992 


.03346 


29.8823 


•05095 


19-6273 


.06847 


14-6059 


5 


56 


.01629 


61.3829 


.03376 


29.6245 


.05124 


19-5156 


.06876 


14-5438 


4 


57 


.01658 


60.3058 


.03405 


29.3711 


•05153 


19-4051 


.06905 


14-4823 


3 


58 


.01687 


59-2659 


.03434 


29.1220 


.05182 


19.2959 


.06934 


14.4212 


2 


f9 


.01716 


58.2612 


.03463 


28.8771 


.05212 


19.1879 


.06963 


14-3607 


I 


60 


.01746 


57.2900 


.03492 


28.6363 


.05241 


I9.081I 


.06993 


14-3007 





/ 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


1 




i 


w 


£ 


58° 


1 8 


70 


8 


;6° 





846 



GENERAL TABLES AND FORMULAE 



4« 5' 

Tan. Co-tan. Tan. ] Co-tan. 



.06993 
.07022 
.07051 
.07080 
.07110 
.07139 
.07168 
.07197 
.07227 
.07256 
.07285 

.07314 
.07344 
•07373 
.07402 
•07431 
.07461 
.07490 
.07519 
.07548 
•07578 
.07607 
•07636 
.07665 
.07695 
.07724 

•07753 
.07782 
.07812 
.07841 
.07870 
.07899 
.07929 
.07958 
.07987 
.08017 
.08046 
.08075 
.08104 
.08134 
.08163 
.08192 
.08221 
.08251 
.08280 
.08309 
.08339 
.08368 
.08-397 
.08427 
.08456 
.08485 
.08514 
.08544 
.08573 
.08602 
.08632 
.08661 
.08690 
.08720 
.08749 



4.3007 
4.2411 
4.1821 
4.123s 
4-0655 
4.0079 
3-9507 
3.8940 
3-8378 
3.7821 
3.7267 
3.6719 
3-6174 
3-5634 
3-5098 
3-4566 
3-4039 
3-3515 
3.2996 
3.2480 
3.1969 
3.1461 
3-0958 
3-0458 
2.9962 
2.9469 
2.8981 
2.8496 
2.8014 
2.7536 
2.7062 

2.6591 
2.6124 
2.5660 
2.5199 
2.4742 
2.4288 
2.3838 
2.3390 
2.2946 
2.2505 
2.2067 
2.1632 
2.1201 
2.0772 
2.0346 
1.9923 
1.9504 
1.9087 
1.8673 
1.8262 

1.7853 
1.7448 
1.7045 
1.6645 
1.6248 
1.5853 
1.5461 
1.5072 
1.4685 
1. 430 1 



Co-tan. Tan. 

85^ 



,08749 
.08778 
.08807 
.08837 
.08866 
.08895 
.08925 
.08954 
.08983 
.09013 
.09042 
.09071 
.09101 
.09130 
.09159 
.09189 
.09218 
.09247 
.09277 
.09306 
•0933s 

.09365 
.09394 
.09423 
.09453 
.09482 
.09511 
.09541 
.09570 
.09600 
.09629 
.09658 
.09688 
.09717 
.09746 
.09776 
.09805 
.09834 
.09864 
.09893 
.09923 

.09952 
,09981 

lOOII 

10040 
10069 
10099 
IOI28 
IOI58 
IOI87 
I02I6 
10246 
10275 
10305 
10334 
10363 
10393 

10422 
10452 
I048I 
I05IO 



1 1. 4301 
II.39I9 
11.3540 
11.3163 
11.2789 
II.24I7 

11.2048 

II.I68I 
II.I3I6 
11.0954 
11.0594 
11.0237 
10.9882 
10.9529 

10.9178 
10.8829 
10.8483 

10.8139 
10.7797 
10.7457 
I0.7II9 

10.6783 

10.6450 
I0.6II8 
10.5789 
10.5462 
10.5136 
10.4813 
10.4491 

10.4172 

10.3854 

10.3538 
10.3224 
10.2913 
10.2602 
10.2294 

10.1988 
10.1683 
IO.I38I 

10.1080 
10.0780 
10.0483 
10.0187 
9.98931 

9.96007 

9.93IOI 

9.902II 

9-87338 

9.84482 
9.8I64I 

9.78817 

9.76009 

9.73217 
9-70441 
9.67680 

9-64935 

9.62205 

9.59490 
9.56791 

9.54106 

9-51436 



Co-tan. Tan. 

84° 



6 





7 





Tan. 


Co-tan. 


Tan. 


Co-tan. 


.10510 


9-51436 


.12278 


8.1443s 


.10540 


9.48781 


.12308 


8.12481 


.10569 


9.46141 


.12338 


8.10536 


.10599 


9-43515 


.12367 


8.08600 


.10628 


9.40904 


.12397 


8.06674 


.10657 


9-38307 


.12426 


8.04756 


.10687 


9-35724 


.12456 


8.02848 


.10716 


9-33154 


.12485 


8.00948 


.10746 


9-30599 


.12515 


7.99058 


.10775 


9.28058 


.12544 


7.97176 


.10805 


9-25530 


.12574 


7-95302 


.10834 


9.23016 


.12603 


7.93438 


.10863 


9.20516 


.12633 


7.91582 


.10893 


9.18028 


.12662 


7-89734 


.10922 


9.15554 


.12692 


7.8789s 


.10952 


9-13093 


.12722 


7.86064 


.10981 


9.10646 


.12751 


7.84242 


.IIOII 


9.082 1 1 


.12781 


7.82428 


.11040 


9.05789 


.12810 


7.80622 


.11070 


9-03379 


.12840 


7-78825 


. 1 1099 


9-00983 


.12869 


7.7703s 


.11128 


8.98598 


.12899 


7.75254 


.11158 


8.96227 


.12929 


7.73480 


.11187 


8.93867 


.12958 


7.71715 


.11217 


8.91520 


.12988 


7-69957 


.11246 


8.89185 


.13017 


7.68208 


.11276 


8.86862 


.13047 


7.66466 


.1130S 


8.84551 


.13076 


7-64732 


•11335 


8.82252 


.13106 


7-63005 


.11364 


8.79964 


.13136 


7.61287 


.11394 


8.77689 


•13165 


7-59575 


.11423 


8.75425 


.13195 


7.57872 


•11452 


8.73172 


.13224 


7.56176 


.11482 


8.70931 


.13254 


7-54487 


.11511 


8.68701 


.13284 


7.52806 


.11541 


8.66482 


.13313 


7-51132 


.11570 


8.64275 


.13343 


7-49465 


.11600 


8.62078 


.13372 


7.47806 


.11629 


8.59893 


.13402 


7.46154 


.11659 


8.57718 


.13432 


7.44509 


.11688 


8.55555 


.13461 


7.42871 


.11718 


8.53402 


.13491 


7.41240 


.11747 


8.51259 


.13521 


7.39616 


.11777 


8.49128 


.13550 


7.37999 


.11806 


8.47007 


.13580 


7-36389 


.11836 


8.44896 


.13609 


7-34786 


.11865 


8.42795 


.13639 


7-33190 


.11895 


8.40705 


.13669 


7.31600 


.11924 


8.38625 


.13698 


7.30018 


•11954 


8.36555 


.13728 


7.28442 


•I 1983 


8.34496 


.13758 


7.26873 


.12013 


8.32446 


.13787 


7.25310 


.12042 


8.30406 


.13817 


7-23754 


.12072 


8.28376 


.13846 


7.22204 


.12101 


8.26355 


.13876 


7.20661 


.12131 


8.24345 


.13906 


7.19125 


.12160 


8.22344 


.13935 


7.17594 


.12190 


8.20352 


.13965 


7.16071 


.12219 


8.18370 


.13995 


7.14553 


.12249 


8.16398 


.14024 


7.13042 


.12278 


8.14435 


.14054 


7-IIS37 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


8 


3° 


8: 


2° 



NATURAI. TANGENTS AND CO-TANGENTS 847 



8^ 
Tan. Co-tan. 



10^ 11° 

Tan. Co-tan. Tan. Co-tan. Tan. Co-tan. 



14054 
14084 
14113 
14143 
14173 
14202 
14232 
14262 
14291 
14321 
14351 
14381 
14410 
14440 
14470 
14499 
14529 
14559 
14588 
14618 
14648 
14678 
14707 
14737 
14767 
14796 
14826 
14856 
14886 
14915 
14945 

14975 
15005 
15034 
15064 
15094 
1 5124 

15153 
15183 
15213 
15243 
15272 
15302 

15362 
15391 
15421 

1 545 1 
15481 

15511 
15540 

15570 
15600 
15630 
15660 
15689 
15719 
15749 
15779 
15809 
15838 



7.11537 
7.10038 
7.08546 
7.07059 
7-05579 
7-04105 
7.02637 
7.01174 
6.99718 
6.98268 
6.96823 

6.95385 
6.93952 
6.92525 
6.91 104 
6.89688 
6.88278 
6-86874 
6.85475 
6.840S2 
6.82694 
6.81312 
6.79936 
6.78564 
6.77199 
6.75838 
6.74483 
6.73133 
6.71789 
6.70450 
6.69116 

6.67787 
6.66463 
6.65144 
6.63831 
6.62523 
6.61219 
6.59921 
6.58627 
6.57339 
6.56055 

6.54777 
6.53503 
6.52234 
6.50970 
6.49710 
6.48456 
6.47206 
6.45961 
6.44720 
6.43484 

6.42253 
6.41026 
6.39804 
6.38587 
6.37374 
6.36165 
6.34961 
6.33761 
6.32566 
6.31375 



.15838 
.15868 
.15898 
.15928 
.15958 
.15988 
.16017 
.16047 
.16077 
.16107 
.16137 
.16167 
.16196 
.16226 
.16256 
.16286 
.16316 
.16346 
.16376 
.16405 
.16435 
.16465 
.16495 
.16525 
.16555 
.16585 
.16615 
.16645 
.16674 
.16704 
.16734 
.16764 

.16794 
.16824 

.16854 
.16884 
.16914 
.16944 
.16974 
.17004 
•17033 
.17063 
.17093 
.17123 

.17153 
.17183 
.17213 
.17243 
.17273 
.17303 
.17333 
•17363 
.17393 
.17423 
.17453 
.17483 
.17513 
.17543 
.17573 
.17603 
.17633 



6.31375 
6.30189 
6.29007 
6.27829 
6.2665s 
6.25486 
6.24321 
6.23160 
6.22003 
6.20851 
6.19703 
6.18559 
6.17419 
6.16283 
6.15151 
6.14023 
6.12899 
6.11779 
6.10664 
6.09552 
6.08444 
6.07340 
6.06240 
6.05143 
6.04051 
6.02962 
6.01878 
6.00797 
5.99720 
5.98646 
5-97576 
5.96510 
5-95448 
5-94390 
5-93335 
5.92283 

5-91235 
5-90191 
5-89151 
5.88114 
5.87080 
5-86051 
5-85024 
5.84001 
5.82982 
5.81966 
5-80953 
5-79944 
5-78938 
5-77936 
5-76937 
5-75941 
5-74949 
5-73960 
5-72974 
5.71992 
5.71013 
5-70037 
■5.69064 
5.68094 
5.67128 



•17633 
.17663 
.17693 
.17723 
•17753 
•17783 
.17813 
•17843 
•17873 
.17903 

•17933 
•17963 
.17993 
.18023 
.18053 
.18083 
.18113 
.18143 
.18173 
.18203 
.18233 
.18263 
.18293 
.18323 
•18353 
.18383 
.18414 
.18444 
.18474 
.18504 
.18534 
.18564 
.18594 
.18624 
.18654 
.18684 
.18714 
.18745 
.18775 
.18805 
.18835 
.18865 
.18895 
.18925 
.18955 
.18986 
.19016 
.19046 
.19076 
.19106 
.19136 
.19166 
.19197 
.19227 
.19257 
.19287 
•19317 
•19347 
.19378 
.19408 
.19438 



5.67128 
5-66165 
5-65205 
5-64248 
5-63295 
5-62344 
5-61397 
5-60452 
5.59511 
5-58573 
5.57638 
5.56706 
5-55777 
5-54851 
5-53927 
5-53007 
5.52090 
5-51176 
5.50264 
5-49356 
5-48451 
5-47548 
5.46648 
S-45751 
5-44857 
5-43966 
5-43077 
5.42192 

5-41309 
5.40429 
5-39552 

5.38677 
5-37805 
5-36936 
5.36070 
5-35206 
5-34345 
5-33487 
5-32631 
5-31778 
5.30928 

5.30080 
5-29235 
5-28393 
5.27553 
5-26715 
5-25880 
5.25048 
5.24218 
5-23391 
5.22566 

5.21744 
5.20925 
5.20I07' 
5.19293 
5.18480 
5.17671 
5.16863 
5.16058 
5.15256 
5.14455 



19438 
19468 
19498 
19529 
19559 
19589 
19619 
19649 
19680 
19710 
19740 

19770 
19801 
19831 
19861 
19891 
19921 
19952 
19982 
20012 
20042 
20073 
20103 
20133 
.20164 
,20194 
20224 
20254 
20285 
20315 
20345 
20376 
20406 
20436 
20466 
20497 
20527 
20557 
20588 
20618 
20648 
20679 
20709 
20739 
.20770 
20800 
.20830 
20861 
.20891 
20921 
.20952 
20982 
21013 
21043 
21073 
,21104 
21134 
21164 
21195 
21225 
21256 



5.14455 
5.13658 
5.12862 
5.12069 
5.11279 
5.10490 
5.09704 
5.08921 
5-08139 
5.07360 
5.06584 
5.05809 
5.05037 
5.04267 
5-03499 
5-02734 
5.01971 
5.01210 
5.00451 
4.99695 
4.98940 

4.98188 
4.97438 
4.96690 
4.95945 
4-95201 
4.94460 
4.93721 
4.92984 
4.92249 
4.91516 

4.90785 
4.90056 
4.89330 
4.83605 
4.87882 
4.87162 
4.86444 
4-85727 
4-85013 
4.84300 

4-83590 
4.82882 
4-82175 
4.81471 
4.80769 
4.80068 
4-7937P 
4-78673 
4-77978 
4.77286 

4-76595 
4-75906 
4.75219 
4.74534 
4.73851 
4.73170 
4.72490 
4.71813 
4.71137 
4.70463 



Co-tan. Tan. Co-tan. Tan. 

81^ • 80° 



Co-tan. Tan. Co-tan. Tan. 
790 730 



848 



GENERAL TABLES AND FORMULA 





12° 


13° 


140 


15<> 




/ 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 





.21256 


4.70463 


.23087 


4-33148 


.24933 


4.01078 


.26795 


3.73205 


60 


I 


.21286 


4.69791 


.23117 


4-32573 


.24964 


4.00582 


.26826 


3.72771 


59 


2 


.21316 


4.69121 


.23148 


4.32001 


.24995 


4.0C086 


•26857 


3.72338 


58 


3 


.21347 


4.68452 


.23179 


4-31430 


.25026 


3-99592 


.26888 


3.71907 


57 


4 


•21377 


4.67786 


.23209 


4.30860 


.25056 


3-99099 


.26920 


3.71476 


56 


5 


.21408 


4.67121 


.23240 


4-30291 


.25087 


3-98607 


.26951 


3-71046 


55 


6 


.21438 


4.66458 


.23271 


4.29724 


.25118 


3-98117 


.26982 


3.70616 


54 


7 


.21469 


4.65797 


•23301 


4.29159 


•25149 


3-97627 


•27013 


3.70188 


53 


8 


.21499 


4-65138 


-23332 


4-28595 


.25180 


3-97139 


.27044 


3-69761 


52 


9 


•21529 


4.64480 


-23363 


4.28032 


.25211 


3-96651 


.27076 


3-69335 


SI 


[O 


.21560 


4.63825 


'23393 


4.27471 


.25242 


3-96165 


.27107 


3.68909 


SO 


[I 


.21590 


4-63171 


.23424 


4.26911 


.25273 


3.95680 


.27138 


3-68485 


49 


[2 


.21621 


4.62518 


.23455 


4.26352 


•25304 


3-95196 


.27169 


3.68061 


48 


13 


.21651 


4.61868 


•23485 


4-25795 


•25335 


394713 


.27201 


3-67638 


47 


14 


.21682 


4.61219 


•23516 


4-25239 


.25366 


3-94232 


.27232 


3-67217 


46 


IS 


.21712 


4-60572 


•23547 


4-24685 


•25397 


3-93751 


•27263 


3-66796 


45 


[6 


.21743 


4-59927 


•23578 


4.24132 


.25428 


3-93271 


.27294 


3-66376 


44 


[7 


.21773 


4-59283 


.23608 


4-23580 


•25459 


3-92793 


.27326 


3-65957 


43 


[8 


.21804 


4-58641 


.23639 


4.23030 


.25490 


3.92316 


.27357 


3-65538 


42 


t9 


.21834 


4.58001 


.23670 


4.22481 


•25521 


3-91839 


•27388 


3-65121 


41 


50 


.21864 


4-57363 


.23700 


4.21933 


.25552 


3.91364 


.27419 


3.64705 


40 


►I 


.21895 


4-56726 


.23731 


4-21387 


.25583 


3-90890 


.27451 


3.64289 


39 


2 


.21925 


4.56091 


•23762 


4.20842 


•25614 


3.90417 


.27482 


3-63874 


38 


'3 


.21956 


4-55458 


.23793 


4.20298 


•25645 


3-89945 


.27513 


3-63461 


37 


4 


.21986 


4-54826 


•23823 


4.19756 


.25676 


3-89474 


.27545 


3.63048 


36 


5 


.22017 


4.54196 


.23854 


4.19215 


.25707 


3-89004 


.27576 


3.62636 


35 


6 


.22047 


4.53568 


.23885 


4.18675 


.25738 


3-88536 


.27607 


3.62224 


34 


7 


.22078 


4.52941 


.23916 


4.18137 


.25769 


3.88068 


.27638 


3.61814 


33 


8 


.22108 


4-52316 


•23946 


4.17600 


.25800 


3.87601 


.27670 


3.61405 


32 


9 


.22139 


4-51693 


.23977 


4.17064 


•25831 


3-87136 


.27701 


3-60996 


31 





.22169 


4.51071 


.24008 


4.16530 


.25862 


3.86671 


.27732 


3.60588 


30 


I 


.22200 


4-50451 


.24039 


4.15997 


.25893 


3.86208 


.27764 


3.60181 


29 


2 


.22231 


4.49832 


.24069 


4-15465 


.25924 


3-85745 


•27795 


3-59775 


28 


3 


.22261 


4.49215 


.24100 


4-14934 


.25955 


3-85284 


.27826 


3-59370 


27 


4 


.22292 


4.48600 


.24131 


4.14405 


.25986 


3.84824 


•27858 


3.58966 


26 


5 


.22322 


4.47986 


.24162 


4-13877 


.26017 


3-84364 


.27889 


3-58562 


25 


6 


.22353 


4-47374 


.24193 


4-13350 


.26048 


3.83906 


.27920 


3-58160 


24 


7 


.22383 


4.46764 


.24223 


4.12825 


.26079 


3-83449 


.27952 


3-57758 


23 


8 


.22414 


4-46155 


•24254 


4.12301 


.26110 


3-82992 


.27983 


3-57357 


22 


9 


.22444 


4-45548 


.24285 


4.11778 


.26141 


3-82537 


.28015 


3-56957 


21 





.22475 


4.44942 


.24316 


4.11256 


.26172 


3-82083 


.28046 


3-56557 


20 


I 


.22505 


4-44338 


.24347 


4-10736 


.26203 


3-81630 


.28077 


3-56159 


19 


2 


.22536 


4-43735 


.24377 


4.10216 


.26235 


3.81177 


.28109 


3-55761 


18 


3 


.22567 


4-43134 


.24408 


4.09699 


.26266 


3.80726 


.28140 


3-55364 


17 


4 


.22597 


4-42534 


.24439 


4.09182 


.26297 


3.80276 


.28172 


3-54968 


16 


5 


.22628 


4.41936 


.24470 


4.08666 


.26328 


3.79827 


.28203 


3-54573 


15 


6 


.22658 


4.41340 


.24501 


4.08152 


.26359 


3-79378 


.28234 


3-54179 


14 


7 


.22689 


4-40745 


-24532 


4.07639 


• .26390 


3-78931 


.28266 


3-53785 


13 


8 


.22719 


4-40152 


.24562 


4.07127 


.26421 


3.78485 


.28297 


3-53393 


12 


9 


.22750 


4-39560 


.24593 


4.06616 


.26452 


3-78040 


.28329 


3-53001 


II 





.22781 


4-38969 


.24624 


4.06107 


.26483 


3-77595 


.28360 


3.52609 


10 


I 


.22811 


4-38381 


.24655 


4-05599 


.26515 


3-77152 


•28391 


3-52219 


9 


2 


.22842 


4-37793 


.24686 


4-05092 


.26546 


3-76709 


.28423 


3.51829 


8 


3 


.22872 


4.37207 


.24717 


4.04586 


•26577 


3.76268 


•28454 


3-51441 


7 


4 


.22903 


4-36623 


.24747 


4.04081 


.26608 


3-75828 


.28486 


3-51053 


6 


5 


.22934 


4.36040 


.24778 


4-03578 


.26639 


3-75388 


.28517 


3.50666 


5 


6 


.22964 


4-35459 


.24809 


4-03075 


.26670 


3-74950 


.28549 


3-50279 


4 


7 


.22995 


4-34879 


.24840 


4.02574 


.26701 


3-74512 


.28580 


3.49894 


3 


8 


.23026 


4.34300 


.24871 


4.02074 


-26733 


3.74075 


.28612 


3-49509 


2 


P 


.23056 


4.33723 


.24902 


4.01576 


.26764 


3-73640 


.28643 


3-49125 


I 





.23087 


4.33148 


•24933 


4.01078 


•26795 


3.73205 


.28675 


3.48741 







Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


f 


1 


7; 


ro 


7e 


►° 


7S 


° 


'74 


t° 





NATURAL TANGENTS AND CO-TANGENTS 849 





16° 


170 


) 18^ 


19° 




/ 


i Tan. 


Co-tan. 


Tan. 


Co-tan, 


! Tan. 


Co-TAN. 


Tan. 


Co-TAN. 


' 





.28675 


3.48741 


.30573 


3.27085 


.32492 


3^07768 


.34433 


2.90421 


60 


X 


.28706 


3-48359 


.30605 


3.26745 


.32524 


3-07464 


•34465 


2.90147 


59 


2 


.28738 


3.47977 


•30637 


3.26406 


•32556 


3.07160 


•34498 


2.89873 


58 


3 


.28769 


3.47596 


.30669 


3.26067 


•32588 


3.06857 


•34530 


2.89600 


57 


4 


.28800 


3.47216 


.30700 


3.25729 


.32621 


3-06554 


•34563 


2.89327 


56 


5 


.28832 


3.46837 


•30732 


3-25392 


•32653 


3.06252 


•34596 


2.89055 


55 


6 


.28864 


3.46458 


•30764 


3-25055 


•32685 


3-05950 


.34628 


2.88783 


54 


7 


.28895 


3.46080 


•30796 


3.24719 


.32717 


3.05649 


.34661 


2.8851I 


53 


8 


.28927 


3.45703 


.30828 


3-24383 


•32749 


3.05349 


•34693 


2.88240 


52 


9 


.28958 


3.45327 


.30860 


3.24049 


.32782 


3.05049 


•34726 


2.87970 


51 


10 


.28990 


3.44951 


.30891 


3-23714 


•32814 


3.04749 


•34758 


2.87700 


50 


11 


.29021 


3.44576 


.30923 


3-23381 


.32846 


3.04450 


•34791 


2.87450 


49 


12 


•29053 


3.44202 


•30955 


3-23048 


.32878 


3.04152 


.34824 


2.87161 


48 


13 


.29084 


3.43829 


•30987 


3.22715 


.32911 


3.03854 


•34856 


2.86892 


47 


14 


.29116 


3.43456 


.31019 


3.22384 


•32943 


3.03556 


•34889 


2.86624 


46 


IS 


.29147 


3.43084 


•31051 


3.22053 


•32975 


3.03260 


•34922 


2.86356 


45 


16 


.29179 


3.42713 


•31083 


3.21722 


•33007 


3-02963 


.34954 


2.86089 


44 


17 


.29210 


3.42343 


•31115 


3.21392 


.33040 


3.02667 


.34987 


2.85822 


43 


18 


.29242 


3.41973 


•31147 


3.21063 


•33072 


3-02372 


.35019 


2.85555 


42 


19 


.29274 


3.41604 


.31178 


3-20734 


•33104 


3-02077 


•35052 


2.85289 


41 


20 


•29305 


3.41236 


.31210 


3.20406 


•33136 


3.01783 


.35085 


2.85023 


40 


21 


.29337 


3.40869 


.31242 


3-20079 


•33160 


3.01489 


•35117 


2.84758 


39 


22 


.29368 


3.40502 


•31274 


3-19752 


•33201 


3.01 196 


•35150 


2.84494 


38 


23 


.29400 


3.40136 


.31306 


3.19426 


•33233 


3.00903 


•35183 


2.84229 


37 


24 


.29432 


3-39771 


•31338 


3.19100 


.33266 


3.0061 1 


.35216 


2.8396s 


36 


25 


.29463 


3.39406 


•31370 


3-18775 


•33298 


3.00319 


.35248 


2.83702 


35 


26 


.29495 


3.39042 


.31402 


3-18451 


'33330 


3.00028 


•35281 


2.83439 


34 


27 


.29526 


3.38679 


•31434 


3-18127 


•33363 


2.99738 


•35314 


2.83176 


33 


28 


•29558 


3.38317 


.31466 


3.17804 


•33395 


2-99447 


•35346 


2.82914 


32 


29 


.29590 


3.37955 


.31498 


3.17481 


•33427 


2.99158 


•35379 


2.82653 


31 


30 


.29621 


3-37594 


•31530 


3-17159 


•33460 


2.98868 


.35412 


2.82391 


30 


31 


•29653 


3-37234 


•31562 


3-16838 


•33492 


2.98580 


.35445 


2.82130 


29 


32 


•29685 


3-36875 


•31594 


3-16517 


•33524 


2.98292 


•35477 


2.81870 


28 


33 


.29716 


3.36516 


.31626 


3.16197 


•33557 


2.98004 


•35510 


2.8161O 


27 


34 


.29748 


3.36158 


.31658 


3-15877 


•33589 


2.97717 


•35543 


2.81350 


26 


35 


.29780 


3-35800 


.31690 


3-15558 


•33621 


2.97430 


•35576 


2.8109I 


25 


36 


.29811 


3-35443 


.31722 


3.15240 


•33654 


2.97144 


•35608 


2.80833 


24 


37 


.29843 


3-35087 


•31754 


3-14922 


.33686 


2.96858 


•35641 


2.80574 


23 


38 


•29875 


3-34732 


.31786 


3.14605 


•33718 


2.96573 


.35674 


2.80316 


22 


39 


.29906 


3-34377 


.31818 


3.14288 


.33751 


2.96288 


•35707 


2.80059 


21 


40 


.29938 


3-34023 


.31850 


3-13972 


•33783 


2.96004 


.35740 


2.79802 


20 


41 


.29970 


3-33670 


.31882 


3-13656 


.33816 


2.95721 


■35772 


2.79545 


19 


42 


.30001 


3-33317 


.31914 


3.13341 


.33848 


2-95437 


.35805 


2.79289 


18 


43 


.30033 


3-32965 


.31946 


3.13027 


.33881 


2.95155 


•35838 


2.79033 


17 


44 


.30065 


3-32614 


•31978 


3.12713 


•33913 


2.94872 


•35871 


2.78778 


16 


45 


•30097 


3-32264 


.32010 


3.12400 


.33945 


2.94590 


•35904 


2.78523 


15 


46 


.30128 


3-31914 


.32042 


3.12087 


•33978 


2.94309 


•35937 


2.78269 


14 


47 


.30160 


3-31565 


.32074 


3.11775 


.34010 


2.94028 


.35969 


2.78014 


13 


48 


.30192 


3-31216 


.32106 


3.11464 


•34043 


2.93748 


.36002 


2.77761 


12 


49 


.30224 


3-30868 


.32139 


3-11153 


.34075 


2.93468 


.36035 


2.77507 


II 


50 


•30255 


3.30521 


.32171 


3.10842 


.34108 


2.93189 


.36068 


2.77254 


10 


51 


.30287 


3-30174 


.32203 


3-10532 


.34140 


2.92910 


.36101 


2.77002 


9 


52 


.30319 


3-29829 


.32235 


3.10223 


•34173 


2.92632 


•36134 


2.76750 


8 


53 


•50351 


3.29483 


.32267 


3.09914 


•34205 


2.92354 


.36167 


2.76498 


7 


54 


.30382 


3.29139 


•32299 


3.09606 


•34238 


2.92076 


•36199 


2.76247 


6 


55 


.30414 


3.28795 


•32331 


3-09298 


•34270 


2.91799 


.36232 


2.75996 


5 


56 


.30446 


3.28452 


•32363 


3-08991 


•34303 


2.91523 


.36265 


2.75746 


4 


57 


•30478 


3.28109 


•32396 


3-08685 


•34335 


2.91246 


.36298 


2.75496 


3 


58 


•30509 


3.27767 


.32428 


3.08379 


•34368 


2.90971 


.36331 


2.75246 


3 


59 


•30541 


3.27426 


.32460 


3.08073 


.34400 


2.90696 


•36364 


2.74997 


I 


60 


.30573 


3.27085 


.32492 ' 


3-07768 


•34433 


2.90421 


.36397 


2.74748 





/ 


Co-tan. 


Tan. 


Co-tan. Tan. 


Co-TAN. 


Tan. 


Co-TAN. 


Tan. 


/ 




7 


3^ 


7 


20 1 


7 


P 


7 


0°. 





8so 



GENERAL TABLES AND FORMUI^iE 





20° 


2P 


22° I 


I 23° 




f 


Tan. 


Co-TAN. 


Tan. 


Co-TAN. 


Tan. 


Co-TAN. 


Tan. 


Co-TAN. 


/ 


o 


.36397 


2.74748 


.38386 


2.60509 


.40403 


2.47509 


.42447 


2.35585 


60 


I 


•36430 


2.74499 


.38420 


2.60283 


.40436 


2.47302 


.42482 


2.35395 


59 


2 


.36463 


2.74251 


.38453 


2.60057 


.40470 


2.47095 


.42516 


2.35205 


58 


3 


.36496 


2.74004 


.38487 


2.59831 


.40504 


2.46888 


.42551 


2.35015 


57 


4 


.36529 


2.73756 


.38520 


2.59606 


•40538 


2.46682 


.42585 


2.34825 


56 


5 


.36562 


2.73509 


.38553 


2.59381 


.40572 


2.46476 


.42619 


2.34636 


55 


6 


•36595 


2.73263 


.38587 


2.59156 


.40606 


2.46270 


•42654 


2.34447 


54 


7 


.36628 


2.73017 


.38620 


2.58932 


.40640 


2.46065 


.42688 


2.34258 


53 


8 


.36661 


2.72771 


.38654 


2.58708 


.40674 


2.45860 


.42722 


2.34069 


52 


9 


.36694 


2.72526 


.38687 


2.58484 


.40707 


2.45655 


•42757 


2.33881 


51 


lO 


.36727 


2.72281 


.38721 


2.58261 


.40741 


2.45451 


.42791 


2.33693 


50 


II 


.36760 


2.72036 


.38754 


2.58038 


.40775 


2.45246 


.42826 


2.33505 


49 


12 


.36793 


2.71792 


.38787 


2.57815 


.40809 


2.45043 


.42860 


2.33317 


48 


13 


.36826 


2.71548 


.38821 


2.57593 


.40843 


2.44839 


.42894 


2.33130 


47 


14 


.36859 


2.71305 


.38854 


2.57371 


.40877 


2.44636 


.42929 


2.32943 


46 


15 


.36892 


2.71062 


.38888 


2.57150 


.40911 


2.44433 


.42963 


2.32756 


45 


i6 


.36925 


2.70819 


•38921 


2.56928 


.40945 


2.44230 


.42998 


2.32570 


44 


17 


.36958 


2.70577 


•38955 


2.56707 


.40979 


2.44027 


•43032 


2.32383 


43 


i8 


.36991 


2.70335 


.38988 


2.56487 


.41013 


2.43825 


■43067 


2.32197 


42 


19 


.37024 


2.70094 


.39022 


2.56266 


.41047 


2.43623 


•43101 


2.32012 


41 


20 


.37057 


2.69853 


.39055 


2.56046 


.41081 


2.43422 


•43136 


2.31826 


40 


21 


.37090 


2.69612 


.39089 


2.55827 


.41115 


2.43220 


•43170 


2.31641 


39 


22 


.37124 


2.69371 


.39122 


2.55608 


.41149 


2.43019 


•43205 


2.31456 


38 


23 


•37157 


2.6913I 


.39156 


2.55389 


.41183 


2.42819 


•43239 


2.31271 


37 


24 


.37190 


2.68892 


.39190 


2.55170 


.41217 


2.42618 


.43274 


2.31086 


36 


25 


•37223 


2.68653 


.39223 


2.54952 


•41251 


2.4241S 


.43308 


2.30902 


35 


26 


.37256 


2.68414 


.39257 


2.54734 


.41285 


2.42218 


•43343 


2.30718 


34 


27 


.37289 


2.';8i75 


.39290 


2.54516 


•41319 


2.42019 


.43378 


2.30534 


33 


28 


.37322 


2.67937 


.39324 


2.54299 


.41353 


2.41819 


.43412 


2.30351 


32 


29 


.37355 


2.67700 


.39357 


2.54082 


.41387 


2.41620 


•43447 


2.30167 


31 


30 


.37388 


2.67462 


.39391 


2.53865 


.41421 


2.41421 


•43481 


2.29984 


30 


31 


.37422 


2.67225 


.39425 


2.53648 


.41455 


2.41223 


•43516 


2.29801 


29 


32 


.37455 


2.66989 


.39458 


2.53432 


.41490 


2.41025 


•43550 


2.29619 


28 


33 


.37488 


2.66752 


.39492 


2.53217 


.41524 


2.40827 


.43585 


2.29437 


27 


34 


.37521 


2.66516 


.39526 


2.53001 


.41558 


2.40629 


.43620 


2.29254 


26 


35 


•37554 


2.66281 


.39559 


2.52786 


.41592 


2.40432 


•43654 


2.29073 


25 


36 


.37588 


2 .66046 


.39593 


2.52571 


.41626 


2.40235 


•43689 


2.28891 


24 


37 


.37621 


2.65811 


.39626 


2.52357 


.41660 


2.40038 


•43724 


2.28710 


23 


38 


.37654 


2.65576 


.39660 


2.52142 


.41694 


2.39841 


•43758 


2.28528 


22 


39 


.37687 


2.65342 


.39694 


2.51929 


.41728 


2.39645 


.43793 


2.28348 


21 


40 


.37720 


2.65109 


.39727 


2.51715 


.41763 


2.39449 


.43828 


2.28167 


20 


41 


.37754 


2.64875 


.39761 


2.51502 


•41797 


2.39253 


.43862 


2.27987 


19 


42 


.37787 


2.64642 


.39795 


2.51289 


.41831 


2.39058 


.43897 


2.27806 


18 


43 


.37820 


2.64410 


.39829 


2.51076 


.41865 


2.38862 


.43932 


2.27626 


17 


44 


.37853 


2.64177 


.39862 


2.50864 


.41899 


2.38668 


.43966 


2.27447 


16 


45 


.37887 


2.63945 


.39896 


2.50652 


.41933 


2.38473 


.44001 


2.27267 


15 


46 


.37920 


2.63714 


.39930 


2.50440 


.41968 


2.38279 


.44036 


2.27088 


14 


47 


.37953 


2.63483 


.39963 


2.50229 


.42002 


2.38084 


.44071 


2.26909 


13 


48 


.37986 


2.63252 


.39997 


2.50018 


.42036 


2.37891 


.44105 


2.26730 


12 


49 


.38020 


2.63021 


.40031 


2.49807 


.42070 


2.37697 


.44140 


2.26552 


II 


SO 


.38053 


2.62791 


.40065 


2.49597 


.42105 


2.37504 


.44175 


2.26374 


10 


51 


.38086 


2.62561 


.40098 


2.49386 


.42139 


2.37311 


.44210 


2.26196 


9 


52 


.38120 


2.62332 


.40132 


2.49177 


.42173 


2.37118 


.44244 


2.26018 


8 


53 


.38153 


2.62103 


.40166 


2.48967 


.42207 


.2.36925 


.44279 


2.25840 


7 


54 


.38186 


2.61874 


.40200 


2.48758 


.42242 


2.36733 


.44314 


2.25663 


6 


55 


.38220 


2.61646 


.40234 


2.48549 


.42276 


2.36541 


.44349 


2.25486 


5 


56 


.38253 


2.61418 


.40267 


2.48340 


.42310 


2.36349 


.44384 


2.25309 


4 


57 


.38286 


2.61190 


.40301 


2.48132 


.42345 


2.36158 


.44418 


2.25132 


3 


58 


.38320 


2.60963 


.40335 


2.47924 


.42379 


2.35967 


.44453 


2.24956 


2 


59 


.38353 


2.60736 


.40369 


2.47716 


.42413 


2.35776 


.44488 


2.24780 


I 


60 


.38386 


2.60509 


.40403 


2.47509 


.42447 


2.35585 


.44523 


2.24604 





/ 


Co-TAN. Tan. I 


Co-TAN. 


Tan. 


Co-TAN. 


Tan. 


Co-TAN. 


Tan. 


f 




6< 


r 1 


6< 


30 


6 


r° 


6( 


50 





NATURAL TANGENTS AND CO-TANGENTS 851 





24° 1 


25° I 


26° 


2 


70 




' 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-TAN. 


Tan. 


Co-TAN. 







•44523 


2.24604 


.46631 


2.14451 


•48773 


2.05030 


•50953 


I.96261 


60 


I 


•44558 


2.24428 


.46666 


2.14288 


.48809 


2.04879 


•50989 


1. 96 1 20 


59 


2 


.44593 


2.24252 


.46702 


2.14125 


.48845 


2.04728 


.51026 


1.95979 


58 


3 


.44627 


2.24077 


•46737 


2.13963 


.48881 


2.04577 


•51063 


1.95838 


57 


4 


.44662 


2.23902 


.46772 


2.13801 


.48917 


2.04426 


.51099 


1.95698 


56 


5 


.44697 


2.23727 


.46808 


2.13639 


•48953 


2.04276 


.51136 


1.95557 


55 


6 


•44732 


2.23553 


.46843 


2.13477 


.48989 


2.04125 


•51173 


1.95417 


54 


7 


•44767 


2.23378 


.46879 


2.13316 


.49026 


2.03975 


.51209 


1.95^-77 


53 


8 


.44802 


2.23204 


.46914 


2.13154 


.49062 


2.03825 


.51246 


1-95137 


52 


9 


•44837 


2.23030 


.46950 


2.12993 


.49098 


2.03675 


•51283 


1.94997 


51 


10 


.44872 


2.22857 


.46985 


2.12832 


•49134 


2.03526 


.51319 


1.94858 


50 


II 


.44907 


2.22683 


.47021 


2.12671 


.49170 


2.03376 


.51356 


I.94718 


49 


12 


•44942 


2.22510 


.47056 


2.12511 


.49206 


2.03227 


.51393 


1-94579 


48 


13 


•44977 


2.22337 


.47092 


2.12350 


.49242 


2.03078 


.51430 


1.94440 


47 


14 


.45012 


2.22164 


.47128 


2.12190 


.49278 


2.02929 


.51467 


1. 9430 1 


46 


15 


.45047 


2.21992 


•47163 


2.12030 


.49315 


2.02780 


.51503 


1. 94162 


45 


16 


.45082 


2.21819 


.47199 


2.11871 


.49351 


2.02631 


•51540 


1.94023 


44 


17 


•45117 


2.21647 


•47234 


2.11711 


.49387 


2.02483 


•51577 


1.9388s 


43 


18 


.45152 


2.21475 


•47270 


2.11552 


•49423 


2.02335 


.51614 


1.93746 


42 


19 


.45187 


2.21304 


•47305 


2.11392 


.49459 


2.02187 


•51651 


1.93608 


41 


20 


.45222 


2.21132 


•47341 


2.11233 


.49495 


2.02039 


.51688 


1.93470 


40 


21 


.45257 


2.20961 


.47577 


2.11075 


.49532 


2.01891 


•51724 


1.93332 


39 


22 


.45292 


2.20790 


.47412 


2.10916 


.49568 


2.01743 


.51761 


I -93 195 


38 


23 


•45327 


2.20619 


•47448 


2.10758 


.49604 


2.01596 


•51798 


1-93057 


37 


24 


.45362 


2.20449 


•47483 


2.10600 


.49640 


2.01449 


•51835 


1.92920 


36 


25 


.45397 


2.20278 


•47519 


2.10442 


.49677 


2.01302 


•51872 


1.92782 


35 


26 


.45432 


2.20108 


•47555 


2.10284 


•49713 


2.OII55 


.51909 


1.92645 


34 


27 


.45467 


2.19938 


•47590 


2.10126 


.49749 


2.01008 


.51946 


1.92508 


33 


28 


.45502 


2.19769 


.47626 


2.09969 


.49786 


2.00862 


•51983 


1.92371 


32 


29 


.45537 


2.19599 


.47662 


2.0981 1 


.49822 


2.00715 


.52020 


1.92235 


31 


30 


.45573 


2.19430 


.47698 


2.09654 


.49858 


2.00569 


•52057 


1.92098 


30 


31 


.45608 


2.19261 


•47733 


2.09498 


•49894 


2.00423 


.52094 


1. 91962 


29 


3^ 


.45643 


2.19092 


•47769 


2.09341 


•49931 


2.00277 


.52131 


1.91826 


28 


33 


.45678 


2.18923 


•47805 


2.09184 


.49967 


2.OOI31 


.52168 


1.91690 


27 


34 


.45713 


2.18755 


.47840 


2.09028 


.50004 


1.99986 


.52205 


1.91554 


26 


35 


.45748 


2.18587 


.47876 


2.08872 


.50040 


1. 99841 


.52242 


1.91418 


25 


36 


.45784 


2.18419 


.47912 


2.08716 


.50076 


1.99695 


.52279 


1.91282 


24 


37 


.45819 


2.18251 


.47948 


2.08560 


.50113 


1.99550 


•52316 


1.91147 


23 


38 


.45854 


2.18084 


•47984 


2.08405 


.50149 


1 .99406 


•52353 


1.91012 


22 


39 


.45889 


2.17916 


.48019 


2.08250 


.50185 


I.99261 


•52390 


1.90876 


21 


40 


.45924 


2.17749 


•48055 


2 .08094 


.50222 


1. 991 16 


.52427 


1.90741 


20 


41 


.45960 


2.17582 


.48091 


2.07939 


.50258 


1.98972 


•52464 


1.90607 


19 


42 


•45995 


2.17416 


.48127 


2.07785 


•50295 


1.98828 


.52501 


1.90472 


18 


43 


.46030 


2.17249 


.48163 


2.07630 


•50331 


1.98684 


.52538 


1.90337 


17 


44 


.46065 


2.17083 


.48198 


2.07476 


•50368 


1.98540 


.52575 


1.90203 


16 


45 


.46101 


2.16917 


.48234 


2.07321 


.50404 


1.98396 


.52613 


1 .90069 


15 


46 


.46136 


2.16751 


.48270 


2.07167 


.50441 


1.98253 


.52650 


1.89935 


14 


47 


.46171 


2.16585 


.48306 


2.07014 


•50477 


1. 98 1 10 


.52687 


1. 89801 


13 


48 


.46206 


2.16420 


.48342 


2.06860 


•50514 


1.97966 


.52724 


1.89667 


12 


49 


.46242 


2.16255 


.48378 


2.06706 


•50550 


1.97823 


.52761 


1.89533 


il 


50 


•46277 


2.16090 


.48414 


2.06553 


•50587 


1.97680 


•52798 


1 .89400 


10 


51 


•46312 


2.15925 


.48450 


2.06400 


.50623 


1.97538 


•52836 


1.89266 


9 


52 


.46348 


2.15760 


.48486 


2.06247 


.50660 


1.97395 


.52873 


1.89133 


8 


S3 


.46383 


2.15596 


.48521 


2.06094 


.50696 


1.97253 


•52910 


1.89000 


7 


54 


.46418 


2.15432 


•48557 


2.05942 


•50733 


I.97111 


•52947 


1.88867 


6 


55 


.46454 


2.15268 


.48593 


2.05790 


•50769 


1.96969 


.52984 


1.88734 


5 


56 


.46489 


2.15104 


.48629 


2.05637 


.50806 


1.96827 


.53022 


1.88602 


4 


57 


•46525 


2.14940 


.48665 


2.05485 


.50843 


1.96685 


.53059 


1.88469 


3 


58 


.46560 


2.14777 


.48701 


2.05333 


.50879 


1.96544 


.53096 


1-88337 


2 


59 


.46595 


2.14614 


•48737 


2.05182 


•50916 


1 .96402 


.53134 


1.88205 


I 


60 


.46631 


2.14451 


.48773 


2.05030 


.50953 


I.96261 


•53171 


1.88073 





/ 


Co-tan . 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


CO-TAN. 


Tan. 


/ 




6 


5° 


6 


40 


) 6 


3° 


6 


2° 





8S2 



GENERAL TABLES AND FORMULA 





28° 1 


29° 




80° I 


3P 






Tan. 


Co-TAN. 


Tan. C 


O-TAN. 


Tan. 


Co-TAN. 


Tan. 


Co-TAN. 




o 


•53171 


1.88073 


.55431 I 


80405 


.57735 


1.73205 


.60086 


1.66428 


60 


I 


.53208 


1. 8 794 1 


•55469 I 


80281 


.57774 


1.73089 


.60126 


1.663 18 


59 


2 


•53246 


1.87809 


•55507 I 


80158 


.57813 


1.7-973 


.60165 


I. 6209 


58 


3 


•53283 


1.87677 


•55545 I 


80034 


.57851 


1.72857 


.60205 


1.66099 


57 


4 


•53320 


1.87546 


•55583 I 


7991I 


.57890 


I.7274I 


.60245 


1.65990 


56 


5 


.53358 


1.87415 


.55621 I 


79788 


■ .57929 


1.72625 


.60284 


1. 65881 


55 


6 


•53395 


1.87283 


.55659 I 


79665 


.57968 


1.72509 


.60324 


1.65772 


54 


7 


•53432 


1.87152 


.55697 I 


79542 


.58007 


1.72393 


.60364 


1.65663 


53 


8 


.53470 


1. 8702 1 


.55736 I 


79419 


.58046 


1.72278 


.60403 


1.65534 


52 


9 


•53507 


1. 86891 


.55774 I 


79296 


.58085 


I.72163 


.60443 


1.65445 


51 


lO 


•53545 


1.86760 


.55812 I 


79174 


.58124 


1.72047 


.60483 


1.65337 


SO 


II 


•53582 


1.86630 


.55850 I 


79051 


.58162 


I.71932 


.60522 


1.65228 


49 


12 


.53620 


1.86499 


.55888 I 


78929 


.58201 


I.71817 


.60562 


1. 65 1 20 


48 


13 


.53657 


1.86369 


.55926 I 


78807 


.58240 


I.71702 


.60602 


1. 650 II 


47 


14 


.53694 


1.86239 


.55964 I 


78685 


.58279 


I.71588 


.60642 


1.64903 


46 


IS 


•53732 


1. 86109 


.56003 I 


78563 


.58318 


1.71473 


.60681 


1.64795 


45 


i6 


•53769 


1.85979 


.56041 I 


78441 


•58357 


I.71358 


.60721 


1.64687 


44 


17 


.53807 


1.85850 


.56079 I 


78319 


•58396 


I.71244 


.60761 


1.64579 


43 


i8 


.53844 


1.85720 


.56117 I 


78198 


.58435 


I.71129 


.60801 


1. 6447 1 


42 


19 


.53882 


1.85591 


.56156 I 


78077 


.58474 


I.71OI5 


.60841 


1.64363 


41 


20 


.53920 


1.85462 


.56194 I 


77955 


.58513 


1. 7090 1 


.60881 


1.64256 


40 


21 


•53957 


1.85333 


.56232 I 


77834 


.58552 


1.70787 


.60921 


1. 64 1 48 


39 


22 


•53995 


1.85204 


.56270 I 


77713 


.58591 


1.70673 


.60960 


1. 6404 1 


38 


23 


•54032 


1.85075 


.56309 I 


77592 


.58631 


1.70560 


.61000 


1.63934 


37 


24 


.54070 


1 .84946 


.56347 I 


77471 


.58670 


1.70446 


.61040 


1.63826 


36 


25 


•54107 


1. 848 1 8 


.56385 I 


77351 


.58709 


1.70332 


.61080 


1-63719 


35 


26 


•54145 


1.84689 


.56424 I 


77230 


.58748 


I.70219 


.61120 


1. 63612 


34 


27 


•54183 


1. 84561 


.56462 I 


77110 


.58787 


1. 70106 


.61160 


1-63505 


33 


28 


.54220 


1.84433 


.56500 I 


76990 


.58826 


1.69992 


.61200 


1.63398 


32 


29 


.54258 


1.84305 


.56539 I 


76869 


.58865 


1.69879 


.61240 


1.63292 


31 


30 


.54296 


1.84177 


.56577 I 


76749 


.58904 


1.69766 


.61280 


1.6318s 


30 


31 


•54333 


1.84049 


.56616 I 


76630 


.58944 


1.69653 


.61320 


1.63079 


29 


32 


.54371 


1.83922 


.56654 I 


76510 


.58983 


1. 69541 


.61360 


1.62972 


28 


33 


.54409 


1.83794 


.56693 I 


76390 


.59022 


1.69428 


.61400 


1.62866 


27 


34 


.54446 


1.83667 


.56731 I 


76271 


.59061 


1. 693 16 


.61440 


1.62760 


26 


35 


•54484 


1.83540 


.56769 I 


76151 


.59101 


1.69203 


.61480 


1.62654 


25 


36 


.54522 


1.83413 


.56808 I 


76032 


.59140 


1. 6909 1 


.61520 


1.62548 


24 


37 


•54560 


1.83286 


.56846 I 


75913 


.59179 


1.68979 


.61561 


1.62442 


23 


38 


.54597 


1-83159 


.56885 I 


75794 


.59218 


1.68866 


.61601 


1.62336 


22 


39 


.54635 


1.83033 


.56923 I 


75675 


.59258 


1.68754 


.61641 


1.62230 


21 


40 


.54673 


1.82906 


.56962 I 


75556 


.59297 


1.68643 


.61681 


I.62125 


20 


41 


.54711 


1.82780 


.57000 I 


75437 


.59336 


1.68531 


.61721 


I.62019 


^? 


42 


.54748 


1.82654 


.57039 I 


75319 


.59376 


1. 684 1 9 


.61761 


I.61914 


18 


43 


.54786 


1.82528 


.57078 I 


75200 


.59415 


1.68308 


.61801 


1. 61808 


17 


44 


.54824 


1.82402 


.57116 I 


75082 


.59454 


1. 68 1 96 


.61842 


1. 6 1 703 


16 


45 


.54862 


1.82276 


.57155 I 


74964 


•59494 


1.68085 


.61882 


1.61598 


IS 


46 


■54900 


1.82150 


.57193 I 


74846 


•59533 


1.67974 


.61922 


1. 6 1 493 


14 


47 


.54938 


1.82025 


.57232 I 


74728 


.59573 


1.67863 


.61962 


1. 6 1 388 


13 


48 


.54975 


1.81899 


.57271 I 


74610 


.59612 


1.67752 


.62003 


1.61283 


12 


49 


.55013 


1.81774 


.57309 I 


74492 


.59651 


1. 67641 


.62043 


1. 61 1 79 


II 


50 


.55051 


1. 8 1 649 


.57348 I 


74375 


.59691 


1.67530 


.62083 


1.61074 


10 


51 


•55089 


1.81524 


•57386 I 


74257 


•59730 


1.67419 


.62124 


1.60970 


9 


52 


.55127 


1.81399 


.57425 I 


74140 


.59770 


1.67309 


.62164 


1.60865 


8 


53 


.55165 


1.8 1 2 74 


.57464 I 


74022 


.59809 


1.67198 


.62204 


1. 60761 


7 


54 


•55203 


1.81150 


•5V503 I 


73905 


.59849 


1.67088 


.62245 


1.60657 


6 


55 


•55241 


1. 81025 


•57S4I I 


73788 


.59888 


1.66978 


.62285 


1.60553 


5 


56 


•55279 


1. 8090 1 


.57580 I 


73671 


.59928 


1.66867 


•62325 


1 .60449 


4 


57 


.55317 


1.80777 


•57619 I 


73555 


.59967 


1.66757 


.62366 


1.60345 


3 


58 


.55355 


1.80653 


•57657 I 


73438 


.60c 3 7 


1.66647 


.62406 


1. 60241 


2 


59 


.55393 


1.80529 


.57696 I 


73321 


.60046 


1.66538 


.62446 


1.60137 


I 


60 


.55431 


1.80405 


.57735 I 


73205 


.60086 


1.66428 


.62487 


1.60033 







Co-TAN. 


Tan. 


Co-tan. 1 


Tan. 


Co-tan. 


Tan. 


Co-TAN. 


Tan. 






6 


P 


60° 




5 


9° 


5 


8° 





NATURAL TANGENTS AND CO-TANGENTS 853 





32^ 


33<^ 


34« 1 


35^ 




/ 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 





.62487 


1.60033 


.64941 


1.53986 


.67451 


1.48256 


.70021 


1.4281S 


~6^ 


I 


.62527 


1.59930 


.64982 


1.53888 


.67493 


1. 48 1 63 


.70064 


1.42726 


59 


2 


.62568 


1.59826 


.65023 


1.53791 


.67536 


1.48070 


.70107 


1.42638 


58 


3 


.62608 


1.59723 


.65065 


1.53693 


•67578 


1.47977 


.70151 


1.42550 


57 


4 


.62649 


1.59620 


.65106 


1.53595 


.67620 


1.47885 


.70194 


1.42462 


56 


5 


.62689 


1.59517 


.65148 


1.53497 


.67663 


1.47792 


.70238 


1.42374 


55 


6 


.62730 


1.59414 


.65189 


1.53400 


•67705 


1.47699 


.70281 


1.42286 


54 


7 


.62770 


i^593ii 


.65231 


1.53302 


•67748 


1.47607 


.70325 


1.42 198 


53 


8 


.62811 


1.59208 


'65272 


1.53205 


.67790 


i^475i4 


.70368 


1.42 1 10 


52 


9 


.62852 


1-59105 


•65314 


1.53107 


.67832 


1.47422 


.70412 


1.42022 


51 


10 


.62892 


1.59002 


•65355 


1.53010 


•67875 


i^47330 


•70455 


1.41934 


50 


II 


.62933 


1.58900 


.65397 


1.52913 


•67917 


1.47238 


.70499 


1.41847 


49 


12 


.62973 


1-58797 


.65438 


1.52816 


.67960 


1. 47 1 46 


.70542 


i^4i759 


-48 


13 


.63014 


1.58695 


.65480 


1.52719 


.68002 


1^47053 


.70586 


1.41672 


47 


14 


.63055 


1.58593 


.65521 


1.52622 


.68045 


1.46962 


.70629 


1.41584 


46 


15 


.63095 


1.58490 


.65563 


1.52525 


.68088 


1.46870 


.70673 


1.41497 


45 


16 


.63136 


1.58388 


.65604 


1.52429 


.68130 


1.46778 


.70717 


1. 4 1 409 


44 


17 


.63177 


1.58286 


.65646 


1.52332 


.68173 


1.46686 


.70760 


1.41322 


43 


18 


.63217 


1.58184 


.65688 


i^52235 


.68215 


1^46595 


.70804 


1.41235 


42 


19 


.63258 


1.58083 


.65729 


1.52139 


.68258 


1.46503 


.70848 


1. 41 148 


41 


20 


.63299 


1.57981 


•65771 


1.52043 


.68301 


1. 464 II 


.70891 


1.41061 


40 


21 


.63340 


1.57879 


.65813 


1^5 1946 


.68343 


1.46320 


.70935 


1.40974 


39 


22 


.63380 


1.57778 


.65854 


1.51850 


.68386 


1.46229 


.70979 


1.40887 


38 


23 


.63421 


1.57676 


.65896 


1.51754 


.68429 


1.46137 


.71023 


1.40800 


37 


24 


.63462 


1.57575 


.65938 


1.51658 


.68471 


1 .46046 


.71066 


1. 407 14 


36 


25 


.63503 


1.57474 


.65980 


1.51562 


.68514 


1.45955 


.71110 


1.40627 


35 


26 


.63544 


1.57372 


.66021 


1.51466 


•68557 


1.45864 


.71154 


1.40540 


34 


27 


•63584 


1.57271 


.66063 


1.51370 


.68600 


1.45773 


.71198 


1.40454 


33 


28 


.63625 


1.57170 


.66105 


1.51275 


.68642 


1.45682 


.71242 


1-40367 


32 


29 


.63666 


1.57069 


.66147 


1.51179 


.68685 


1-45592 


.71285 


1. 40281 


31 


30 


•63707 


1.56969 


.66189 


1. 5 1084 


.68728 


1.45501 


.71329 


1. 40 1 95 


30 


31 


.63748 


1.56868 


.66230 


1.50988 


.68771 


1. 45410 


.71373 


1. 40 109 


29 


32 


.63789 


1.56767 


.66272 


1.50893 


.68814 


1.45320 


.71417 


1.40022 


28 


33 


.63830 


1.56667 


.66314 


1.50797 


.68857 


1.45229 


.71461 


1.39936 


27 


34 


.63371 


1.56566 


.66356 


1.50702 


.68900 


1.45139 


.71505 


1^39850 


26 


35 


.63912 


1.56466 


.66398 


1.50607 


.68942 


1.45049 


.71549 


1.39764 


25 


36 


.63953 


1.56366 


.66440 


1.50512 


.68985 


1.44958 


.71593 


1.39679 


24 


37 


.63994 


1.56265 


.66482 


1. 5041 7 


.69028 


1.44868 


.71637 


1-39593 


23 


38 


.64035 


1.56165 


.66524 


1.50322 


.69071 


1.44778 


.71681 


1-39507 


22 


39 


.64076 


1.56065 


.66566 


1.50228 


.69114 


1.44688 


.71725 


I -3942 1 


21 


40 


.64117 


1.55966 


.66608 


1.50133 


.69157 


1.44598 


.71769 


1-39336 


20 


41 


.64158 


1.55866 


.66650 


1.50038 


.69200 


1.44508 


.71813 


1.39250 


19 


42 


.64199 


1.55766 


•66692 


1.49944 


•69243 


1.44418 


.71857 


1.39165 


18 


43 


.64240 


1.55666 


•66734 


1.49849 


.69286 


1.44329 


.71901 


1.39079 


17 


44 


.64281 


1.55567 


.66776 


1.49755 


.69329 


1.44239 


.71946 


1.38994 


16 


45 


.64322 


1.55467 


.66818 


1. 49661 


.69372 


1.44149 


.71990 


1.38909 


15 


46 


•64363 


1.55368 


.66860 


1.49566 


.69416 


1 .44060 


.72034 


1.38824 


14 


47 


.64404 


1.55269 


.66902 


1.49472 


.69459 


1.43970 


.72078 


1.38738 


13 


48 


.64446 


1.55170 


.66944 


1.49378 


.69502 


1. 43881 


.72122 


1.38653 


12 


49 


.64487 


1.55071 


.66986 


1.49284 


.69545 


1.43792 


.72166 


1.38568 


II 


50 


.64528 


1.54972 


.67028 


1. 49190 


.69588 


1^43703 


.72211 


1.38484 


10 


51 


.64569 


1.54873 


.67071 


1.49097 


.69631 


1. 43614 


•72255 


1.38399 


9 


52 


.64610 


1-54774 


.67113 


1.49003 


.69675 


1^43525 


.72299 


1.38314 


8 


53 


.64652 


1.54675 


•67155 


1.48909 


.69718 


1.43436 


•72344 


1.38229 


7 


54 


.64693 


1.54576 


.67197 


1. 488 16 


.69761 


1.43347 


•72388 


1.38145 


6 


55 


.64734 


1.54478 


.67239 


1.48722 


.69804 


1.43258 


.72432 


1.38060 


5 


56 


•64775 


1.54379 


.67282 


1.48629 


.69847 


1. 43 1 69 


•72477 


1.37976 


4 


57 


.64817 


1.54281 


•67324 


1.48536 


.69891 


1.43080 


•72521 


1. 37891 


3 


58 


.64858 


1-54183 


•67366 


1.48442 


.69934 


1.42992 


•72565 


1.37807 


2 


59 


.64899 


1.54085 


.67409 


1.48349 


.69977 


1.42903 


.72610 


1.37722 


I 


60 


.64941 


1.53986 


.67451 


1.48256 


.70021 


1.4281S 


•72654 


1.37638 





/ 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


/ 




5 


70 


5 


6° 


5 


5° 


5 


40 





8S4 



GENERAL TABLES AND FORMULA 





36° 


37^ 


38° 


39° 




/ 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


/ 


o 


.72654 


1.37638 


.75355 


1.32704 


.78129 


1.27994 


.80978 


1.23490 


60 


I 


.72699 


1.37554 


.75401 


1.32624 


.78175 


1.27917 


.81027 


1.23416 


59 


2 


.72743 


1.37470 


.75447 


1.32544 


.78222 


1. 2 7841 


.81075 


1.23343 


58 


3 


.72788 


I ^3 7386 


•75492 


1.32464 


.78269 


1.27764 


.81123 


1.23270 


57 


4 


.72832 


1.37302 


.75538 


1.32384 


.78316 


1.27688 


.81171 


1.23196 


56 


5 


.72877 


1.37218 


.75584 


1.32304 


.78363 


1.27611 


.81220 


1.23123 


55 


6 


.72921 


1^37134 


.75629 


1.32224 


.78410 


1.27535 


.81268 


1.23050 


54 


7 


.72966 


1.37050 


.75675 


1.32144 


.78457 


1.27458 


.81316 


1.22977 


53 


8 


.73010 


1^36967 


.75721 


1.32064 


.78504 


1.27382 


.81364 


1.22904 


52 


9 


.73055 


i^36883 


.75767 


1. 3 1 984 


.78551 


1.27306 


.81413 


1.22831 


51 


TO 


.73100 


1.36800 


.75812 


1^3 1904 


.78598 


1.27230 


.81461 


1.22758 


50 


II 


.73144 


1.36716 


.75858 


i^3i825 


.78645 


1-27153 


.81510 


1.22685 


49 


12 


.73189 


1.36633 


.75904 


i^3i745 


.78692 


1.27077 


.81558 


1.22612 


48 


13 


.73234 


1^36549 


.75950 


1. 3 1 666 


.78739 


1.27001 


.81606 


1.22539 


47 


14 


.73278 


1.36466 


.75996 


i^3i586 


.78786 


1.26925 


.81655 


1.22467 


46 


15 


.73323 


1.36383 


.76042 


i^3i507 


.78834 


1.26849 


.81703 


1-22394 


45 


i6 


.73368 


1.36300 


.76088 


1.31427 


.78881 


1.26774 


.81752 


1.22321 


44 


17 


.73413 


1.36217 


.76134 


1.31348 


.78928 


1.26698 


.81800 


1.22249 


43 


i8 


.73457 


1.36133 


.76180 


1.31269 


.78975 


1.26622 


.81849 


1.22176 


42 


19 


.73502 


1.36051 


.76226 


1.31190 


.79022 


1.26546 


.81898 


1.22104 


41 


20 


.73547 


1.35968 


.76272 


1.31110 


.79070 


1.26471 


.81946 


1.22031 


40 


21 


.73592 


i^35885 


.76318 


1.31031 


.79117 


1.2639s 


.81995 


1.21959 


39 


22 


.73637 


1.35802 


.76364 


1.30952 


.79164 


1.26319 


.82044 


1. 2 1886 


38 


23 


.73681 


1.35719 


.76410 


1.30873 


.79212 


1.26244 


.82092 


1.21814 


37 


24 


.73726 


1.35637 


.76456 


1.30795 


.79259 


1.26169 


.82141 


1.21742 


36 


25 


.73771 


1.35554 


.76502 


1.30716 


.79306 


1.26093 


.82190 


1.21670 


35 


26 


.73816 


1^35472 


.76548 


1-30637 


.79354 


1.26018 


.82238 


1.21598 


34 


27 


.73861 


i^35389 


.76594 


1.30558 


.79401 


1.25943 


.82287 


1.21526 


33 


28 


.73906 


1.35307 


.76640 


1,30480 


.79449 


1.25C67 


.82336 


1.21454 


32 


29 


.73951 


1.35224 


.76686 


1. 3040 1 


.79496 


1.25792 


^2385 


1.21382 


31 


30 


.73996 


i^35i42 


.76733 


1-30323 


.79544 


1.25717 


.82434 


1.21310 


30 


31 


.74041 


1.35060 


.76779 


1.30244 


.79591 


1.25642 


.82483 


1.21238 


29 


32 


.74086 


1.34978 


.76825 


1.30166 


.79639 


1.25567 


.82531 


1.21x66 


23 


33 


.74131 


1.34896 


.76871 


1.30087 


.79686 


1.25492 


.82580 


1. 2 1 094 


27 


34 


.74176 


1.34814 


.76918 


1.30009 


•79734 


1.25417 


.82629 


1.21023 


26 


35 


.74221 


1.34732 


.76964 


1.29931 


•79781 


1.25343 


.82678 


1.20951 


25 


36 


.74267 


1.34650 


.77010 


1.29853 


.79829 


1.25268 


.82727 


1.20879 


24 


37 


.74312 


1.34568 


•77057 


1.29775 


.79877 


1.25193 


.82776 


1.20808 


23 


38 


.74357 


1.34487 


.77103 


1.29696 


.79924 


1.25118 


.82825 


1.20736 


22 


39 


.74403 


1^34405 


.77149 


1.29618 


.79972 


1.25044 


.82874 


1.2066s 


21 


40 


.74447 


1^34323 


.77196 


1.29541 


.80020 


1.24969 


.82923 


1.20593 


20 


41 


.74492 


1.34242 


.77242 


1-29463 


.80067 


1.24895 


.82972 


1.20522 


19 


42 


.74538 


1.34160 


.77289 


1.29385 


.80115 


1.24820 


.83022 


1. 2045 1 


18 


43 


.74583 


1.34079 


.77335 


1.29307 


.80163 


1.24746 


.83071 


1.20379 


17 


44 


.74628 


1^33998 


.77382 


1.29229 


.80211 


1.24672 


.83120 


1.20308 


16 


45 


.74674 


1.33916 


.77428 


1.^^9152 


.80258 


1.24597 


.83169 


1.20237 


15 


46 


.74719 


1.33835 


.77475 


1.29074 


.80306 


1.24523 


.83218 


1. 20166 


14 


47 


•74764 


1.33754 


.77521 


1.28997 


-80354 


1.24449 


.83268 


1.2009s 


13 


48 


.74810 


1-33673 


.77568 


1.28919 


.80402 


1.24375 


.83317 


1.20024 


12 


49 


•74855 


1.33592 


.77615 


1.28842 


.80450 


1. 24301 


•83366 


1.19953 


11 


50 


.74900 


1.33511 


.77661 


1.28764 


.80498 


1.24227 


•83415 


1.19882 


10 


SI 


•74946 


1^33430 


.77708 


1.28687 


.80546 


1. 24153 


.83465 


1. 19811 


9 


52 


.74991 


1-33349 


.77754 


1.28610 


.80594 


1.24079 


.83514 


1.19740 


8 


53 


.75037 


1^33268 


.77801 


1.28533 


.80642 


1.24005 


.83564 


1.19669 


7 


54 


.75082 


1^33187 


.77848 


1.28456 


.80690 


1.23931 


.83613 


1.19599 


6 


55 


.75128 


1.33107 


.77895 


1.28379 


.80738 


1^23858 


.83662 


1.19528 


5 


56 


.75173 


1.33026 


•77941 


1.28302 


.80786 


1.23784 


.83712 


1. 19457 


4 


57 


.75219 


1.32946 


.77988 


1.28225 


.80834 


1.23710 


.83761 


1.19387 


3 


58 


.75264 


1.32865 


.78035 


1.28148 


.80882 


1.23637 


.83811 


1.19316 


2 


59 


.75310 


1.32785 


.78082 


1.28071 


.80930 


1.23563 


.83860 


1. 19246 


I 


60 


.75355 


1.32704 


.78129 


1.27994 


.80978 


1.23490 


.83910 


1.19175 







Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan 


Tan. 


Co-tan. 


Tan 


f 




5. 


30 


51 


2° 


5 


L° 


5( 


r 1 





NATUR.4L TANGENTS AND CO-TANGENTS 855 





40° 


410 


42° 


\ 43° 




/ 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


f 





•83910 


1.19175 


.86929 


1.15037 


.90040 


1.11061 


.93252 


1.07237 


60 


I 


.83960 


1.19105 


.86980 


1. 1 4969 


.90093 


1. 10996 


.93306 


1. 07 1 74 


59 


2 


.84009 


1.19035 


.87031 


1. 1 4902 


.90146 


1.10931 


.93360 


1.07112 


58 


3 


.84059 


1. 18964 


.87082 


1. 14834 


.90199 


1. 10867 


•93415 


1.07049 


57 


4 


.84108 


1.18894 


.87133 


1.14767 


.90251 


1. 10802 


.93469 


1.06987 


56 


5 


.84158 


1. 18824 


.87184 


1. 14699 


.93304 


1. 10737 


.93524 


1.06925 


55 


6 


.84208 


1.18754 


.87236 


1. 14632 


.90357 


1. 10672 


.93578 


1.06862 


54 


7 


.84258 


1. 18684 


.87287 


1-14565 


.90410 


1. 10607 


.93633 


1.06800 


53 


8 


.84307 


1.18614 


.87338 


1. 14498 


.90463 


I.I0543 


.93688 


1.06738 


52 


9 


•84357 


1. 18544 


.87389 


1. 14430 


.90516 


1. 10478 


.93742 


1.06676 


51 


10 


.84407 


1.18474 


.87441 


1.14363 


.90569 


1.10414 


•93797 


1. 066 1 3 


50 


II 


.84457 


1. 1 8404 


.87492 


1. 14296 


.90621 


1. 10349 


.93852 


1.06551 


49 


12 


.84507 


1. 18334 


.87543 


1. 14229 


.90674 


1. 10285 


.93906 


1.06489 


48 


13 


.84556 


1. 18264 


.87595 


1.14162 


.90727 


I. 10220 


.93961 


1.06427 


47 


14 


.84606 


1.18194 


.87646 


1. 14095 


.90781 


1.10156 


.94016 


1.06365 


46 


15 


.84656 


1.18125 


.87698 


1. 14028 


.90834 


1.10091 


.94071 


1.06303 


45 


16 


.84706 


1.18055 


.87749 


1.13961 


.90887 


1. 10^-27 


.94125 


1. 06241 


44 


17 


.84756 


1. 1 7986 


.87801 


1. 13894 


.90940 


1.09963 


.94180 


1.06179 


43 


18 


.84806 


1.17916 


.87852 


1.13828 


.90993 


1.09899 


.94235 


1.06117 


42 


19 


.84856 


1. 1 7846 


.87904 


1.13761 


.91046 


1.09834 


.94290 


1.06056 


41 


20 


.84906 


1. 17777 


.87955 


1.13694 


.91099 


1.09770 


•94345 


1.05994 


40 


21 


•84956 


1-17708 


.88007 


1. 13627 


.91153 


1.09706 


.94400 


1.05932 


39 


22 


.85006 


1.17638 


.88059 


1.13561 


.91206 


1 .09642 


•94455 


1.05870 


3S 


23 


.85057 


1.17569 


.88110 


1 .13494 


.91259 


1.09578 


.94510 


1.05809 


37 


24 


.85107 


1. 17500 


.88162 


1. 13428 


.91313 


1. 095 14 


.94565 


1.05747 


36 


25 


•85157 


1. 1 7430 


.88214 


1.13361 


.91366 


1.09450 


.94620 


1.05685 


35 


26 


.85207 


1.17361 


.88265 


1.13295 


.91419 


1.09386 


.94676 


1.05624 


34 


27 


•85257 


1.17292 


.88317 


1. 13228 


.91473 


1.09322 


•94731 


1.05562 


33 


28 


.85307 


1. 17223 


.88369 


1.13162 


.91526 


1.09258 


.94786 


1. 05501 


32 


29 


.85358 


1.17154 


.88421 


1. 1 3096 


.91580 


1. 09 1 95 


.94841 


1.05439 


31 


30 


.85408 


1. 1 7085 


.88473 


1. 13029 


.91633 


1.09131 


.94896 


1.05378 


30 


31 


.85458 


1.17016 


.88524 


1.12963 


.91687 


1.09067 


.94952 


1.05317 


29 


32 


.85509 


1. 16947 


.88576 


1. 12897 


.91740 


1.09003 


.95007 


1.05255 


28 


33 


.85559 


1. 16878 


.88628 


1.128^31 


.91794 


1 .08940 


.95062 


1. 05 1 94 


27 


34 


.85609 


1. 16809 


.88680 


1.12765 


.91847 


1.08876 


.95118 


1.05133 


26 


35 


.85660 


1.16741 


.88732 


1.12699 


.91901 


1. 088 1 3 


.95173 


1.05072 


25 


36 


•85710 


1. 16672 


.88784 


1. 12633 


.91955 


1.08749 


.95229 


1. 05010 


24 


37 


.85761 


1.16603 


.88836 


1. 12567 


.92008 


1.08686 


.95284 


1.04949 


23 


38 


.85811 


1.16535 


.88888 


1.12501 


.92062 


1.08622 


.95340 


1.04888 


22 


39 


.85862 


1. 16466 


.88940 


1. 12435 


.92116 


1.08559 


•95395 


1.04827 


21 


^0 


•85912 


1.16398 


.88992 


1. 12369 


.92170 


1 .08496 


.95451 


1.04766 


20 


*i 


.85963 


1. 16329 


.89045 


1. 12303 


.92224 


1.08432 


•95506 


1.04705 


19 


*2 


.86014 


1.16261 


.89097 


1. 12238 


.92277 


1.08369 


.95562 


1.04644 


18 


*3 


.86064 


1.16192 


.89149 


1.12172 


.92331 


1.08306 


.95618 


1.04583 


17 


U 


.86115 


1.16124 


.89201 


1.12106 


•92385 


1.08243 


.95673 


1.04522 


16 


45 


.86166 


1. 16056 


•89253 


1.12041 


.92439 


1. 08 1 79 


•95729 


1. 0446 1 


15 


46 


.86216 


1.15987 


.89306 


1.11975 


.92493 


1.08116 


.95785 


1. 0440 1 


14 


*7 


.86267 


1.15919 


.89358 


1.11909 


.92547 


1.08053 


.95841 


1.04340 


13 


48 


.86318 


1.15851 


.89410 


1.11844 


.92601 


1.07990 


.95897 


1.04279 


12 


49 


.86368 


1^15783 


.89463 


1.11778 


.92655 


1.07927 


.95952 


1. 042 18 


II 


50 


.86419 


1.15715 


.89515 


1.11713 


.92709 


1.07864 


.96008 


1. 04 1 58 


10 


51 


.86470 


1.15647 


.89567 


1. 1 1648 


.92763 


1. 0780 1 


.96064 


1.04097 


9 


52 


.86521 


i^i5579 


.89620 


1.11582 


.92817 


1.07738 


.96120 


1.04036 


8 


53 


.86572 


1-15511 


.89672 


1.11517 


.92872 


1.07676 


.96176 


1.03976 


7 


54 


.86623 


I -1 5443 


.89725 


1.11452 


.92926 


1.07613 


.96232 


1.03915 


6 


55 


.86674 


1^15375 


.89777 


1.11387 


.92980 


1.07550 


.96288 


1.03855 


5 


56 


.86725 


1.15308 


.89830 


1.11321 


•93034 


1.07487 


.96344 


1.03794 


4 


57 


.86776 


1. 15240 


.89883 


1.11256 


.93088 


1.07425 


.96400 


1.03734 


3 


58 


.86827 


i^i5i72 


.89935 


1.11191 


.93143 


1.07362 


.96457 


1.03674 


2 


59 


.86878 


1.15104 


.899,88 


1.11126 


.93197 


1.07299 


.96513 


1.03613 


I 


5o 


.86929 


1. 15037 


.90040 


1.11061 


.93252 


1.07237 


•96569 


1.03553 





/ 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


Co-tan. 


Tan. 


f 




4i 


)° 


4 


SO 


4 


7° 


4i 


3° 





856 



GENERAL TABLES AND FORMULA 





440 






440 






440 




/ 


Tan. 


Co-TAN. 


' 


' 


Tan. 


Co-TAN. 


39 


/ 


Tan. 


Co-TAN. 


' 


o 


.96569 


1^03553 


60 


21 


.97756 


1.02295 


41 


.98901 


I.OIII2 


19 


I 


.96625 


1^03493 


59 


22 


.97813 


1.02236 


38 


42 


.98958 


I.OIO53 


18 


2 


.96681 


1.03433 


58 


23 


.97870 


1.02 1 76 


37 


43 


.99016 


1.00994 


17 


3 


.96738 


1.03372 


57 


24 


.97927 


I.02I17 


36 


44 


.99073 


1.00935 


16 


4 


.96794 


I.03312 


56 


25 


.97984 


1.02057 


35 


45 


.99131 


1.00876 


IS 


5 


.96850 


1.03252 


55 


26 


.98041 


1. 01 998 


34 


46 


.99189 


1. 008 1 8 


14 


6 


.96907 


I.03192 


54 


27 


.98098 


1. 01 939 


33 


47 


.99247 


1.00759 


13 


7 


.96963 


I.03132 


53 


28 


•98155 


1.01879 


32 


48 


.99304 


1. 00 70 1 


12 


8 


.97020 


1.03072 


52 


29 


.98213 


1.01820 


31 


49 


.99362 


1.00642 


II 


9 


.97076 


1. 030 1 2 


51 


30 


.98270 


1.01761 


30 


50 


.99420 


1.00583 


10 


lO 


.97133 


1.02952 


50 


31 


.98327 


1. 01 702 


29 


51 


.99478 


1.00525 


9 


II 


.97189 


1.02892 


49 


32 


•98384 


1.01642 


28 


52 


.99536 


1.00467 


8 


12 


.97246 


1.02832 


48 


33 


.98441 


1.01583 


27 


53 


.99594 


1 .00408 


7 


13 


.97302 


1.02772 


47 


34 


.98499 


1.01524 


26 


54 


.99652 


1.00350 


6 


14 


•97359 


1.02713 


46 


35 


.98556 


1.01465 


25 


55 


.99710 


1. 00291 


5 


IS 


.97416 


1.02653 


45 


36 


.98613 


1. 01 406 


24 


56 


.99768 


1.00233 


4 


i6 


.97472 


1.02593 


44 


37 


.98671 


1.01347 


23 


57 


.90826 


I.OOI75 


3 


17 


.97529 


1 .02533 


43 


38 


.98728 


1.01288 


22 


58 


.99884 


I.OOII6 


£ 


i8 


.97586 


1.02474 


42 


39 


.98786 


1.01229 


21 


59 


.99942 


1.00058 


I 


19 


•97643 


I.O2414 


41 


40 


.98843 


I. on 70 


20 


60 


I 


I 





2© 


.97700 


1^02355 


40 










f 








/ 


Co-TAN. 


Tan. 


/ 


t 


Co-TAN. 


Tan. 


~T 


Co-TAN. 


Tan. 


/ 




4 


5^ 






4 


5° 






45° 





NATURAL SINES AND COSINES 





0° 






0° 






0° 




f 


Sine 


Cosine 


/ 


t 


Sine 


Cosine 


' 


' 


Sine 


Cosine 


/ 





.00000 




60 


21 


.00611 


.99998 


39 


41 


.01193 


•99993 


~I9 


I 


.00029 




59 


22 


.00640 


.99998 


38 


42 


.01222 


•99993 


18 


2 


.00058 




58 


^Z 


.00669 


.99998 


37 


43 


.01251 


.99992 


17 


3 


.00087 




57 


24 


.00698 


.99998 


36 


44 


.01280 


•99992 


16 


4 


.00116 




56 


25 


.00727 


.99997 


35 


45 


.01309 


.99991 


15 


5 


.00145 




55 


26 


.00756 


.99997 


34 


46 


.01338 


.99991 


14 


6 


.00175 




54 


27 


.00785 


.99997 


33 


47 


.01367 


.99991 


13 


7 


.00204 




53 


28 


.00814 


.99997 


2>2 


48 


.01396 


.99990 


12 


8 


.00233 




52 


29 


.00844 


.99996 


31 


49 


.01425 


.99990 


II 


9 


.00262 




51 


30 


.00873 


.99996 


30 


50 


.01454 


.99989 


10 


10 


.00291 




50 


31 


.00902 


•99996 


29 


SI 


.01483 


.99989 


9 


II 


.00320 


.99999 


49 


32 


.00931 


.99996 


28 


52 


• .01513 


.99989 


8 


12 


.00349 


.99999 


48 


zz 


.00960 


.99995 


27 


SZ 


.01542 


.99988 


7 


13 


.00378 


.99999 


47 


34 


.00989 


•99995 


26 


54 


.01571 


.99988 


6 


14 


.00407 


.99999 


46 


35 


.01018 


•99995 


25 


55 


.01600 


.99987 


5 


15 


.00436 


.99999 


45 


36 


.01047 


•99995 


24 


56 


.01629 


.99987 


4 


16 


.00465 


.99999 


44 


37 


.01076 


.99994 


23 


57 


.01658 


.99986 


3 


17 


.00495 


.99999 


43 


38 


.01105 


.99994 


22 


58 


.01687 


.99986 


2 


18 


.00524 


.99999 


42 


39 


.01134 


.99994 


21 


59 


.01716 


.99985 


I 


19 


.00553 


•99998 


41 


40 


.01164 


•99993 


20 


60 


.01745 


.99985 





20 


.00582 


.99998 


40 


















f 


Cosine 

8 


Sine 
9° 


' 


/ 


Cosine 

8 


Sine 
9° 


t 


/ 


Cosine 
81 


Sine 


/ 



NATURAL SINES AND COSINES 



857 





] 


L<^ 


2° I 


3° 1 


40 , 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


' 


c 


.01745 


•99985 


•03490 


•99939 


.05234 


.99863 


.06976 


.99756 


60 


I 


•01774 


.99984 


.03519 


•99938 


.05263 


.99861 


.07005 


•99754 


5P 


2 


.01803 


.99984 


.03548 


•99937 


.05292 


.99860 


.07034 


.99752 


58 


3 


.01832 


•99983 


•03577 


.99936 


.05321 


.99858 


.07063 


.99750 


57 


4 


.01862 


.99983 


.03606 


•99935 


.05350 


•99857 


.07092 


.99748 


56 


5 


.01891 


.99982 


•03635 


•99934 


.05379 


.99855 


.07121 


.99746 


55 


6 


.01920 


.99982 


.03664 


.99933 


.05408 


.99854 


.07150 


.99744 


54 


7 


.01949 


.99981 


.03693 


•99932 


.05437 


.99852 


.07179 


.99742 


S3 


8 


.01978 


.99980 


•03723 


•99931 


.05466 


.99851 


.07208 


.99740 


52 


9 


.02007 


.99980 


•03752 


.99930 


.05495 


•99849 


.07237 


.99738 


51 


10 


.02036 


.99979 


.03781 


.99929 


.05524 


•99847 


.07266 


•99736 


50 


II 


.02065 


.99979 


.03810 


.99927 


.05553 


.99846 


.07295 


.99734 


49 


12 


.02094 


•99978 


•03839 


.99926 


.05582 


•99844 


.07324 


•99731 


48 


13 


.02123 


•99977 


.03868 


•99925 


.05611 


.99842 


•07353 


•99729 


47 


14 


.02152 


•99977 


.03897 


.99924 


.05640 


.99841 


.07382 


.99727 


46 


15 


.02181 


.99976 


.03926 


.99923 


.05669 


•99839 


.07411 


.99725 


45 


16 


.02211 


.99976 


•03955 


.99922 


.05698 


•99838 


.07440 


.99723 


44 


17 


.02240 


•99975 


•03984 


.99921 


.05727 


•99836 


.07469 


.99721 


43 


18 


.02269 


•99974 


.04013 


.99919 


.05756 


•99834 


.07498 


.99719 


42 


19 


.02298 


•99974 


.04042 


.99918 


.05785 


•99833 


.07527 


.99716 


41 


20 


.02327 


•99973 


.04071 


.99917 


.05814 


.99831 


•07556 


•99714 


40 


21 


.02356 


.99972 


.04100 


.99916 


.05844 


.99829 


.07585 


.99712 


39 


22 


.02385 


.99972 


.04129 


•99915 


.05873 


.99827 


.07614 


.99710 


38 


23 


.02414 


.99971 


.04159 


•99913 


.05902 


.99826 


.07643 


.99708 


37 


24 


.02443 


•99970 


.04188 


.99912 


.05931 


.99824 


.07672 


•99705 


36 


25 


.02472 


.99969 


.04217 


.99911 


.05960 


.99822 


.07701 


•99703 


35 


26 


.02501 


.99969 


.04246 


.99910 


.05989 


.99821 


.07730 


.99701 


34 


27 


.02530 


.99968 


.04275 


.99909 


.06018 


.99819 


.07759 


.99699 


33 


28 


.02560 


.99967 


•04304 


.99907 


.06047 


.99817 


.07788 


.99696 


32 


29 


.02589 


.99966 


.04333 


.99906 


.06076 


.99815 


.07817 


.99694 


31 


30 


.02618 


.99966 


.04362 


.99905 


.06105 


.99813 


.07846 


.99692 


30 


31 


.02647 


.99965 


•04391 


.99904 


.06134 


.99812 


.07875 


.99689 


29 


32 


.02676 


•99964 


.04420 


.99902 


.06163 


.99810 


.07904 


.99687 


28 


33 


.02705 


.99963 


.04449 


.99901 


.06192 


.99808 


.07933 


.99685 


27 


34 


.02734 


•99963 


.04478 


.99900 


.06221 


.99806 


.07962 


.99683 


26 


35 


.02763 


.99962 


.04507 


.99898 


.06250 


.99804 


.07991 


.99680 


25 


36 


.02792 


.99961 


.04536 


.99897 


.06279 


.99803 


.08020 


.99678 


24 


37 


.02821 


.99960 


.04565 


.99896 


.06308 


.99801 


.08049 


.99676 


23 


38 


.02850 


•99959 


.04594 


.99894 


.06337 


.99799 


.08078 


.99673 


22 


39 


.02879 


•99959 


.04623 


.99893 


.06366 


.99797 


.08107 


.99671 


21 


40 


.02908 


.99958 


.04653 


.99892 


.06395 


.99795 


.08136 


.99668 


20 


41 


.02938 


•99957 


.04682 


.99890 


.06424 


.99793 


.08165 


.99666 


19 


42 


.02967 


.99956 


.04711 


.99889 


.06453 


.99792 


.08194 


.99664 


18 


43 


.02996 


.99955 


.04740 


.99888 


.06482 


.99790 


.08223 


.99661 


17 


44 


.03025 


.99954 


.04769 


.99886 


.06511 


.99788 


.08252 


.99659 


16 


45 


.03054 


•99953 


.04798 


.99885 


.06540 


.99786 


.08281 


.99657 


IS 


46 


.03083 


.99952 


.04827 


.99883 


.06569 


.99784 


.08310 


.99654 


14 


47 


.03112 


.99952 


.04856 


.99882 


.06598 


.99782 


•08339 


.99652 


13 


48 


.03141 


•99951 


.04885 


.99881 


.06627 


.99780 


.08368 


.99649 


12 


49 


.03170 


•99950 


.04914 


.99879 


.06656 


.99778 


.08397 


.99647 


II 


50 


.03199 


.99949 


.04943 


.99878 


.06685 


.99776 


.08426 


.99644 


10 


51 


.03228 


.99948 


.04972 


.99876 


.06714 


.99774 


.08455 


.99642 


9 


52 


.03257 


•99947 


.05001 


•99875 


.06743 


.99772 


.08484 


.99639 


8 


53 


.03286 


.99946 


.05030 


•99873 


.06773 


.99770 


.08513 


.99637 


7 


54 


.03316 


•99945 


.05059 


.99872 


.06802 


.99768 


.08542 


.99635 


6 


55 


.03345 


•99944 


.05088 


.99870 


.06831 


.99766 


.08571 


.99632 


5 


S6 


.03374 


•99943 


.05117 


.99869 


.06860 


.99764 


.08600 


.99630 


4 


57 


•03403 


.99942 


.05146 


.99867 


.06889 


.99762 


.08629 


.99627 


3 


58 


.03432 


.99941 


.05175 


.99866 


.06918 


.99760 


.08658 


.99625 


2 


59 


.03461 


•99940 


.05205 


.99864 


.06947 


.99758 


.08687 


.99622 


I 


60 


.03490 


•99939 


.05234 


•99863 


.06976 


.99756 


.08716 


.99619 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 




8^ 


J° 


8 


7° 


8 


5° 


8 


5° 





8s8 



GENERAL TABLES AND FORMULA 





5° II 


6° II 


70 1 


8° I 


/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


o 


.08716 


.99619 


10453 


.99452 


12187 


.99255 


.13917 


.99027 


I 


.08745 


.99617 


10482 


.99449 


12216 


.99251 


.13946 


•99023 


2 


.08774 


.99614 


10511 


.99446 


12245 


.99248 


.13975 


.99019 


3 


.08803 


.99612 


10540 


.99443 


12274 


.99244 


.14004 


•99015 


4 


.08831 


.99609 


10569 


•99440 


12302 


.99240 


•14033 


.99011 


5 


.08860 


.99607 


10597 


•99437 


12331 


•99237 


.14061 


.99006 


6 


.08889 


.99604 


10626 


•99434 


12360 


•99233 


.14090 


.99002 


7 


.08918 


.99602 


10655 


•99431 


12389 


.99230 


.14119 


.98998 


8 


.08947 


.99599 


10684 


.99428 


12418 


.99226 


.14148 


•98994 


9 


.08976 


.99596 


10713 


.99424 


12447 


.99222 


.14177 


.98990 


lO 


.09005 


.99594 


10742 


.99421 


12476 


.99219 


.14205 


.98986 


II 


.09034 


•99591 


10771 


.99418 


12504 


.99215 


.14234 


.98982 


12 


.09063 


.99588 


10800 


•99415 


12533 


.99211 


.14263 


.98978 


13 


.09092 


.99586 


10829 


.99412 


12562 


.99208 


.14292 


•98973 


14 


.09121 


.99583 


10858 


.99409 


12591 


.99204 


.14320 


.98969 


IS 


.09150 


.99580 


10887 


.99406 


12620 


.99200 


.14349 


.98965 


i6 


.09179 


.99578 


10916 


.99402 


12649 


.99197 


.14378 


.98961 


17 


.09208 


.99575 


10945 


•99399 


12678 


•99193 


.14407 


.98957 


i8 


.09237 


.99572 


10973 


•99396 


12706 


.99189 


.14436 


•98953 


19 


.09266 


.99570 


1 1002 


•99393 


12735 


.99186 


.14464 


.98948 


20 


.09295 


.99567 


11031 


•99390 


12764 


.99182 


•14493 


•98944 


21 


.09324 


.99564 


1 1060 


•99386 


12793 


.99178 


.14522 


.98940 


22 


.09353 


.99562 


11089 


•99383 


12822 


.99175 


.14551 


.98936 


23 


.09382 


.99559 


11118 


•99380 


12851 


.99171 


.14580 


.98931 


24 


.09411 


.99556 


11147 


•99377 


12880 


.99167 


.14608 


.98927 


25 


.09440 


.99553 


11176 


•99374 


12908 


.99163 


.14637 


.98923 


26 


.09469 


.99551 


II 205 


•99370 


12937 


.99160 


.14666 


.98919 


27 


.09498 


.99548 


11234 


•99367 


12966 


.99156 


.14695 


.98914 


28 


.09527 


•99545 


11263 


•99364 


12995 


•99152 


.14723 


.98910 


29 


•09556 


•99542 


11291 


•99360 


13024 


.99148 


.14752 


.98906 


30 


.09585 


•99540 


11320 


•99357 


13053 


.99144 


.14781 


.98902 


31 


.09614 


•99537 


1 1 349 


•99354 


1 308 1 


.99141 


.14810 


.98897 


32 


.09642 


.99534 


11378 


•99351 


13110 


•99137 


.14838 


.98893 


33 


.09671 


.99531 


1 1407 


•99347 


13139 


•99133 


.14867 


.98889 


34 


.09700 


.99528 


1 1436 


•99344 


13168 


.99129 


.14896 


.98884 


35 


.09729 


.99526 


11465 


•99341 


13197 


.99125 


.14925 


.98880 


36 


.09758 


.99523 


1 1494 


.99337 


13226 


.99122 


•14954 


.98876 


37 


.09787 


.99520 


11523 


•99334 


13254 


.99118 


.14982 


.98871 


38 


.09816 


•99517 


11552 


•99331 


13283 


.99114 


.15011 


.98867 


39 


.09845 


.99514 


1 1 580 


•99327 


13312 


.99110 


.15040 


.98863 


40 


.09874 


.99511 


1 1609 


.99324 


13341 


.99106 


.15069 


.98858 


41 


.09903 


.99508 


11638 


•99320 


13370 


.99102 


.15097 


.98854 


42 


.09932 


.99506 


11667 


•99317 


13399 


.99098 


.15126 


.98849 


43 


.09961 


•99503 


1 1696 


•99314 


13427 


.99094 


.15155 


.98845 


44 


.09990 


.99500 


11725 


.99310 


13456 


.99091 


.15184 


.98841 


45 


.10019 


•99497 


11754 


.99307 


13485 


.99087 


.15212 


.98836 


46 


.10048 


•99494 


11783 


.99303 


13514 


.99083 


.15241 


.98832 


47 


.10077 


.99491 


11812 


.99300 


13543 


.99079 


.15270 


.98827 


48 


.10106 


.99488 


1 1 840 


.99297 


13572 


.99075 


.15299 


.98823 


49 


.10135 


.99485 


1 1869 


.99293 


13600 


.99071 


•15327 


.98818 


50 


.10164 


.99482 


1 1898 


.99290 


13629 


.99067 


•15356 


.98814 


51 


.10192 


.99479 


11927 


.99286 


13658 


.99063 


.15385 


.98809 


52 


.10221 


.99476 


11956 


.99283 


13687 


.99059 


•15414 


.98805 


53 


.10250 


•99473 


11985 


•99279 


13716 


.99055 


•15442 


.98800 


54 


.10279 


.99470 


12014 


.99276 


13744 


.99051 


•15471 


.98796 


55 


.10308 


.99467 


12043 


.99272 


13773 


.99047 


.15500 


•98791 


56 


•10337 


.99464 


12071 


.99269 


13802 


•99043 


.15529 


.98787 


57 


.10366 


.99461 


1 2 100 


.99265 


13831 


.99039 


.15557 


.98782 


58 


.10395 


•99458 


12129 


.99262 


13860 


•99035 


.15586 


.98778 


59 


.10424 


.99455 


12158 


.99258 


13889 


.99031 


.15615 


•98773 


60 


.10453 


.99452 


12187 


.99255 


13917 


.99027 


.15643 


.98769 


f 


Cosine 


Sine ( 


Cosine 


Sine C 


"OSINE 


Sine 


Cosine 


Sine 




8^ 


|o 


8: 


J° 


8^ 


\^ 


81 


L° 



NATURAL SINES AND COSINES 



8S9 





9^ 


10° 


IP 


12° 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


f 


o 


.15643 


.98769 


.17365 


.98481 


.19081 


.98163 


.20791 


•97815 


60 


I' 


.15672 


.98764 


.17393 


.98476 


.19109 


•98157 


.20820 


.97809 


59 


2 


.15701 


.98760 


.17422 


.98471 


.19138 


.98152 


.20848 


.97803 


58 


3 


.15730 


•98755 


.17451 


.98466 


.19167 


.98146 


.20877 


.97797 


57 


4 


.15758 


.98751 


.17479 


.98461 


.19195 


.98140 


.20905 


.97791 


56 


5 


.15787 


.98746 


.17508 


.98455 


.19224 


•98135 


.20933 


.97784 


55 


6 


.15816 


.98741 


.17537 


.98450 


.19252 


.98129 


.20962 


.97778 


54 


7 


•15845 


•98737 


.17565 


.98445 


.19281 


.98124 


.20990 


.97772 


53 


8 


.15873 


.98732 


•17594 


.98440 


.19309 


.98118 


.21019 


.97766 


52 


9 


.15902 


.98728 


.17623 


•98435 


.19338 


.98112 


.21047 


.97760 


51 


lO 


.15931 


.98723 


.17651 


.98430 


.19366 


.98107 


.21076 


.97754 


50 


II 


.15959 


.98718 


.17680 


.98425 


.19395 


.98101 


.21104 


.97748 


49 


12 


.15988 


.98714 


.17708 


.98420 


.19423 


.98096 


.21132 


.97742 


48 


13 


.16017 


.98709 


.17737 


.98414 


.19452 


.98090 


.21161 


.97735 


47 


14 


.16046 


.98704 


.17766 


.98409 


.19481 


.98084 


.21189 


.97729 


46 


IS 


.16074 


.98700 


.17794 


.98404 


.19509 


.98079 


.21218 


.97723 


45 


i6 


.16103 


.98695 


.17823 


.98399 


.19538 


.98073 


.21246 


.97717 


44 


17 


.16132 


.98690 


.17852 


•98394 


.19566 


.98067 


.21275 


.97711 


43 


i8 


.16160 


.98689 


.17880 


.98389 


.19595 


.98061 


.21303 


.97705 


42 


19 


.16189 


.98681 


.17909 


.98383 


.19623 


.98056 


.21331 


.97698 


41 


20 


.16218 


.98676 


.17937 


.98378 


.19652 


.98050 


.21360 


.97692 


40 


21 


.16246 


.98671 


.17966 


.98373 


.19680 


.98044 


.21388 


.97686 


39 


22 


.16275 


.98667 


.17995 


.98368 


.19709 


.98039 


.21417 


.97680 


38 


23 


.16304 


.98662 


.18023 


.98362 


.19737 


•98033 


.21445 


.97673 


37 


24 


.16333 


•98657 


.18052 


.98357 


.19766 


.98027 


.21474 


.97667 


36 


25 


.16361 


.98652 


.18081 


•98352 


.19794 


.98021 


.21502 


.97661 


35 


26 


.16390 


.98648 


.18109 


•98347 


.19823 


.98016 


.21530 


.97655 


34 


27 


.16419 


.98643 


.18138 


.98341 


.19851 


.98010 


•21559 


.97648 


33 


28 


.16447 


.98638 


.18166 


•98336 


.19880 


.98004 


.21587 


.97642 


32 


29 


.16476 


.98633 


.18195 


•98331 


.19908 


.97987 


.21616 


.97636 


31 


30 


.16505 


.98629 


.18224 


.98325 


.19937 


.97992 


.21644 


.97630 


30 


31 


.16533 


.98624 


.18252 


.98320 


.19965 


•97987 


.21672 


.97623 


29 


32 


.16562 


.98619 


.18281 


.98315 


.19994 


•97981 


.21701 


.97617 


28 


33 


.16591 


.98614 


.18309 


.98310 


.20022 


•97975 


.21729 


.97611 


27 


34 


.16620 


.98609 


.18338 


.98304 


.20031 


•97969 


.21758 


.97604 


26 


35 


.16648 


.98604 


.18367 


.98299 


.20079 


•97963 


.21786 


.97598 


25 


36 


.16677 


.98600 


.18395 


.98294 


.20108 


•97958 


.21814 


.97592 


24 


37 


.16706 


•98595 


.18424 


.98288 


.20136 


•97952 


.21843 


.97585 


23 


38 


.16734 


.98590 


.18452 


.98283 


.20165 


.97946 


.21871 


.97579 


22 


39 


.16763 


•98585 


.18481 


•98277 


.20193 


.97940 


.21899 


.97573 


21 


40 


.16792 


.98580 


.18509 


.98272 


.20222 


.97934 


.21928 


.97566 


20 


41 


.16820 


•98575 


.18538 


.98267 


.20250 


.97928 


.21956 


•97560 


19 


42 


.16849 


.98570 


.18567 


.98261 


.20279 


.97922 


.21985 


•97553 


18 


43 


.16878 


•98565 


•18595 


.98256 


.20307 


.97916 


.22013 


.97547 


17 


44 


.16906 


•98561 


.18624 


.98250 


.20336 


.97910 


.22041 


.97541 


16 


45 


.16935 


.98556 


.18652 


•98245 


.20364 


.97905 


.22070 


.97534 


15 


46 


.16964 


.98551 


.18681 


.98240 


.20393 


.97899 


.22098 


.97528 


14 


47 


.16992 


.98546 


.18710 


•98234 


.20421 


.97893 


.22126 


.97521 


13 


48 


.17021 


.98541 


.18738 


.98229 


.20450 


.97887 


.22155 


•97515 


12 


49 


.17050 


.98536 


.18767 


.98223 


.20478 


.97881 


.22183 


.97508 


II 


50 


.17078 


•98531 


.18795 


.98218 


.20507 


•97875 


.22212 


•97502 


10 


51 


.17107 


.98526 


.18824 


.98212 


•20535 


.97869 


.22240 


.97496 


9 


52 


.17136 


.98521 


.18852 


.98207 


.20563 


.97863 


.22268 


•97489 


8 


53 


.17164 


.98516 


.18881 


.98201 


.20592 


•97857 


.22297 


•97483 


7 


54 


.17193 


.98511 


.18910 


.98196 


.20620 


•97851 


.22325 


•97476 


6 


55 


.17222 


.98506 


.18938 


.98190 


.20649 


.97845 


.22353 


.97470 


5 


56 


.17250 


.98501 


.18967 


.98185 


.20677 


.97839 


.22382 


.97463 


4 


^1 


.17279 


.98496 


.18995 


•98179 


.20706 


.97833 


.22410 


.97457 


3 


58 


.17308 


.98491 


.19024 


•98174 


.20734 


.97827 


.22438 


.97450 


2 


59 


•17336 


.98486 


.19052 


.98168 


.20763 


.97821 


.22467 


.97444 


I 


60 


.17365 


.98481 


.19081 


•98163 


.20791 


.97815 


.22495 


•97437 







Cosine 


Sine 
1- \ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 




8f 


7S 





7£ 


)° 1 


77 


'O 





86o 



GENERAL TABLES AND FORMULA 





13° 


140 


15° 


1 


6° 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


f 


o 


.22495 


•97437 


.24192 


.97030 


.25882 


.96593 


.27564 


.96126 


60 


I 


.22523 


•97430 


.24220 


.97023 


.25910 


.96585 


.27592 


.96118 


59 


2 


.22552 


•97424 


.24249 


.97015 


.25938 


.96578 


.27620 


.96110 


58 


3 


.22580 


.97417 


.24277 


.97008 


.25966 


.96570 


.27648 


.96102 


57 


4 


.22608 


.97411 


•24305 


.97001 


.25994 


.96562 


.27676 


.96094 


56 


5 


.22637 


.97404 


.24333 


.96994 


.26022 


.96555 


.27704 


.96086 


55 


6 


.22665 


•97398 


.24362 


.96987 


.26050 


.96547 


.27731 


.96078 


54 


7 


.22693 


•97391 


.24390 


.96980 


.26079 


.96540 


.27759 


.96070 


53 


8 


.22722 


•97384 


.24418 


.96973 


.26107 


.96532 


.27787 


.96062 


52 


9 


.22750 


.97378 


.24446 


.96966 


•26135 


•96524 


.27815 


.96054 


51 


lO 


.22778 


•97371 


.24474 


.96959 


.26163 


.96517 


.27843 


.96046 


50 


11 


.22807 


•97365 


.24503 


•96952 


.26191 


.96509 


.27871 


.96037 


49 


12 


• .22835 


.97358 


.24531 


.96945 


.26219 


.96502 


.27899 


.96029 


48 


13 


.22863 


•97351 


.24559 


•96937 


.26247 


.96494 


.27927 


.96021 


47 


14 


.22892 


•97345 


.24587 


•96930 


.26275 


.96486 


.27955 


.96013 


46 


15 


.22920 


•97338 


.24615 


.96923 


.26303 


.96479 


.27983 


.96005 


45 


i6 


.22948 


•97331 


.24644 


.96916 


.26331 


.96471 


.28011 


•95997 


44 


17 


.22977 


•97325 


.24672 


.96909 


.26359 


.96463 


.28039 


.95989 


43 


i8 


.23005 


.97318 


.24700 


.96902 


.26387 


.96456 


.28067 


.95981 


42 


19 


.23033 


•97311 


.24728 


.96894 


.26415 


.96448 


.28095 


.95972 


41 


20 


.23062 


•97304 


.24756 


.96887 


.26443 


.96440 


.28123 


•95964 


40 


21 


.23090 


.97298 


.24784 


.96880 


.26471 


•96433 


.28150 


.95956 


39 


22 


.23118 


•97291 


•24813 


•96873 


.26500 


.96425 


.28178 


.95948 


38 


23 


.23146 


.97284 


.24841 


.96866 


.26528 


.96417 


.28206 


.95940 


37 


24 


.23175 


•97278 


.24869 


.96858 


.26556 


.96410 


.28234 


.95931 


36 


25 


.23203 


.97271 


.24897 


•96851 


.26584 


.96402 


.28262 


.95923 


35 


26 


.23231 


.97264 


.24925 


.96844 


.26612 


.96394 


.28290 


.95915 


34 


27 


.23260 


•97257 


.24954 


.96837 


.26640 


.96386 


.28318 


.95907 


33 


28 


.23288 


•97251 


.24982 


.96829 


.26668 


.96379 


.28346 


.95898 


32 


29 


.23316 


.97244 


.25010 


.96822 


.26696 


•96371 


.28374 


.95890 


31 


30 


.23345 


.97237 


.25038 


.96815 


.26724 


.96363 


.28402 


.95882 


30 


31 


.23373 


.97230 


.25066 


.96807 


.26752 


.96355 


.28429 


.95874 


29 


32 


.23401 


•97223 


.25094 


.96800 


.26780 


.96347 


.28457 


.95865 


28 


33 


.23429 


.97217 


.25122 


•96793 


.26808 


.96340 


.28485 


.95857 


27 


34 


.23458 


.97210 


•25151 


.96786 


.26836 


.96332 


.28513 


•95849 


26 


35 


.23486 


.97203 


.25179 


.96778 


.26864 


.96324 


.28541 


.95841 


25 


36 


.23514 


.97196 


.25207 


.96771 


.26892 


.96316 


.28569 


.95832 


24 


37 


.23542 


•97189 


.25235 


.96764 


.26920 


.96308 


.28597 


.95824 


23 


38 


•23571 


.97182 


.25263 


.96756 


.26948 


.96301 


.28625 


.95816 


22 


39 


.23599 


•97176 


.25291 


•96749 


.26976 


.96293 


.28652 


.95807 


21 


40 


.23627 


.97169 


.25320 


.96742 


.27004 


.96285 


.28680 


.95799 


20 


41 


.23656 


.97162 


.25348 


•96734 


.27032 


.96277 


.28708 


.95791 


19 


42 


.23684 


•97155 


.25376 


.96727 


.27060 


.96269 


.28736 


.95782 


18 


43 


.23712 


.97148 


.25404 


.96719 


.27088 


.96261 


.28764 


.95774 


17 


44 


•23740 


.97141 


.25432 


.96712 


.27116 


.96253 


.28792 


.95766 


16 


45 


.23769 


•97134 


.25460 


•96705 


.27144 


.96246 


.28820 


.95757 


15 


46 


.23797 


.97127 


.25488 


.96697 


.27172 


.96238 


.28847 


.95749 


14 


47 


.23825 


.97120 


.25516 


.96690 


.27200 


.96230 


.28875 


.95740 


13 


48 


•23853 


•97113 


•25545 


.96682 


.27228 


.96222 


.28903 


.95732 


12 


49 


.23882 


.97106 


.25573 


•96675 


.27256 


.96214 


.28931 


.95724 


II 


50 


.23910 


.97100 


.25601 


.96667 


.27284 


.96206 


.28959 


.95715 


10 


51 


.23938 


.97093 


.25629 


.96660 


.27312 


.96198 


.28987 


.95707 


9 


52 


.23966 


.97086 


.25657 


.96653 


.27340 


.96190 


.29015 


.95698 


8 


53 


.23995 


.97079 


.25685 


.96645 


•27368 


.96182 


.29042 


.95690 


7 


54 


.24023 


.97072 


.25713 


.96638 


.27396 


.96174 


.29070 


.95681 


6 


55 


.24051 


.97065 


.25741 


.96630 


.27424 


.96166 


.29098 


.95673 


5 


56 


.24079 


.97058 


.25769 


.96623 


.27452 


.96158 


.29126 


.95664 


4 


57 


.24108 


.97051 


.25798 


.96615 


.27480 


.96150 


.29154 


.95656 


3 


58 


.24136 


.97044 


.25826 


.96608 


.27508 


.96142 


.29182 


•95647 


2 


59 


.24164 


.97037 


.25854 


.96600 


.27536 


.96134 


.29209 


•95639 


I 


60 


.24192 


.97030 


.25882 


•96593 


.27564 


.96126 


.29237 


.95630 





f 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


f 




76 





75 





74 





73 








NATURAL SINES AND COSINES 



86i 





170 


18° 


19° 


20° 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


/ 


o 


.29237 


.95630 


.30902 


.95106 


.32557 


•94552 


.34202 


.93969 


60 


I 


.29265 


.95622 


.30929 


.95097 


.32584 


.94542 


.34229 


.93959 


59 


2 


.29293 


.95613 


.30957 


.95088 


.32612 


•94533 


.34257 


•93949 


58 


3 


.29321 


•95605 


•30985 


.95079 


.32639 


•94523 


.34284 


•93939 


57 


4 


.29348 


•95596 


.31012 


.95070 


.32667 


•94514 


•34311 


.93929 


56 


5 


.29376 


.95588 


.31040 


.95061 


.32694 


•94504 


•34339 


•93919 


55 


6 


.29404 


•95579 


.31068 


.95052 


.32722 


•94495 


•34366 


.93909 


54 


7 


.29432 


•95571 


•31095 


•95043 


•32749 


•94485 


•34393 


.93899 


53 


8 


.29460 


•95562 


•31123 


•95033 


.32777 


•94476 


.34421 


.93889 


52 


9 


.29487 


.95554 


•31151 


.95024 


.32804 


.94466 


•34448 


•93879 


51 


lO 


.29515 


•95545 


.31178 


.95015 


^32832 


•94457 


•34475 


.93869 


50 


II 


•29543 


.95536 


.31206 


.95006 


.32859 


•94447 


•34503 


.93859 


49 


12 


.29571 


.95528 


.31233 


•94997 


.32887 


•94438 


•34530 


.93849 


48 


13 


.29599 


.95519 


.31261 


.94988 


.32914 


.94428 


.34557 


.93839 


47 


14 


.29626 


.95511 


.31289 


.94979 


.32942 


.94418 


.34584 


.93829 


46 


15 


.29654 


.95502 


.31316 


.94970 


.32969 


•94409 


.34612 


•93819 


45 


i6 


.29682 


.95493 


.31344 


.94961 


•32997 


•94399 


.34639 


.93809 


44 


17 


.29710 


.95485 


.31372 


.94952 


•33024 


.94390 


.34666 


•93799 


43 


i8 


.29737 


.95476 


•31399 


•94943 


.33051 


.94380 


.34694 


•93789 


42 


19 


.29765 


.95467 


•31427 


•94933 


.33079 


.94370 


.34721 


.93779 


41 


20 


.29793 


•95459 


.31454 


.94924 


.33106 


.94361 


.34748 


.93769 


40 


21 


.29821 


.95450 


.31482 


•94915 


.33134 


•94351 


.34775 


•93759 


39 


22 


.29849 


.95441 


•31510 


.94906 


.33161 


.94342 


.34803 


•93748 


38 


23 


.29876 


•95433 


.31537 


•94897 


.33189 


•94332 


.34830 


•93738 


37 


24 


.29904 


.95424 


.31565 


.94888 


.33216 


.94322 


.34857 


.93728 


36 


25 


.29932 


•95415 


.31593 


.94878 


.33244 


•94313 


.34884 


•93718 


35 


26 


.29960 


•95407 


.31620 


.94869 


.33271 


•94303 


.34912 


.93708 


34 


27 


.29987 


•95398 


.31648 


.94860 


.33298 


.94293 


.34939 


.93698 


33 


28 


.30015 


•95389 


.31675 


.94851 


.33326 


.94284 


.34966 


.93688 


32 


29 


.30043 


•95380 


.31703 


.94842 


■33353 


•94274 


.34993 


.93677 


31 


30 


.30071 


.95372 


•31730 


.94832 


'333^1 


.94264 


.35021 


.93667 


30 


31 


.30098 


•95363 


.31758 


.94823 


•33408 


.94254 


.35048 


.93657 


29 


32 


.30126 


•95354 


.31786 


.94814 


.33436 


•94245 


.35075 


•93647 


28 


33 


•30154 


.95345 


.31813 


.94805 


•33463 


•94235 


.35102 


•93637 


27 


34, 


.30182 


•95337 


.31841 


•94795 


•33490 


.94225 


.35130 


.93626 


26 


35 


.30209 


.95328 


.31868 


.94786 


•33518 


.94215 


.35157 


•93616 


25 


36 


•30237 


•95319 


.31896 


•94777 


•33545 


.94206 


.35184 


.93606 


24 


37 


.30265 


•95310 


.31923 


.94768 


.33573 


.94196 


•35211 


•93596 


23 


38 


.30292 


•95301 


.31951 


•94758 


.33600 


.94186 


•35239 


•93585 


22 


39 


•30320 


•95293 


.31979 


.94749 


.33627 


.94176 


•35266 


•93575 


21 


40 


•30348 


•95284 


.32006 


.94740 


.33655 


.94167 


•35293 


•93565 


20 


41 


•30376 


•95275 


.32034 


.94730 


.33682 


•94157 


•35320 


.93555 


19 


42 


•30403 


.95266 


.32061 


.94721 


.33710 


.94147 


•35347 


•93544 


18 


43 


•30431 


.95257 


.32089 


.94712 


•33737 


•94137 


•35375 


•93534 


17 


44 


•30459 


.95248 


.32116 


.94702 


•33764 


.94127 


.35402 


•93524 


16 


45 


.30486 


.95240 


.32144 


•94693 


•33792 


.94118 


.35429 


.93514 


15 


46 


•30514 


•95231 


.32171 


.94684 


•33819 


.94108 


.35456 


.93503 


14 


47 


•30542 


.95222 


•32199 


•94674 


.33846 


.94098 


.35484 


•93493 


13 


48 


•30570 


•95213 


.32227 


•94665 


.33874 


.94088 


.35511 


.93483 


12 


49 


•30597 


•95204 


•32254 


.94656 


.33901 


.94078 


.35538 


.93472 


II 


50 


.30625 


•95195 


.32282 


.94646 


.33929 


.9406S 


.35565 


.93462 


10 


51 


.30653 


.95186 


.32309 


•94637 


•33956 


.94058 


.35592 


.93452 


9 


52 


.30680 


•95177 


•32337 


.94627 


.33983 


•94049 


.35619 


.93441 


8 


53 


•30708 


.95168 


•32364 


.94618 


.34011 


•94039 


.35647 


.93431 


7 


54 


•30736 


.95159 


.32392 


.94609 


.34038 


.94029 


•35674 


.93420 


6 


55 


.30763 


•95150 


.32419 


•94599 


•34065 


.94019 


•35701 


.93410 


5 


56 


.30791 


.95142 


•32447 


.94590 


.34093 


.94009 


.35728 


.93400 


4 


57 


•30819 


•95133 


•32474 


.94580 


.34120 


•93999 


.35755 


•93389 


3 


58 


.30846 


.95124 


.32502 


•94571 


•34147 


"93989 


.35782 


•93379 


2 


59 


.30874 


•95115 


.32529 


•94561 


.34175 


•93979 


.35810 


.93368 


I 


60 


.30902 


.95106 


.32557 


.94552 


.34202 


.93969 


.35837 


.93358 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 




7^ 




7] 


L° 


7( 


r 


6^ 


r 





862 



GENERAL TABLES AND FORMULA 





21^ 


22° 


23° 


24<^ 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


/ 


o 


•35837 


.93358 


.37461 


.92718 


•39073 


.92050 


.40674 


.91355 


6a 


I 


.35864 


.93348 


•37488 


.92707 


.39100 


.92039 


.40700 


.91343 


55 


2 


.35891 


.93337 


.37515 


.92697 


.39127 


.92028 


.40727 


.91331 


58 


3 


.35918 


.93327 


.37542 


.92686 


.39153 


.92016 


.40753 


.91319 


57 


4 


.35945 


.93316 


.37569 


.92675 


.39180 


.92005 


.40780 


.91307 


5^ 


5 


.35973 


.93306 


.37595 


.92664 


.39207 


.91994 


.40806 


.91295 


55 


6 


.36000 


.93295 


.37622 


.92653 


.39234 


.91982 


.40833 


.91283 


SA 


7 


.36027 


.93285 


.37649 


.92642 


.39260 


.91971 


.40860 


.91272 


53 


8 


.36054 


.93274 


.37676 


.92631 


.39287 


.91959 


.40886 


.91260 


Sa 


9 


.36081 


•93264 


.37703 


.92620 


.39314 


.91948 


.40913 


.91248 


51 


lO 


.36108 


•93253 


.37730 


.92609 


.39341 


.91936 


.40939 


.91236 


50 


II 


.36135 


.93243 


•37757 


.92598 


.39367 


.91925 


.40966 


.91224 


45 


12 


.36162 


.93232 


.37784 


.92587 


.39394 


.91914 


.40992 


.91212 


4? 


13 


.36190 


.93222 


.37811 


.92576 


.39421 


.91902 


.41019 


.91200 


4^ 


14 


.36217 


.93211 


.37838 


.92565 


.39448 


.91891 


.41045 


.91188 


4^ 


15 


.36244 


.93201 


.37865 


•92554 


.39474 


.91879 


.41072 


.91176 


45 


i6 


.36271 


.93190 


.37892 


•92543 


.39501 


.91868 


.41098 


.91164 


4^ 


17 


.36298 


.93180 


.37919 


•92532 


.39528 


.91856 


.41125 


.91152 


43 


i8 


.36325 


.93169 


•37946 


•92521 


.39555 


.91845 


.41151 


.91140 


42 


19 


.36352 


•93159 


•37973 


•92510 


.39581 


.91833 


.41178 


.91128 


41 


20 


.36379 


.93148 


•37999 


.92499 


.39608 


.91822 


.41204 


.91116 


4C 


21 


.36406 


.93137 


.38026 


.92488 


.39635 


.91810 


.41231 


.91104 


3? 


22 


.36434 


.93127 


•38053 


.92477 


.39661 


.91799 


.41257 


.91092 


3« 


23 


.36461 


.93116 


.38080 


.92466 


.39688 


.91787 


.41284 


.91080 


3) 


24 


.36488 


.93106 


.38107 


.92455 


.39715 


.91775 


.41310 


.91068 


3^ 


25 


.36515 


•93095 


•38134 


.92444 


.39741 


.91764 


.41337 


.91056 


35 


26 


.36542 


•93084 


.38161 


.92432 


.39768 


.91752 


.41363 


.91044 


3A 


27 


.36569 


•93074 


.38188 


.92421 


.39795 


.91741 


.41390 


.91032 


3Z 


28 


.36596 


•93063 


.38215 


.92410 


.39822 


.91729 


.41416 


.91020 


32 


29 


.36623 


.93052 


.38241 


.92399 


.39848 


.91718 


.41443 


.91008 


31 


30 


.36650 


.93042 


.38268 


.92388 


.39875 


.91706 


.41469 


.90996 


30 


31 


.36677 


•93031 


.38295 


.92377 


.39902 


.91694 


.41496 


.90984 


2g 


32 


.36704 


.93020 


.38322 


.92366 


.39928 


.91683 


.41522 


.90972 


28 


33 


.36731 


.93010 


.38349 


.92355 


.39955 


.91671 


.41549 


.90960 


27 


34 


.36758 


.92999 


.38376 


.92343 


.39982 


.91660 


•41575 


.90948 


26 


ZS 


.36785 


.92988 


.38403 


.92332 


.40008 


.91648 


^1602 


.90936 


25 


36 


.36812 


.92978 


.38430 


.92321 


.40035 


.91636 


.41628 


.90924 


24 


37 


.36839 


.92967 


.38456 


.92310 


.40062 


.91625 


.41655 


.90911 


23 


38 


.36867 


.92956 


.38483 


.92299 


.40088 


.91613 


.41681 


.90899 


22 


39 


.36894 


.92945 


.38510 


.92287 


.40115 


.91601 


.41707 


.90887 


21 


40 


.36921 


.92935 


.38537 


.92276 


.40141 


.91590 


.41734 


.90875 


20 


41 


.36948 


.92924 


.38564 


.92265 


.40168 


.91578 


.41760 


.90863 


19 


42 


.36975 


.92913 


.38591 


.92254 


.40195 


.91566 


.41787 


.90851 


18 


43 


.37002 


.92902 


.38617 


.92243 


.40221 


.91555 


.41813 


.90839 


17 


44 


.37029 


.92892 


.38644 


.92231 


.40248 


.91543 


.41840 


.90826 


16 


45 


•37056 


.92881 


.38671 


.92220 


.40275 


.91531 


.41866 


.90814 


15 


46 


.37083 


.92870 


.38698 


.92209 


.40301 


.91519 


.41892 


.90802 


14 


47 


.37110 


•92859 


.38725 


.92198 


.40328 


.91508 


.41919 


.90790 


13 


48 


.37137 


.92849 


.38752 


.92186 


.40355 


.91496 


.41945 


.90778 


12 


49 


.37164 


.92838 


.38778 


•92175 


.40381 


.91484 


.41972 


.90766 


II 


50 


•37191 


.92827 


.38805 


.92164 


.40408 


.91472 


.41998 


.90753 


10 


51 


.37218 


.92816 


.38832 


.92152 


.40434 


.91461 


.42024 


.90741 


9 


S2 


.37245 


.92805 


•38859 


.92141 


.40461 


.91449 


.42051 


.90729 


8 


53 


.37272 


.92794 


.38886 


.92130 


.40488 


.91437 


.42077 


.90717 


7 


54 


.37299 


.92784 


.38912 


.92119 


.40514 


.91425 


.42104 


.90704 


6 


55 


.37326 


.92773 


.38939 


.92107 


.40541 


.91414 


.42130 


.90692 


5 


56 


.37353 


.92762 


.38966 


.92096 


•40567 


.91402 


.42156 


.90680 


4 


57 


•37380 


.92751 


.38993 


.92085 


.40594 


.91390 


.42183 


.90668 


3 


58 


.37407 


.92740 


.39020 


.92073 


.40621 


.91378 


.42209 


•90655 


2 


59 


.37434 


.92729 


.39046 


.92062 


.40647 


.91366 


.42235 


.90643 


I 


60 


.37461 


.92718 


.39073 


.92050 


.40674 


.91355 


.42262 


.90631 




/ 


f 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


•Sine 


Cosine 


Sine 


i 


6S 


? 1 


6' 


JO \ 


66 


>° 


6i 


)° 





NATURAL SINES AND COSINES 



863 





25^ 


26° 


27° 


28° 




/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


/ 





.42262 


.90631 


•43837 


.89879 


.45399 


.89101 


•46947 


.88295 


60 


I 


.42288 


.90618 


•43863 


.89867 


.45425 


.89087 


•46973 


.88281 


59 


2 


.42315 


.90606 


.43889 


•89854 


•45451 


.89074 


.46999 


.88267 


58 


3 


.42341 


.90594 


.43916 


.89841 


•45477 


.89061 


.47024 


.88254 


57 


4 


.42367 


.90582 


.43942 


.89828 


•45503 


.89048 


.47050 


.88240 


56 


5 


.42394 


.90569 


.43968 


.89816 


•45529 


•89035 


.47076 


.88226 


55 


J 6 


.42420 


•90557 


.43994 


.89803 


•45554 


.89021 


.47101 


.88213 


54 


7 


.42446 


.90545 


.44020 


.89790 


•45580 


.89008 


.47127 


.88199 


53 


8 


•42473 


•90532 


.44046 


•89777 


.45606 


.88995 


.47153 


.88185 


52 


9 


.42499 


.90520 


.44072 


.89764 


•45632 


.88981 


.47178 


.88172 


51 


10 


•42525 


•90507 


.44098 


.89752 


•45658 


.88968 


.47204 


.88158 


50 


II 


.42552 


•90495 


.44124 


.89739 


.45684 


•88955 


.47229 


.88144 


49 


13 


.42578 


•90483 


.44151 


.89726 


•45710 


.88942 


.47255 


.88130 


48 


13 


.42604 


.90470 


.44177 


.89713 


•45736 


.88928 


.47281 


.88117 


47 


14 


.42631 


.90458 


.44203 


.89700 


•45762 


.88915 


.47306 


.88103 


46 


15 


•42657 


.90446 


.44229 


.89687 


•45787 


.88902 


.47332 


.88089 


45 


16 


.42683 


•90433 


•44255 


.89674 


•45813 


.88888 


.47358 


.88075 


44 


17 


.42709 


.90421 


.44281 


.89662 


.45839 


.88875 


.47383 


.88062 


43 


18 


.42736 


.90408 


.44307 


.89649 


.45865 


.88862 


.47409 


.88048 


42 


19 


.42762 


.90396 


•44333 


.89636 


.45891 


.88848 


.47434 


.88034 


41 


20 


.42788 


•90383 


.44359 


.89623 


.45917 


•88835 


.47460 


.88020 


40 


21 


.42815 


.90371 


•44385 


.89610 


.45942 


.88822 


.47486 


.88006 


39 


22 


.42841 


.90358 


.44411 • 


.89597 


.45968 


.88808 


.47511 


.87993 


38 


23 


.42867 


.90346 


.44437 


.89584 


•45994 


.88795 


.47537 


.87979 


37 


24 


.42894 


.90334 


.44464 


.89571 


.46020 


.88782 


.47562 


.87965 


36 


25 


.42920 


.90321 


.44490 


.89558 


.46046 


.887^8 


.47588 


.87951 


35 


26 


.42946 


.90309 


.44516 


.89545 


.46072 


•88755 


•47614 


.87937 


34 


27 


.42972 


.90296 


.44542 


.89532 


.46097 


.88741 


.47639 


.87923 


33 


28 


.42999 


.90284 


.44568 


.89519 


.46123 


.88728 


.47665 


.87909 


32 


29 


•43025 


.90271 


.44594 


.89506 


.46149 


•88715 


.47690 


.87896 


31 


30 


•43051 


.90259 


.44620 


89493 


.46175 


.88701 


.47716 


.87882 


30 


31 


•43077 


.90246 


.44646 


.89480 


.46201 


.88688 


.47741 


.87868 


29 


32 


.43104 


.90233 


.44672 


•89467 


.46226 


.88674 


.47767 


•87854 


28 


33 


•43130 


.90221 


.44698 


.89454 


.46252 


.88661 


.47793 


.87840 


27 


34 


.43156 


.90208 


•44724 


.89441 


.46278 


.88647 


.47818 


.87826 


26 


35 


.43182 


.90196 


•44750 


.89428 


.46304 


.88634 


.47844 


.87812 


25 


36 


.43209 


.90183 


.44776 


.89415 


•46330 


.88620 


.47869 


.87798 


24 


37 


.43235 


.90171 


.44802 


.89402 


.46355 


.88607 


.47895 


.87784 


23 


38 


.43261 


.90158 


.44828 


.89389 


.46381 


.88593 


.47920 


.87770 


22 


39 


.43287 


.90146 


.44854 


.89376 


.46407 


.88580 


.47946 


.87756 


21 


40 


.43313 


•90133 


.44880 


.89363 


.46433 


.88566 


.47971 


.87743 


20 


41 


.43340 


.90120 


.44906 


.89350 


.46458 


.88553 


.47997 


.87729 


19 


42 


.43366 


.90108 


•44932 


.89337 


.46484 


.88539 


.48022 


.87715 


18 


43 


.43392 


.90095 


.44958 


.89324 


.46510 


.88526 


.48048 


.87701 


17 


44 


.43418 


.90082 


•44984 


.89311 


.46536 


.88512 


.48073 


.87687 


16 


45 


.43445 


.90070 


.45010 


.89298 


.46561 


.88499 


.48099 


.87673 


15 


46 


.43471 


•90057 


•45036 


.89285 


.46587 


.88485 


.48124 


•87659 


14 


47 


.43497 


•90045 


.45062 


.89272 


.46613 


.88472 


.48150 


.87645 


13 


48 


.43523 


.90032 


.45088 


.89259 


•46639 


.88458 


.48175 


•87631 


12 


49 


.43549 


.90019 


•45114 


.89245 


.46664 


.88445 


.48201 


.87617 


II 


50 


•43575 


.90007 


.45140 


.89232 


.46690 


•88431 


.48226 


•87603 


10 


51 


.43602 


•89994 


.45166 


.89219 


.46716 


.88417 


.48252 


.87589 


9 


52 


.43628 


.89981 


45192 


.89206 


.46742 


.88404 


.48277 


•87575 


8 


53 


.43654 


.89968 


•45218 


.89193 


•46767 


.88390 


.48303 


•87561 


7 


54 


.43680 


•89956 


•45243 


.89180 


•46793 


•88377 


.48328 


.87546 


6 


55 


•43706 


.89943 


.45269 


.89167 


.46819 


.88363 


.48354 


.87532 


5 


56 


•43733 


.89930 


.45295 


.89153 


.46844 


•88349 


.48379 


.87518 


4 


57 


.43759 


.89918 


•45321 


.89140 


.46870 


•88336 


.48405 


.87504 


3 


58 


.43785 


.89905 


•45347 


.89127 


.46896 


.88322 


.48430 


.87490 


3 


59 


.43811 


.89892 


•45373 


.89114 


.46921 


.88308 


.48456 


.87476 


I 


60 


.43837 


.89879 


•45399 


.89101 


•46947 


.88295 


.48481 


.87462 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 




6^ 


[" 


6c 


5^ 


6^ 


}o 


6] 








864 


GENERAL TABLES AND 


FORMULA 








29° 1 


30° 




31° 


32° 




/ 


Sine 


Cosine 


Sine ( 


:OSINE 


Sine 


Cosine 


Sine 


Cosine 


60 


O 


.48481 


.87462 


.50000 


86603 


•51504 


•85717 


.52992 


.84805 


I 


.48506 


.87448 


.50025 


86588 


.51529 


.85702 


.53017 


.84789 


59 


2 


•48532 


.87434 


.50050 


86573 


.51554 


.85687 


.53041 


.84774 


58 


3 


.48557 


.87420 


.50076 


86559 


.51579 


.85672 


•53066 


.84759 


57 


4 


.48583 


.87406 


.50101 


86544 


,.51604 


.85657 


.53091 


.84743 


56 


5 


.48608 


.87391 


.50126 


86530 


.51628 


.85642 


•53115 


.84728 


55 


6 


.48634 


.87377 


•50151 


86515 


•51653 


.85627 


•53140 


.84712 


54 


7 


.48659 


.87363 


.50176 


86501 


•51678 


.85612 


•53164 


.84697 


53 


8 


.48684 


.87349 


.50201 


86486 


•51703 


.85597 


•53189 


.84681 


52 


9 


.48710 


•87335 


.50227 


86471 


•51728 


.85582 


.53214 


.84666 


51 


lO 


.48735 


•87321 


.50252 


86457 


•51753 


.85567 


•53238 


.84650 


50 


11 


.48761 


.87306 


.50277 


86442 


.51778 


•85551 


•53263 


•84635 


49 


12 


.48786 


.87292 


.50302 


86427 


•51803 


.85536 


•53288 


.84619 


48 


13 


.48811 


.87278 


•50327 


86413 


.51828 


•85521 


•53312 


.84604 


47 


14 


.48837 


.87264 


•50352 


86398 


.51852 


.85506 


•53337 


.84588 


46 


15 


.48862 


.87250 


.50377 


86384 


.51877 


.85491 


.53361 


•84573 


45 


16 


.48888 


.87235 


•50403 


86369 


•51902 


•85476 


.53386 


•84557 


44 


17 


.48913 


.87221 


.50428 


86354 


•51927 


.85461 


.53411 


.84542 


43 


18 


.48938 


.87207 


•50453 


86340 


.51952 


.85446 


.53435 


.84526 


42 


19 


.48964 


.87193 


.50478 


86325 


.51977 


.85431 


.53460 


.84511 


41 


20 


.48989 


.87178 


.50503 


86310 


.52002 


.85416 


•53484 


.84495 


40 


21 


.49014 


.87164 


.50528 


8629"; 


.52026 


.85401 


•53509 


.84480 


39 


22 


.49040 


.87150 


•50553 


86281 


.52051 • 


.85385 


•53534 


.84464 


38 


23 


.49065 


.87136 


•50578 


86266 


•52076 


.85370 


.53558 


.84448 


37 


24 


.49090 


.87121 


.50603 


86251 


.52101 


.85355 


•53583 


.84433 


36 


25 


.49116 


.87107 


.50628 


86237 


.52126 


.85340 


.53607 


.84417 


35 


26 


.49141 


.87093 


•50654 


86222 


•52151 


.85325 


.53632 


.84402 


34 


27 


49166 


.87079 


.50679 


86207 


•52175 


.85310 


.53656 


.84386 


33 


28 


.49192 


.87064 


.50704 


86192 


.52200 


.85294 


.53681 


.84370 


32 


29 


.49217 


.87050 


.50729 


86178 


•52225 


•85279 


.53705 


.84355 


31 


30 


.49242 


•87036 


•50754 


86163 


.52250 


.85264 


.53730 


.84339 


30 


31 


.49268 


.87021 


•50779 


86148 


•52275 


.85249 


.53754 


.84324 


29 


32 


.49293 


.87007 


.50804 


86133 


.52299 


.85234 


.53779 


.84308 


28 


33 


.49318 


.86993 


.50829 


86II9 


•52324 


.85218 


.53804 


.84292 


27 


34 


.49344 


.86978 


.50854 


86104 


•52349 


.85203 


.53828 


.84277 


26 


35 


.49369 


.86964 


•50879 


86089 


.52374 


.85188 


.53853 


.84261 


25 


36 


.49394 


.86949 


•50904 


86074 


•52399 


.85173 


.53877 


.84245 


24 


37 


.49419 


.86935 


.50929 


86059 


•52423 


.85157 


.53902 


.84230 


23 


38 


.49445 


.86921 


•50954 


86045 


.52448 


.85142 


.53926 


.84214 


22 


39 


.49470 


.86906 


•50979 


86030 


•52473 


.85127 


.53951 


.84198 


21 


40 


•49495 


.86892 


.51004 


86015 


.52498 


.85112 


.53975 


.84182 


20 


41 


.49521 


.86878 


.51029 


86000 


.52522 


.85096 


.54000 


.84167 


19 


42 


.49546 


.86863 


•51054 


85985 


.52547 


.85081 


.54024 


.84151 


18 


43 


.49571 


.86849 


•51079 


85970 


•52572 


.85066 


.54049 


.84135 


17 


44 


.49596 


.86834 


.51104 


85956 


•52597 


.85051 


.54073 


.84120 


16 


45 


.49622 


.86820 


.51129 


85941 


.52621 


•85035 


•54097 


.84104 


15 


46 


.49647 


.86805 


.51154 


85926 


.52646 


.85020 


.54122 


.84088 


14 


47 


.49672 


.86791 


.51179 


859II 


.52671 


.85005 


•54146 


.84072 


13 


48 


.49697 


.86777 


.51204 


85896 


.52696 


.84989 


•54171 


.84057 


12 


49 


.49723 


.86762 


.51229 


85881 


•52720 


•84974 


•54195 


.84041 


II 


50 


.49748 


.86748 


.51254 


85866 


•52745 


.84959 


.54220 


.84025 


10 


51 


.49773 


.86733 


.51279 


85851 


.52770 


.84943 


•54244 


.84009 


9 


52 


.49798 


.86719 


•51304 


85836 


.52794 


.84928 


.54269 


.83994 


8 


53 


.49824 


.86704 


•51329 


85821 


.52819 


.84913 


•54293 


.83978 


7 


54 


.49849 


.86690 


•51354 


85806 


.52844 


.84897 


•54317 


.83962 


6 


55 


.49874 


.86675 


.51379 


85792 


.52869 


.84882 


•54342 


.83946 


5 


56 


.49899 


.86661 


.51404 


85777 


.52893 


.84866 


.54366 


.83930 


4 


57 


.49924 


.86646 


.51429 


85762 


.52918 


.84851 


.54391 


.83915 


3 


58 


.49950 


.86632 


.51454 


85747 


•52943 


.84836 


•54415 


•83899 


2 


59 


•49975 


.86617 


.51479 


85732 


.52967 


.84820 


.54440 


.83883 


I 


60 


.50000 


.86603 


•51504 


85717 


.52992 


.84805 


•54464 


.83867 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


'1 
1 




61 


[)° 


59° 




5i 


^° 


5: 


r° 



NATURAL SINES AND COSINES 



865 





33^ 


34° 


35° I 


36 







/ 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosnie 


/ 


^ 


.54464 


.83867 


.55919 


.82904 


.57358 


.81915 


.58779 


.80902 


60 


^ I 


.54488 


.83851 


.55943 


.82887 


.57381 


.81899 


.58802 


.80885 


59 


? 2 


.54513 


.83835 


.55968 


.82871 


.57405 


.81882 


.58826 


.80867 


58 


3 


.54537 


•83819 


.55992 


.82855 


.57429 


.81865 


.58849 


.80850 


57 


4 


.54561 


.83804 


.56016 


.82839 


.57453 


.81848 


.58873 


.80833 


56 


5 


.54586 


.83788 


.56040 


.82822 


.57477 


.81832 


.58896 


.80816 


55 


6 


.54610 


.83772 


.56064 


.82806 


.57501 


.81815 


.58920 


.80799 


54 


' 7 


.54635 


.83756 


.56088 


.82790 


.57524 


.81798 


.58943 


.80782 


53 


. 8 


.54659 


•83740 


.56112 


.82773 


.57548 


.81782 


.58967 


.80765 


52 


9 


.54683 


.83724 


.56136 


.82757 


.57572 


.81765 


.58990 


.80748 


51 


10 


.54708 


.83708 


.56160 


.82741 


•57596 


.81748 


.59014 


.80730 


50 


II 


.54732 


83692 


•56184 


.82724 


.57619 


.81731 


.59037 


.80713 


49 


12 


.54756 


.83676 


.56208 


.82708 


.57643 


.81714 


.59061 


.80696 


48 


13 


.54781 


.83660 


.56232 


.82692 


•57667 


.81698 


.59084 


.80679 


47 


14 


.54805 


.83645 


.56256 


.82675 


.57691 


.81681 


•59108 


.80662 


46 


15 


.54829 


.83629 


.56280 


.82659 


.57715 


.81664 


•59131 


.80644 


45 


16 


.54854 


.83613 


■56305 


.82643 


.57738 


.81647 


•59154 


.80627 


44 


17 


.54878 


.83597 


.56329 


.82626 


.57762 


.81631 


.59178 


.80610 


43 


18 


.54902 


.83581 


.56353 


.82610 


.57786 


.81614 


.59201 


.80593 


42 


19 


.54927 


.83565 


.56377 


.82593 


.57810 


.81597 


.59225 


.80576 


41 


20 


.54951 


.83549 


.56401 


.82577 


.57833 


.81580 


.59248 


.80558 


40 


21 


.54975 


■^3533 


.56425 


.82561 


.57857 


.81563 


.59272 


.80541 


39 


22 


.54999 


.83517 


.56449 


.82544 


.57881 


.81546 


.59295 


.80524 


38 


23 


.55024 


.83501 


.56473 


.82528 


.57904 


.81530 


.59318 


.80507 


37 


24 


.55048 


.83485 


.56497 


.82511 


.57928 


.81513 


.59342 


.80489 


36 


25 


.55072 


.83469 


.56521 


.82495 


.57952 


.81496 


•5936s 


.80472 


35 


26 


.55097 


•83453 


•56545 


.82478 


.57976 


•81479 


•59389 


.80455 


34 


27 


.55121 


.83437 


•56569 


.82462 


.57999 


.81462 


.59412 


.80438 


33 


28 


.55145 


•83421 


•56593 


.82446 


.58023 


•81445 


.59436 


.80420 


32 


29 


•55169 


•83405 


.56617 


.82429 


.58047 


.81428 


.59459 


.80403 


31 


30 


.55194 


.83389 


.56641 


.82413 


.58070 


.81412 


.59482 


.80386 


30 


31 


.55218 


.83373 


.56665 


.82396 


.58094 


.81395 


.59506 


.80368 


29 


32 


.55242 


.83356 


.56689 


.82340 


.58118 


.81378 


.59529 


.80351 


28 


33 


.55266 


•83340 


.56713 


.82363 


.58141 


.81361 


.59552 


.80334 


27 


34 


•55291 


•83324 


.56736 


.82347 


.58165 


.81344 


.59576 


.80316 


26 


35 


.55315 


•83308 


.56760 


.82330 


^58x89 


.81327 


.59599 


.80299 


25 


36 


.55339 


.83292 


.56784 


.82314 


.58212 


.81310 


.59622 


.80282 


24 


37 


.55363 


.83276 


.56808 


.82297 


.58236 


.81293 


.59646 


.80264 


23 


38 


.55388 


.83260 


.56832 


.82281 


.58260 


.81276 


.59669 


.80247 


22 


39 


.55412 


.83244 


.56856 


.82264 


.58283 


.81259 


.59693 


.80230 


21 


40 


.55436 


.83228 


.56880 


.82248 


.58307 


.81242 


.59716 


.80212 


20 


41 


.55460 


.83212 


.56904 


.82231 


.58330 


.81225 


.59739 


.80195 


19 


42 


.55484 


.83195 


.56928 


.82214 


.58354 


.81208 


.59763 


.80178 


18 


43 


.55509 


•83179 


•56952 


.82198 


.58378 


.81191 


.59786 


.80160 


17 


44 


.55533 


.83163 


•56976 


.82181 


•58401 


.81174 


.59809 


.80143 


16 


45 


.55557 


•83147 


•57000 


.82165 


•58425 


.81157 


.59832 


.80125 


15 


46 


.55581 


.83131 


•57024 


.82148 


.58449 


.81140 


.59856 


.80108 


14 


47 


.55605 


•83115 


•57047 


.82132 


.58472 


.81123 


.59879 


.80091 


13 


48 


.55630 


.83098 


•57071 


.82115 


.58496 


.81106 


.59902 


.80073 


12 


49 


.55654 


.83082 


•57095 


.82098 


.58519 


.81089 


.59926 


.80056 


II 


SO 


.55678 


.83066 


•57119 


.82082 


.58543 


.81072 


•59949 


.80038 


10 


SI 


.55702 


.83050 


•57143 


.82065 


.58567 


.81055 


.59972 


.80021 


9 


52 


.55726 


.83034 


•57167 


.82048 


.58590 


.81038 


.59995 


.80003 


8 


53 


.55750 


.83017 


•57191 


.82032 


.58614 


.81021 


.60019 


.79986 


7 


54 


.55775 


.83001 


•57215 


.82015 


.58637 


.81004 


.60042 


.79968 


6 


55 


.55799 


.82985 


.57238 


.81999 


.58661 


.80987 


.60065 


.79951 


5 


56 


.55823 


.82969 


.57262 


.81982 


.58684 


.80970 


.60089 


•79934 


4 


57 


.55847 


•82953 


•57286 


.81965 


•58708 


.80953 


.60112 


.79916 


3 


58 


.55871 


.82936 


.57310 


.81949 


.58731 


.80936 


.60135 


•79899 


2 


59 


.55895 


.82920 


.57334 


.81932 


•58755 


.80919 


.60158 


.79881 


I 


60 


.55919 


.82904 


•57358 


.81915 


.58779 


.80902 


.60182 


.79864 





f 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


/ 




5( 


P 


51 


)° 


5^ 


1° 


53 


3 





866 



GENERAL TABLES AND FORMULA 





37° 


38° 


39° 


40° 







Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


/ 


o 


.60182. 


.79864 


.61566 


.78801 


.62932 


.77715 


.64279 


.76604 


60 


I 


.60205 


.79846 


.61589 


.78783 


.62955 


.77696 


.64301 


.76586 


59 


a 


.60228 


.79829 


.61612 


•78765 


.62977 


•77678 


.64323 


.76567 


58 


3 


.60251 


.79811 


.61635 


.78747 


.63000 


.77660 


.64346 


.76548 


57 


4 


.60274 


.79793 


.61658 


.78729 


.63022 


.77641 


.64368 


.76530 


56 


5 


.60298 


.79776 


.61681 


.78711 


.63045 


•77623 


.64390 


.76511 


55 


6 


.60321 


.79758 


.61704 


.78694 


.63068 


.77605 


.64412 


.76492 


54 


7 


.60344 


.79741 


.61726 


.78676 


.63090 


.77586 


.64435 


•76473 


53 


8 


.60367 


.79723 


.61749 


.78658 


.63113 


•77568 


.64457 


•76455 


52 


9 


.60390 


.79706 


.61772 


.78640 


.63135 


.77550 


.64479 


.76436 


51 


lO 


.60414 


.79688 


.61795 


.78622 


.63158 


•77531 


.64501 


.76417 


50 


II 


.60437 


.79671 


.61818 


.78604 


.63180 


•77513 


.64524 


•76398 


49 


12 


.60460 


.79653 


.61841 


.78586 


.63203 


.77494 


.64546 


•76380 


48 


13 


.60483 


.79635 


.61864 


.78568 


.63225 


•77476 


.64568 


•76361 


47 


14 


.60506 


.79618 


.61887 


.78550 


.63248 


.77458 


.64590 


•76342 


46 


15 


.60529 


.79600 


.61909 


.78532 


.63271 


.77439 


.64612 


•76323 


45 


i6 


.60553 


.79583 


.61932 


.78514 


.63293 


.77421 


.64635 


.76304 


44 


17 


.60576 


•79565 


.61955 


.78496 


.63316 


.77402 


.64657 


.76286 


43 


i8 


.60599 


.79547 


.61978 


.78478 


.63338 


.77384 


.64679 


.76267 


42 


19 


.60622 


.79530 


.62001 


.78460 


.63361 


.77366 


.64701 


.76248 


41 


20 


.60645 


.79512 


.62024 


.78442 


.63383 


.77347 


.64723 


.76229 


40 


21 


.60668 


.79494 


.62046 


.78424 


.63406 


.77329 


.64746 


.76210 


39 


22 


.60691 


.79477 


.62069 


.78405 


.63428 


.77310 


.64768 


.76192 


38 


23 


.60714 


.79459 


.62092 


.78387 


•63451 


.77292 


.64790 


•76173 


37 


24 


.60738 


.79441 


.62115 


.78369 


.63473 


.77273 


.64812 


•76154 


36 


25 


.60761 


.79424 


.62138 


.78351 


.63496 


.77255 


.64834 


.76135 


35 


26 


.60784 


.79406 


.62160 


•78333 


.63518 


.77236 


.64856 


.76116 


34 


27 


.60807 


.79388 


.62183 


•78315 


.63540 


.77218 


.64878 


.76097 


33 


28 


.60830 


.79371 


.62206 


.78297 


.63563 


.77199 


.64901 


.76078 


32 


29 


.60853 


•79353 


.62229 


.78279 


.63585 


.77181 


.64923 


.76059 


31 


30 


.60876 


.79335 


.62251 


.78261 


.63608 


.77162 


.64945 


.76041 


30 


31 


.60899 


.79318 


.62274 


.78243 


.63630 


.77144 


.64967 


.76022 


29 


32 


.60922 


.79300 


.62297 


.78225 


.63653 


•77125 


.64989 


.76003 


28 


33 


.60945 


.79282 


.62320 


.78206 


.63675 


.77107 


.65011 


•75984 


27 


34 


.60968 


.79264 


.62342 


.78188 


.63698 


.77088 


.65033 


•75965 


26 


35 


.60991 


.79247 


.62365 


.78170 


.63720 


.77070 


•65055 • 


.75946 


25 


36 


.61015 


.79229 


.62388 


.78152 


.63742 


•77051 


•65077 


.75927 


24 


37 


.61038 


.79211 


.62411 


.78134 


.^3765 


.77033 


.65100 


.75908 


23 


38 


.61061 


•79193 


.62433 


:78ii6 


.63787 


.77014 


.65122 


.75889 


22 


39 


.61084 


.79176 


.62456 


.78098 


.63810 


.76996 


.65144 


.75870 


21 


40 


.61107 


•79158 


.62479 


.78079 


.63832 


.76977 


.65166 


•75851 


20 


*i 


.61130 


.79140 


.62502 


.78061 


.63854 


.76959 


.65188 


.75832 


19 


*2 


.61153 


.79122 


.62524 


.78043 


.63877 


.76940 


.65210 


•75813 


18 


13 


.61176 


.79105 


.62547 


.78025 


.63899 


.76921 


.65232 


•75794 


17 


»4 


.61199 


.79087 


.62570 


.78007 


.63922 


.76903 


.65254 


•75775 


16 


♦5 


.61222 


.79069 


.62592 


.77988 


.63944 


.76884 


.65276 


•75756 


15 


%6 


.61245 


.79051 


.62615 


.77970 


.63966 


.76866 


.65298 


.75738 


14 


\7 


.61268 


.79033 


.62638 


.77952 


.63989 


.76847 


.65320 


.75719 


13 


18 


.61291 


•79016 


.62660 


.77934 


.64011 


.76828 


•(>53A2 


.75700 


12 


\9 


.61314 


.78998 


.62683 


.77916 


.64033 


.76810 


.65364 


.75680 


II 


>o 


.61337 


.78980 


.62706 


.77897 


.64056 


.76791 


.65386 


.75661 


10 


)i 


.61360 


.78962 


.62728 


.77879 


.64078 


.76772 


.65408 


•75642 


9 


)2 


.61383 


.78944 


.62751 


.77861 


.64100 


.76754 


.65430 


•75623 


8 


>3 


.61406 


.78926 


.62774 


.77843 


.64123 


.76735 


.65452 


.75604 


7 


)4 


.61429 


.78908 


.62796 


•77824 


.64145 


.76717 


.65474 


.75585 


6 


)S 


.61451 


.78891 


.62819 


.77806 


.64167 


.76698 


.65496 


.75566 


5 


)6 


.61474 


.78873 


.62842 


.77788 


.64190 


.76679 


.65518 


.75547 


4 


•7 


.61497 


.78855 


.62864 


•77769 


.64212 


.76661 


.65540 


.75528 


3 


)8 


.61520 


•78837 


.62887 


.77751 


.64234 


.76642 


.65562 


.75509 


2 


•9 


•61543 


.78819 


.62909 


.77733 


.64256 


.76623 


.65584 


.75490 


I 


)0 


.61566 


.78801 


.62932 


•77715 


.64279 


.76604 


.65606 


.75471 





/ 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


Cosine 


Sine 


' 




52 


« 1 


51 





50 





49 








NATURAL SINES AND COSINES 



867 



41 

Sine Cosine 



.65606 
.65628 
.65650 
.65672 
.65694 
.65716 
.65738 
.65759 
.65781 
.65803 
.65825 

.65847 
.65869 
.65891 
.65913 
.65935 
.65956 
.65978 
.66000 
.66022 
.66044 
.66066 
.66088 
.66109 
.66131 
.66153 
.66175 
.66197 
.66218 
.66240 
.66262 
.66284 
.66306 
.66327 
.66349 
•66371 
.66393 
.66414 
.66436 
.66458 
.66480 

.66501 
.66523 
.66545 
.66566 
.66588 
.66610 
.66632 
.66653 
.66675 
.66697 

.66718 
.66740 
.66762 
.66783 
.66805 
.66827 
.66848 
.66870 
.66891 
.66913 



.75471 
.75452 
.75433 
.75414 
.75395 
.75375 
.75356 
.75337 
.75318 
.75299 
.75280 

.75261 
.75241 
.75222 
•75203 
.75184 
.75165 
.75146 
.75126 
.75107 
.75088 

.75069 
.75050 
.75030 
.75011 
.74992 
.74973 
.74953 
.74934 
.74915 
.74896 
.74876 
.74857 
.74838 
.74818 
.74799 
.74780 
.74760 
.74741 
.74722 
.74703 
.74683 
.74664 
.74644 
.74625 
.74606 
.74586 
.74567 
.74548 
.74528 
.74509 

.74489 
.74470 
.74451 
.74431 
.74412 
.74392 
.74373 
.74353 
.74334 
.74314 



420 430 440 
Sine Cosine Sine Cosine Sine Cosine 



Cosine Sine Cosine Sine 
430 I 470 



.66913 
.66935 
.66956 
.66978 
.66999 
.67021 
.67043 
.67064 
.67086 
.67107 
.67129 

.67151 
.67172 
.67194 
.67215 
.67237 
.67258 
.67280 
.67301 
.67323 
.67344 
.67366 
.67387 
.67409 
.67430 
.67452 
•67473 
•67495 
.67516 
.67538 
.67559 
.67580 
.67602 
.67623 
.67645 
.67666 
.67688 
.67709 
.67730 
.67752 
.67773 

.67795 
.67816 
.67837 
.67859 
.67880 
.67901 
.67923 
.67944 
.67965 
.67987 
.68008 
.68029 
.68051 
.68072 
.68093 
.68115 
.68136 
.68157 
.68179 
.68200 



.74314 
.74295 
.74276 
.74256 
•74237 
.74217 
.74198 
.74178 
.7^159 
.74139 
•74120 

.74100 
.74080 
.74061 
.74041 
.74022 
.74002 
•73983 
.73963 
.73944 
•73924 

.73904 
.73885 
.73865 
.73846 
.73826 
.73806 
•73787 
•73767 
.73747 
.73728 

.73708 
•73688 
.73669 
•73649 
•73629 
.73610 
.73590 
.73570 
.73551 
.73531 
.73511 
.73491 
.73472 
.73452 
.73432 
•73413 
•73393 
•73373 
•73353 
•73333 
•73314 
•73294 
•73274 
•73254 
•73234 
•73215 
•73195 
•73175 
.73155 
.73135 



.68200 
.68221 
.68242 
.68264 
•68285 
.68306 
.68327 
.68349 
.68370 
.68391 
.68412 
.68434 
.68455 
.68476 
.68497 
.68518 

•68539 
.68561 
.68582 
.68603 
.68624 

.68645 
.68666 
.68688 
.68709 
.68730 
•68751 
.68772 

•68793 
.68814 
.68835 

•68857 
.68878 
.68899 
.68920 
.68941 
.68962 
.68983 
.69004 
.69025 
.69046 
.69067 
.69088 
.69109 
.69130 
•69151 
.69172 
.69193 
.69214 
•69235 
.69256 

.69277 
.69298 
.69319 
.69340 
.69361 
.69382 
.69403 
.69424 
•69445 
.69466 



.73135 
.73116 
.73096 
.73076 
.73056 
.73036 
.73016 
.72996 
.72j)76 
•72957 
.72937 
.72917 
.72897 
.72377 
•72857 
•72837 
.72O17 
.72797 
.72777 
.72757 
•72737 

.72717 
.72697 
.72677 
.72657 
.72637 
.72617 
.72597 
.72577 
•72557 
•72537 
•72517 
•72497 
•72477 
•72457 
•72437 
.72417 
•72397 
•72377 
•72357 
•72337 
.72317 
.72297 
.72277 
.72257 
•72236 
.72216 
.72196 
.72176 
.72156 
.72136 
.72116 
•72095 
•72075 
•7205s 
•72035 
.72015 
•71995 
.71974 
.71954 
•71934 



Cosine I Sine Cosine Sine 

46° II 45° 



.69466 
.69487 
.69508 
.69529 
.69549 
.69570 
.69591 
.69612 
.69633 
•69654 
•69675 
.69696 
.69717 
•69737 
.69758 
•69779 
.69800 
.69821 
.69842 
.69862 
.69883 
.69904 
•69925 
.69946 
.69966 
.69987 
.70008 
.70029 
.70049 
.70070 
.70091 
.70112 
.70132 
•70153 
.70174 
•70195 
.70215 
.70236 
.70257 
.70277 
.70298 

.70319 
•70339 
.70360 
• 70381 
.70401 
.70422 
•70443 
•70463 
.70484 
•70505 

•70525 
•70546 
•70567 
•70587 
.70608 
.70628 
.70649 
.70670 
.70690 
.70711 



•71934 
.71914 
.71894 
.71873 
.71853 
.71833 
.71813 
.71792 
.71772 
.71752 
.71732 

.71711 
.71691 
.71671 
.71650 
.71630 
.71610 
.71590 
.71569 
.71549 
•71529 
.71508 
.71488 
.71468 
•71447 
.71427 
.71407 
•71386 
.71366 
•71345 
.71325 
.71305 
.71284 
.71264 
•71243 
.71223 
.71203 
.71182 
.71162 
.71141 
.71121 

.71100 
.71080 
•71059 
.71039 
.71019 
.70998 
.70978 
.70957 
.70937 
.70916 

.70896 
.70875 
.70855 
.70834 
.70813 

.70793 

.70772 
.70752 
.70731 
.70711 



868 



GENERAL TABLES AND FORMULA 








^ 


1 





2 





3 







' 


Sec. 


1 Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


/ 


o 


I 


Infinite. 


1. 000 1 


57.299 


1 .0006 


28.654 


1. 00 14 


19.107 


60 


I 


I 


3437-70 


1. 000 1 


56.359 


1 .0006 


28.417 


1.0014 


19.002 


59 


2 


I 


1718.90 


1.0002 


55.450 


1 .0006 


28.184 


1. 00 14 


18.897 


58 


3 


I 


1145-90 


1.0002 


54.570 


1 .0006 


27-955 


1.0014 


18.794 


57 


4 


I 


859-44 


1.0002 


53./18 


1 .0006 


27.730 


1.0014 


18.692 


56 


5 


I 


687.55 


1.0002 


52.891 


1.0007 


27.508 


1.0014 


18.591 


55 


6 


I 


572.96 


1.0002 


52.090 


1.0007 


27.290 


1.0015 


18.491 


54 


7 


I 


491. II 


1.0002 


51.313 


1.0007 


27.075 


1. 001 5 


18.393 


sz 


8 


I 


429.72 


1.0002 


50.558 


1.0007 


26.864 


1.0015 


18.295 


52 


9 


I 


381.97 


1.0002 


49.826 


1.0007 


26.655 


1.0015 


18.198 


51 


lO 


I 


343.77 


1 .0002 


49.114 


1.0007 


26.450 


1.0015 


18.103 


50 


II 


I 


312.52 


1.0002 


48.422 


1.0007 


26.249 


1.0015 


18.008 


49 


12 


I 


286.48 


1.0002 


47.750 


1.0007 


26.050 


1.0016 


17.914 


48 


13 


I 


264.44 


1 .0002 


47-096 


1.0007 


25-854 


1.0016 


17.821 


47 


14 


I 


245-55 


1 .0002 


46.460 


1 .0008 


25.661 


1.0016 


17.730 


46 


15 


I 


229.18 


1.0002 


45-840 


1.0008 


25-471 


1. 00 16 


17.639 


45 


i6 


I 


214-86 


1.0002 


45-237 


1.0008 


25.284 


1.0016 


17.549 


44 


17 


I 


202.22 


1 .0002 


44.650 


1.0008 


25.100 


1. 0016 


17.460 


43 


i8 


I 


190.99 


1.0002 


44-077 


1.0008 


24.918 


1.0017 


17.372 


42 


19 


I 


180.73 


1.0003 


43-520 


1 .0008 


24-739 


1.0017 


17.285 


41 


20 


I 


171.89 


1.0003 


42.976 


1.0008 


24.562 


1.0017 


17.198 


40 


21 


I 


163.70 


1.0003 


42.445 


1.0008 


24.358 


1.0017 


17.113 


39 


22 


I 


156.26 


1 .0003 


41.928 


1.0008 


24.216 


1.0017 


17.028 


38 


23 


I 


149.47 


1.0003 


41.423 


1 0009 


24.047 


1.0017 


16.944 


37 


24 


I 


143-24 


1.0003 


40-930 


1 .0009 


23.880 


1.0018 


16.861 


36 


25 


I 


137-51 


1.0003 


40.448 


1 .0009 


23.716 


1.0018 


16.779 


35 


26 


I 


132.22 


1.0003 


39.978 


1.0009 


23.553 


1. 0018 


1O.698 


34 


27 


I 


127.32 


1.0003 


39.518 


1 .0009 


23-393 


1.0018 


16.617 


33 


28 


I 


122.78 


1.0003 


39.069 


1 .0009 


23-235 


1.0018 


16.538 


32 


29 


I 


118.54 


1.0003 


38.631 


1 .0009 


23.079 


1.0018 


16.459 


31 


30 


I 


114-59 


1.0003 


38.201 


1 .0009 


22.925 


1. 0019 


16.380 


30 


31 


I 


110.90 


1.0003 


37.782 


1.00 10 


22.774 


1. 0019 


16.303 


29 


32 


I 


107.43 


1.0003 


37.371 


1. 0010 


22.624 


1. 0019 


16.226 


28 


33 


I 


104.17 


1 .0004 


36-969 


1.00 10 


22.476 


1. 0019 


16.150 


27 


34 


I 


lOI.II 


1 .0004 


36.576 


1.00 10 


22.330 


1. 0019 


16.075 


26 


35 


I 


98.223 


1 .0004 


36.191 


1. 0010 


22.186 


1.0019 


16.000 


25 


36 


I 


95.495 


1.0004 


35.814 


1. 00 10 


22.044 


1.0020 


15.926 


24 


H 


I 


92.914 


1 .0004 


35.445 


1.00 10 


21.904 


1 .0020 


15.853 


23 


38 


1. 000 1 


92.469 


1.0004 


35-084 


1.00 10 


21.765 


1 .0020 


15.780 


22 


39 


1. 000 1 


88.149 


1 .0004 


34.729 


l.OOIl 


21.629 


1.0020 


15.708 


21 


40 


1. 000 1 


85.946 


1 .0004 


34.382 


1. 0011 


21.494 


1.0020 


15.637 


20 


41 


1. 000 1 


83.849 


1 .0004 


34.042 


l.OOIl 


21.360 


1.0021 


15.566 


19 


42 


1. 000 1 


81.853 


1.0004 


33-708 


1.0011 


21.228 


1. 002 1 


15.496 


18 


43 


1. 000 1 


79-950 


1 .0004 


33-381 


l.OOIl 


21.098 


1. 002 1 


15.427 


17 


44 


1. 000 1 


78.133 


1.0004 


33.060 


l.OOIl 


20.970 


1. 002 1 


15-358 


16 


45 


1. 000 1 


76.396 


1.0005 


32-745 


l.OOIl 


20.843 


1.0021 


15-290 


15 


46 


1. 000 1 


74.736 


1.0005 


32.437 


1.0012 


20.717 


1.0022 


15.222 


14 


47 


1. 000 1 


73.146 


1.0005 


32.134 


1.0012 


20.593 


1.0022 


15.155 


13 


48 


1. 000 1 


71.622 


1.0005 


31.836 


1.0012 


20.471 


1.0022 


15.089 


12 


49 


1. 000 1 


71.160 


1.0005 


31.544 


1. 0012 


20.350 


1.0022 


15.023 


II 


50 


1. 000 1 


68.757 


1.0005 


31.257 


1.0012 


20.230 


1.0022 


14.958 


10 


51 


1. 0001 


67.409 


1.0005 


30.976 


1.0012 


20.112 


1.0023 


14.893 


9 


52 


1. 000 1 


66.113 


1 .0005 


30.699 


1.0012 


19-995 


1.0023 


14.829 


8 


53 


1. 000 1 


64.866 


1.0005 


30.428 


1.0013 


19.880 


1.0023 


14-765 


7 


54 


1. 000 1 


63.664 


1.0005 


30.161 


I.OOI3 


19.766 


1.0023 


14.702 


6 


55 


1. 000 1 


62.507 


1 .0005 


29.899 


I.00I3 


19.653 


1.0023 


14.640 


5 


56 


1. 000 1 


61.391 


1 .0006 


29.641 


I.00I3 


19-541 


1.0024 


14.578 


4 


57 


1. 0001 


61.314 


1 .0006 


29.388 


I.00I3 


19.431 


1.0024 


14.517 


3 


58 


1. 000 1 


59.274 


1.0006 


29.139 


1.0013 


19.322 


1.0024 


14.456 


2 


59 


1. 0001 


58.270 


1 .0006 


28.894 


1.0013 


19.214 


1.0024 


14-395 


I 


60 


1. 000 1 


57.299 


1 .0006 


28.654 


1.0014 


19.107 


1.0024 


14-335 





/ 


Co-sec. 


Sec. 


Co-sec- 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 




8^ 


r 


Si 


r 


8 


7° 


8( 


3° 





NATURAL SECANTS AND CO-SECANTS 



869 





40 


5° 


1 ^ 


° 


70 




/ 


Sec. 


Co-sEa 


Sec. 


Co-sec. 


Sec. 


Co-sec 


Sec. 


Co-sec. 


/ 





1.0024 


14.335 


1.0038 


11.474 


1.0055 


9.5668 


1.0075 


?-^?^^^ 


60 


I 


1.0025 


14.276 


1.0038 


11.436 


1.0055 


9.5404 


1.0075 


8.1861 


59 


2 


1.0025 


14.217 


1.0039 


11.398 


1.0056 


9-5141 


1.0076 


8.1668 


58 


3 


1.0025 


14.159 


1.0039 


11.360 


1.0056 


9.4880 


1.0076 


8.1476 


57 


4 


1.0025 


14.101 


1.0039 


11.323 


1.0056 


9.4620 


1.0076 


8.1285 


56 


5 


1.0025 


14.043 


1.0039 


11.286 


1.0057 


9-4362 


1.0077 


8.1094 


55 


6 


1.0026 


13.986 


1.0040 


11.249 


1.0057 


9.4105 


1.0077 


8.0905 


54 


7 


1.0026 


13.930 


1.0040 


11.213 


1.0057 


9-3850 


1.0078 


8.0717 


53 


8 


1.0026 


13.874 


1.0040 


I I. I 76 


1.0057 


9-3596 


1.0078 


8.0529 


52 


9 


1.0026 


13.818 


1 .0040 


1 1. 140 


1.0058 


9-3343 


1.D078 


8.0342 


51 


10 


1.0026 


13-763 


1. 0041 


1 1. 104 


1.0058 


9.3092 


' 1.0079 


8.0156 


50 


11 


1.0027 


13.708 


1. 0041 


11.069 


1.0058 


9.2842 


1.0079 


7.9971 


49 


12 


1.0027 


13.654 


1. 0041 


11-033 


1.0059 


9-2593 


i 1.0079 


7.9787 


48 


13 


1.0027 


13.600 


1. 004 1 


10.988 


1.0059 


9-2346 


1.0080 


7.9604 


47 


14 


1.0027 


13-547 


1.0042 


10.963 


1.0059 


9.2100 


1 .0080 


7.9421 


46 


15 


1.0027 


13.494 


1 .0042 


10.929 


1 .0060 


9-1855 


1 .0080 


7.9240 


45 


16 


1.0028 


13.441 


1.0042 


10.894 


1.0060 


9.1612 


1.0081 


7-9059 


44 


17 


1.0028 


13-389 


1.0043 


10.860 


1 .0060 


9.1370 


1.0081 


7.8879 


43 


18 


1.0028 


13.337 


1.0043 


10.826 


1. 006 1 


9.1129 


1.0082 


7.8700 


42 


19 


1.0028 


13.286 


1.0043 


10.792 


1. 006 1 


9.0890 


1 .0082 


7.8522 


41 


20 


1 .0029 


13.235 


1.0043 


10.758 


1. 006 1 


9-0651 


1 .0082 


7.8344 


40 


21 


1.0029 


13.184 


1.0044 


10.725 


1.0062 


9.0414 


1.0083 


7.8168 


39 


22 


1.0029 


13-134 


1.0044 


10.692 


I 0062 


9.0179 


1.0083 


7.7992 


38 


23 


1.0029 


13.084 


1.0044 


10.659 


1 .0062 


8.9944 


1.0084 


7-7817 


37 


24 


1.0029 


13-034 


1.0044 


10.626 


1.0063 


8.9711 


1.0084 


7-7642 


36 


25 


1.0030 


12.985 


1.0045 


10.593 


1.0063 


8.9479 


1 .0084 


7.7469 


35 


26 


1.0030 


12.937 


1.0045 


10.561 


1.0063 


8.9248 


1.0085 


7.7296 


34 


27 


1.0030 


12.888 


1.0045 


10.529 


1.0064 


8.9018 


1.0085 


7.7124 


33 


28 


1.0030 


12.840 


1.0046 


10.497 


1 .0064 


8.8790 


1.0085 


7.6953 


32 


29 


1. 003 1 


12.793 


1 .0046 


10.465 


1 .0064 


8.8563 


1.0086 


7.6783 


31 


30 


1. 003 1 


12.745 


1.0046 


10.433 


1.0065 


8.8337 


1.0086 


7.6613 


30 


31 


1. 003 1 


12.698 


1 .0046 


10.402 


1 .0065 


8.8112 


1.0087 


7.6444 


29 


32 


1. 003 1 


12.652 


1.0047 


10.371 


1.0065 


8.7888 


1.0087 


7.6276 


28 


33 


1.0032 


12.606 


1.0047 


10.340 


1.0066 


8.7665 


1.0087 


7.6108 


27 


34 


1.0032 


12.560 


1.0047 


10.309 


1 .0066 


8.7444 


1.0088 


7.5942 


26 


35 


1.0032 


12.514 


1.0048 


10.278 


1.0066 


8.7223 


1.0088 


7.5776 


25 


35 


1.0032 


12.469 


1.0048 


10.248 


1.0067 


8.7004 


1 .0089 


7.5611 


24 


37 


1.0032 


12.424 


1 .0048 


10.217 


1.0067 


8.6786 


1.0089 


7.5446 


23 


38 


1.0033 


12.379 


1 .0048 


10.187 


1.0067 


8.6569 


1.0089 


7.5282 


22 


39 


1.0033 


12.335 


1.0049 


10.157 


1.0068 


l-^^^ 


1.0090 


7.5119 


21 


40 


1 .0033 


12.291 


1.0049 


10.127 


1.0068 


8.6138 


1*0090 


7.4957 


20 


41 


1.0033 


12.248 


1.0049 


10.098 


1.0068 


8.5924 


1.0090 


7-4795 


19 


42 


1.0034 


12.204 


1.0050 


10.068 


1.0069 


8.5711 


1. 0091 


7-4634 


18 


43 


1.0034 


12. 161 


1.0050 


10.039 


1 .0069 


8.5499 


1.0091 


7.4474 


17 


44 


1.0034 


12. 118 


1.0050 


10.010 


1.0069 


8.5289 


1.0092 


7.4315 


16 


45 


1.0034 


12.076 


1.0050 


9.9812 


1.0070 


8.5079 


1.0092 


7.4156 


15 


46 


1.0035 


12.034 


1.0051 


9-9525 


1.0070 


8.4871 


1.0092 


7-3998 


14 


47 


1.0035 


11.992 


1. 005 1 


9.9239 


1.0070 


8.4663 


1.0093 


7-3840 


13 


48 


1.0035 


11.950 


1. 005 1 


9.8955 


1. 0071 


8-4457 


1.0093 


7.3683 


12 


49 


1.0035 


11.909 


1.0052 


9.8672 


1. 007 1 


8.4251 


1.0094 


7.3527 


11 


50 


1.0036 


11.868 


1.0052 


9.8391 


1. 007 1 


8.4046 


1.0094 


7.3372 


10 


51 


1.0036 


11.828 


1.0052 


9.8112 


1.0072 


8.3843 


1.0094 


7.3217 


9 


52 


1.0036 


11.787 


1.0053 


9.7834 


1.0072 


8.3640 


1.0095 


7.3063 


8 


53 


1.0036 


11.747 


1.0053 


9.7558 


1.0073 


8.3439 


1.0095 


7.2909 


7 


54 


1.0037 


11.707 


1.0053 


9.7283 


1.0073 


8.3238 


1.0096 


7.2757 


6 


55 


1.0037 


11.668 


1.0053 


9.7010 


1.0073 


8.3039 


1 .0096 


7.2604 


5 


56 


1.0037 


11.628 


1.0054 


9-6739 


1.0074 


8.2840 


1.0097 


7.2453 


4 


^1 


1.0037 


11.589 


1.0054 


9.6469 


1.0074 


8.2642 


1.0097 


7.2302 


3 


58 


1.0038 


1 1 -550 


1.0054 


9.6200 


1.0074 


8.2446 


1.0097 


7.2152 


2 


59 


1.0038 


11.512 


1.0055 


9-5933 


1.0075 


8.2250 


t.0098 


7.2002 


I 


5o 


1.0038 


11.474 


1.0055 


9.5668 


1.0075 


8.2055 


1 .0098 


7.1853 





/ 


Co-sec. 


Stc. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


f 




8. 


3° 


S^ 


^o 


82 


;° 


8^ 


)0 





870 



GENERAL TABLES AND EORMUL^. 





8^ 


9° 


w 


11° 




/ 


Sec. 


Co-SEC. 


Sec. 


Co-sec. 


Sec. 


Co. SEC. 


Sec. 


Co-SEC. 


f 





1.0098 


7.1853 


1.0125 


6.3924 


1-0154 


5.7588 


1.6187 


5.2408 


60 


I 


1.0099 


7.1704 


1.0125 


6.3807 


1-0155 


5.7493 


1.0188 


5.2330 


59 


2 


1.0099 


7-1557 


1.0125 


6.3690 


1-0155 


5.7398 


1.0188 


5,2252 


58 


3 


1.0099 


7.1409 


1.0126 


6.3574 


1.0156 


5.7304 


1.0189 


5.2174 


57 


4 


1. 0100 


7.1263 


1.0126 


6.3458 


1.0156 


5-7210 


1. 0189 


5.2097 


56 


5 


1. 0100 


7-1117 


1.0127 


6.3343 


1.0157 


5-7II7 


1.0190 


5.2019 


55 


6 


I.OIOI 


7.0972 


1.0127 


6.3228 


1.0157 


5-7023 


1.0191 


S.I942 


54 


7 


I.OIOI 


7.0827 


1.0128 


6.3113 


1.0158 


5-6930 


1.0191 


5.186s 


53 


8 


1. 0102 


7.0683 


1.0128 


6.2999 


1.0158 


5.6«38 


1.0192 


5.1788 


■52 


9 


1. 0102 


7-0539 


1.0129 


6.2885 


1.0159 


5-6745 


1.0192 


5.1712 


SI 


10 


1. 0102 


7.0396 


1.0129 


6.2772 


1.0159 


5-6653 


1. 0193 


5.1636 


50 


II 


I.OI03 


7.0254 


1. 0130 


6.2659 


1. 0160 


5-6561 


1. 0193 


5.1560 


49 


12 


I.OI03 


7.0112 


1.0130 


6.2546 


1.0160 


5-6470 


1.0194 


5.1484 


48 


t3 


1. 0104 


6.9971 


1.0131 


6.2434 


1.0161 


5-6379 


1.0195 


5.1409 


47 


14 


1. 0104 


6.9830 


1.0131 


6.2322 


1.0162 


5.6288 


1.0195 


5.1333 


46 


15 


1. 0104 


6.9690 


1.0132 


6.2211 


1.0162 


5-6197 


1,0196 


5.1258 


45 


16 


1. 0105 


6.9550 


1.0132 


6.2100 


I. 163 


5-6107 


1.0196 


5.II83 


44 


17 


I.OIOS 


6.941 1 


1.0133 


6.1990 


1. 0163 


5-6017 


1.0197 


5.1 109 


43 


18 


1. 0106 


6.9273 


1.0133 


6.1880 


1.0164 


5-5928 


1. 0198 


5.1034 


42 


19 


1. 0106 


6.9135 


1.0134 


6.1770 


1. 0164 


5-5838 


1.0198 


S.0960 


41 


20 


1.0107 


6.8998 


1-0134 


6.1661 


1.0165 


5.5749 


1.0199 


5.0886 


40 


21 


1.0107 


6.8861 


I-OI35 


6.1552 


1.0165 


5.5660 


1.0199 


5.0812 


39 


22 


1.0107 


6.8725 


1.0135 


6.1443 


1.0166 


5.5572 


1.0200 


5.0739 


38 


23 


1. 0108 


6.8589 


1. 01 36 


6.1335 


1.0166 


5.5484 


1.0201 


5.0666 


37 


24 


1. 0108 


6.8454 


1. 01 36 


6.1227 


1.0167 


5.5396 


1. 0201 


5.- 593 


36 


25 


1. 0109 


6.8320 


1.0136 


6.1120 


1.0167 


5.5308 


1.0202 


5-0520 


35 


26 


1. 0109 


6.8185 


1.0137 


6.1013 


1.0168 


5.5221 


1.0202 


5.0447 


34 


27 


I.OIIO 


6.8052 


1.0137 


6.0906 


1. 0169 


5.5134 


1.0203 


50375 


33 


28 


I.OIIO 


6.7919 


1.0138 


6.0800 


1.0169 


5.5047 


1 .0204 


5.0302 


32 


29 


I.OIII 


6.7787 


1.0138 


6.0694 


1.0170 


5.4960 


1 .0204 


5.0230 


31 


30 


1. 01 1 1 


6.7655 


1.0139 


6.0588 


1. 01 70 


5.4874 


1.0205 


5.0158 


30 


31 


I.OIII 


6.7523 


1.0139 


6.0483 


1.0171 


5.4788 


1.0205 


5.0087 


29 


32 


I.OII2 


6.7392 


1. 0140 


6.0379 


1.0171 


5.4702 


1.0206 


5.001s 


28 


33 


I.OII2 


6.7262 


1.0140 


6.0274 


1.0172 


5.4617 


1.0207 


4.9944 


27 


34 


I.OII3 


6.7132 


1.0141 


6.0170 


1.0172 


5.4532 


1.0207 


4.9873 


26 


35 


I.OII3 


6.7003 


1.0141 


6.0066 


1.0173 


5.4447 


1.0208 


4.9802 


25 


36 


I.OII4 


6.6874 


1.0142 


5.9963 


1.0174 


5.4362 


1.0208 


4.9732 


24 


H 


I.OII4 


6.6745 


1.0142 


5.9860 


1.0174 


5-4278 


1.0209 


4.9661 


23 


38 


I.OII5 


6.6617 


1.0143 


5.9758 


1.0175 


5-4194 


1.0210 


4.9591 


22 


39 


I.OII5 


6.6490 


1.0143 


5.9655 


1.0175 


5-4110 


1. 02 10 


4.9521 


21 


40 


i.oiis 


6.6363 


1. 0144 


5.9554 


1.0176 


5.4026 


1.0211 


4.9452 


20 


41 


I.0II6 


6.6237 


1. 0144 


5-9452 


1.0176 


5-3943 


1.0211 


4.9382 


^? 


42 


I.0II6 


6.6111 


1-0145 


5.9351 


1.0177 


5-3860 


1.0212 


4.9313 


18 


43 


I.0II7 


6.5985 


1.0145 


5.9250 


1.0177 


5-3777 


1.0213 


4.9243 


17 


44 


I.OII7 


6.5860 


1.0146 


5.9150 


1. 01 78 


5-3695 


1.0213 


4.9175 


16 


45 


I.0II8 


6.5736 


1. 0146 


5.9049 


1.0179 


5-3612 


1.0214 


4.9106 


15 


46 


1. 01 18 


6.5612 


1.0147 


5.8950 


1.0179 


5-3530 


1.0215 


4.9037 


14 


47 


I.0II9 


6.5488 


1.0147 


5-8850 


1.0180 


5 3449 


1.0215 


4.8969 


13 


48 


I.0II9 


6.5365 


1. 0148 


5-8751 


1.0180 


5-3367 


1. 02 16 


4.8901 


12 


49 


I.OII9 


6.5243 


1. 0148 


5.8652 


1.0181 


5-3286 


1. 02 16 


4.8833 


II 


50 


1. 0120 


6.5121 


1. 0149 


5.8554 


1.0181 


5.3205 


1.0217 


4.8765 


10 


51 


I.0I20 


6.4999 


1.0150 


5.8456 


1. 0182 


5.3124 


1. 02 18 


4.8697 


9 


52 


I.OI2I 


6.4878 


1.0150 


5.8358 


1.0182 


5.3044 


1.0218 


4.8630 


8 


53 


I.OI2I 


6.4757 


1.0151 


5.8261 


1.0183 


5.2963 


1.0219 


4.8563 


7 


54 


. I.OI22 


6.4637 


1.0151 


5.8163 


1.0184 


5.2883 


1.0220 


4.8496 


6 


55 


I.OI22 


6.4517 


1.0152 


5.8067 


1.0184 


5.2803 


1.0220 


4.8429 


5 


56 


I.OI23 


6.4398 


1.0152 


5.7970 


1.0185 


5.2724 


1.0221 


4.8362 


4 


57 


I.OI23 


6.4279 


I.OI53 


5.7874 


1.0185 


5.2645 


1.0221 


4.8296 


3 


58 


I.OI24 


6.4160 


1.0153 


5.7778 


1.0186 


5.2566 


1.0222 


4.8229 


2 


59 


1. 01 24 


6.4042 


1. 01 54 


5.7683 


1.0186 


5.2487 


1.0223 


4.8163 


I 


60 


I.OI25 


6.3924 


1. 01 54 


5.7588 


1. 0187 


5-2408 


1.0223 


4.8097 





/ 


Co-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-SEC. 


Sec. 


Co-sec. 


Sec. 


/ 




81 





8C 


f 


79 





78 


° 





NATURAL SECANTS AND CO-SECANtS 



871 





12° 


13° 1 


140 


15° 




/ 


Sec. - 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


f 





1.0223 


4.8097 


1.0263 


4-4454 


1.0306 


4.1336 


1.0353 


3.8637 


60 


I 


1.0224 


4.8032 


1.0264 


4.4398 


1.0307 


4.1287 


1.0353 


3-8595 


59 


2 


1.0225 


4.7966 


1.0264 


4-4342 


1.0308 


4.1239 


1.0354 


3-8553 


58 


3 


1.0225 


4.7901 


1.0265 


4.4287 


1.0308 


4.II91 


1.0355 


3-8512 


57 


4 


1.0226 


4-7835 


1.0266 


4-4231 


1.0309 


4.II44 


1.0356 


3-8470 


56 


5 


1.0226 


4.7770 


1.0266 


4.4176 


1.0310 


4.1096 


I.0357 


3.8428 


55 


6 


1.0227 


4.7706 


1.0267 


4.4121 


1.0311 


4.1048 


1.0358 


3-8387 


54 


7 


1.0228 


4.7641 


1.0268 


4-4065 


1.0311 


4.1001 


1.0358 


3.8346 


53 


8 


1.0228 


4-7576 


1.0268 


4.40 II 


1.0312 


4.0953 


1.0359 


3.8304 


52 


9 


1.0229 


4.7512 


1.0269 


4-3956 


1.0313 


4.0906 


1.0360 


3-8263 


51 


10 


1.0230 


4.7448 


1.0270 


4.3910 


1. 03 14 


4-0859 


1.0361 


3.8222 


SO 


II 


1.0230 


4-7384 


1.0271 


4-3847 


1.0314 


4.0812 


1.0362 


3.8181 


49 


12 


1.0231 


4-7320 


1.0271 


4.3792 


1.0315 


4.0765 


1.0362 


3.8140 


48 


13 


1.0232 


4-7257 


1.0272 


4.3738 


1. 03 16 


4.0718 


1.0363 


3.8100 


47 


14 


1.0232 


4-7193 


1.0273 


4-3684 


1.0317 


4.0672 


1.0364 


3-8059 


46 


IS 


1.0233 


4-7130 


1.0273 


4-3630 


1.0317 


4.0625 


1.0365 


3.8018 


45 


16 


1.0234 


4.7067 


1.0274 


4-3576 


1.0318 


4-0579 


1.0366 


3-7978 


44 


17 


1.0234 


4.7004 


1.0275 


4-3522 


1.0319 


4-0532 


1.0367 


3.7937 


43 


18 


I.0235 


4.6942 


1.0276 


4.3469 


1.0320 


4.0486 


1.0367 


3.7897 


42 


19 


1.0235 


4.6879 


1.0276 


4-3415 


1.0320 


4.0440 


1.0368 


3.7857 


41 


20 


1.0236 


4.6817 


1.0277 


4.3362 


1.032 1 


4.0394 


1.0369 


3.7816 


40 


21 


1.0237 


4-6754 


1.0278 


4.3309 


1.0322 


4.0348 


1.0370 


3.7776 


39 


22 


1.0237 


4.6692 


1.0278 


4.3256 


1.0323 


4.0302 


1.0371 


3-7736 


38 


23 


1.0238 


4.6631 


1.0279 


4.3203 


1.0323 


4.0256 


1.0371 


3.7697 


37 


24 


1.0239 


4.6569 


1.0280 


4.3150 


1.0324 


4.O2II 


1.0372 


3-7657 


36 


25 


1.0239 


4-6507 


1.0280 


4-3098 


1.0325 


4.0165 


1.0373 


3-7617 


35 


26 


1.0240 


4.6446 


1.0281 


4-3045 


1.0326 


4.0120 


1.0374 


3-7577 


34 


27 


1.0241 


4-6385 


1.0282 


4.2993 


1.0327 


4.0074 


1.0375 


3-7538 


33 


28 


1. 0241 


4.6324 


1.0283 


4.2941 


1.0327 


4.0029 


1.0376 


3-7498 


32 


29 


1.0242 


4.6263 


1.0283 


4.2888 


1.0328 


3.9984 


1.0376 


3-7459 


3t 


30 


1.0243 


4.6202 


1 .0284 


4.2836 


1.0329 


3-9939 


1.0377 


3-7420 


30 


31 


1.0243 


4.6142 


1.0285 


4.2785 


1.0330 


3.9894 


1.0378 


3.7380 


29 


32 


1.0244 


4.6081 


1.0285 


4-2733 


1.0330 


3-9850 


1.0379 


3-7341 


28 


33 


1.0245 


4.6021 


1.0286 


4.2681 


1. 0331 


3-9805 


1.0380 


3.7302 


27 


34 


1.0245 


4.5961 


1.0287 


4.2630 


1.0332 


3-9760 


1.0381 


3-7263 


26 


35 


1.0246 


4.5901 


1.0288 


4-2579 


^1.0333 


3-9716 


1.0382 


3-7224 


25 


36 


1.0247 


4.5841 


1.0288 


4.2527 


I -0334 


3.9672 


1.0382 


3.7186 


24 


37 


1.0247 


4.5782 


1.0289 


4.2476 


1.0334 


3.9627 


1.0383 


3-7147 


23 


38 


1.0248 


4.5722 


1.0290 


4.2425 


1.0335 


3-9583 


1.0384 


3.7108 


22 


39 


1.0249 


4.5663 


1. 0291 


4-2375 


1.0336 


3-9539 


1.0385 


3.7070 


21 


40 


1.0249 


4.56cf4 


1.0291 


4.2324 


1.0337 


3-9495 


1.0386 


3-7031 


20 


41 


1.0250 


4.5545 


1.0292 


4.2273 


1.0338 


3.9451 


1.0387 


3.6993 


19 


42 


1.0251 


4.5486 


1.0293 


4.2223 


1.0338 


3-9408 


1.0387 


3.6955 


18 


43 


1. 0251 


4.5428 


1.0293 


4.2173 


1.0339 


3-9364 


1.0388 


3.6917 


17 


44 


1.0252 


4-5369 


1.0294 


4.2122 


1.0340 


3.9320 


1.0389 


3.6878 


16 


45 


1.0253 


4.5311 


1.0295 


4.2072 


1. 0341 


3-9277 


1.0390 


3.6840 


15 


46 


1.0253 


45253 


1.0296 


4.2022 


1. 0341 


3-9234 


1.0391 


3.6802 


14 


47 


1.0254 


4.5195 


1.0296 


4.1972 


1.0342 


3-9199 


1.0392 


3-6765 


13 


48 


1.0255 


4.5137 


1.0297 


4.1923 


1.0343 


3.9147 


1.0393 


3.6727 


12 


49 


1.0255 


4.5079 


1.0298 


4-1873 


1.0344 


3.9104 


1.0393 


3.6689 


II 


SO 


1.0256 


4.5021 


1.0299 


4.1824 


1.0345 


3.9061 


1.0394 


3-6651 


10 


51 


1.0257 


4.4964 


1.0299 


4.1774 


1-0345 


3-9018 


1.0395 


3.6614 


9 


52 


1.0257 


4.4907 


1.0300 


4-1725 


1-0346 


3-8976 


1.0396 


3.6576 


8 


S3 


1.0258 


4.4850 


1. 030 1 


4.1676 


1.0347 


3-8933 


1.0397 


3.6539 


7 


54 


I.02S9 


4.4793 


1.0302 


4.1627 


1.0348 


3.8990 


1.0398 


3.6502 


6 


^1 


1.0260 


4.4736 


1.0302 


4.1578 


1.0349 


3.8848 


1.0399 


3.6464 


5 


56 


1.0260 


4.4679 


1.0303 


4.1529 


1.0349 


3-8805 


1.0399 


3-6427 


4 


^l 


1. 0261 


4.4623 


1.0304 


4.1481 


1.0350 


3-8763 


1.0400 


3.6390 


3 


S8 


1.0262 


4-4566 


1.0305 


4.1432 


1. 0351 


3.8721 


1.0401 


3-6353 


2 


59 


1.0262 


4.4510 


1.0305 


4.1384 


1.0352 


3.8679 


1.0402 


3.6316 


I 


60 


1.0263 


4.4454 


1.0306 


4.1336 


I.0353 


3.8637 


1.0403 


3-6279 





/ 


CO-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


/ 




7< 


r 


7( 


)° 


71 


f 


7^ 


P 





872 



GENERAL TABLES AND FORMULA 





16° 


17° 


18° 


19^ 




/ 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


/ 


o 


1.0403 


3.6279 


1.0457 


3.4203 


1.0515 


3.2361 


1.0576 


3.0715 


60 


I 


1 .0404 


3-6243 


1.0458 


3-4170 


1.0516 


3.2332 


1.0577 


3.0690 


59 


2 


1.0405 


3.6206 


1.0459 


3-4138 


1.0517 


3.2303 


1.0578 


3.0664 


58 


3 


1.0406 


3.6169 


1.0460 


3-4106 


1.0518 


3.2274 


1.0579 


3.0638 


57 


4 


1.0406 


3-6133 


1. 0461 


3.4073 


1.0519 


3.2245 


1.0580 


3.0612 


56 


5 


1.0407 


5.6096 


1. 0461 


3.4041 


1.0520 


3.2216 


1.0581 


3.0586 


55 


6 


1.0408 


3.6060 


1.0462 


3.4009 


1.0521 


3.2188 


1.0582 


3.0561 


54 


7 


1.0409 


3.6024 


1.0463 


3.3977 


1.0522 


3.2159 


1.0584 


3.053s 


53 


8 


1.0410 


3-5987 


1 .0464 


3.3945 


1.0523 


3.2I3I 


1.0585 


3.0509 


52 


9 


1.0411 


3-5951 


1.0465 


3.3913 


1.0524 


3.2102 


1.0586 


3.0484 


51 


lO 


1. 041 2 


3-5915 


1.0466 


3.3881 


1.0525 


3.2074 


1.0587 


3.0458 


50 


II 


1.0413 


3-5879 


1.0467 


3.3849 


1.0526 


3.2045 


1.0588 


3-0433 


49 


12 


1.0413 


3.5843 


1.0468 


3.3817 


1.0527 


3.2017 


1.0589 


3.0407 


48 


13 


1. 0414 


3.5807 


1.0469 


3-3785 


1.0528 


3.1989 


1.0590 


3-0382 


47 


14 


1.0415 


3-5772 


1.0470 


3.3754 


1.0529 


3.1960 


1. 0591 


3-0357 


46 


IS 


1.0416 


3.5736 


1.0471 


3.3722 


1.0530 


3.1932 


1.0592 


3-0331 


45 


i6 


1. 041 7 


3 -5 700 


1.0472 


3.3690 


1.0531 


3.1904 


1.0593 


3.0306 


44 


17 


1. 0418 


3-5665 


1 .0473 


3.3659 


1.0532 


3-1876 


1.0594 


3.0281 


43 


i8 


1.0419 


3.5629 


1.0474 


3-3627 


1.0533 


3.1848 


1.0595 


3.0256 


43 


19 


1.0420 


3.5594 


1.0475 


3.3596 


1-0534 


3.1820 


1.0596 


3.0231 


41 


20 


1.0420 


3.5559 


1.0476 


3.3565 


1.0535 


3.1792 


1.0598 


3.0206 


40 


21 


1. 042 1 


3.5523 


1.0477 


3-3<34 


1.0536 


3.1764 


1.0599 


3.0I8I 


39 


22 


1.0422 


3.5488 


1.0478 


3.3502 


1.0537 


3.1736 


1 .0600 


3.0156 


38 


23 


1.0423 


3-5453 


1.0478 


3-3471 


1.0538 


3.1708 


1. 060 1 


3.0I3I 


37 


24 


1.0424 


3-5418 


1.0479 


3.3440 


1.0539 


3.I68I 


1.0602 


3.0106 


36 


25 


1.0425 


3-5383 


1 .0480 


3.3409 


1.0540 


3.1653 


1.0603 


3.0081 


35 


26 


1.0426 


3-5348 


1. 048 1 


3.3378 


1. 0541 


3.1625 


1.0604 


3.0056 


34 


27 


1.0427 


3-5313 


1.0482 


3-3347 


1.0542 


3.1598 


1.0605 


3.0031 


33 


28 


1.0428 


3-5279 


1.0483 


3-3316 


1.0543 


3.1570 


1.0606 


3.0007 


32 


39 


1.0428 


3-5244 


1.0484 


3-3286 


1.0544 


3.1543 


1.0607 


2.9982 


31 


30 


1.0429 


3.5209 


1.0485 


3.3255 


1.0545 


3.I5I5 


1.0608 


2.9957 


30 


31 


1.0430 


3.5175 


1.0486 


3.3224 


1.0546 


3.1488 


1 .0609 


2.9933 


29 


32 


1. 043 1 


3-5140 


1.0487 


3-3194 


1.0547 


3.I46I 


1.0611 


2.9908 


28 


33 


1.0432 


3.5106 


1.0488 


3-3163 


1.0548 


3.1433 


1.0612 


2.9884 


27 


34 


1.0433 


3.5072 


1.0489 


3-3133 


1.0549 


3.1406 


1.0613 


2.9859 


26 


35 


1.0434 


3.5037 


1.0490 


3-3102 


1.0550 


3.1379 


1. 0614 


2.983s 


25 


36 


I -0435 


3.5003 


1. 0491 


3-3072 


1.0551 


3.1352 


1.0615 


2.9810 


24 


37 


1.0436 


3.4969 


1.0492 


3-3042 


1.0552 


3.1325 


1.0616 


2.9786 


23 


38 


1 .0437 


3.4935 


1.0493 


3-3011 


1.0553 


3.1298 


1. 061 7 


2.9762 


22 


39 


1.0438 


3.4901 


1.0494 


3.2981 


1.0554 


3.I27I 


1.0618 


2.9738 


21 


*o 


1.0438 


3.4867 


1.0495 


3.2951 


1.0555 


3.1244 


1.0619 


2.9713 


20 


^i 


1.0439 


3.4833 


1 .0496 


3.2921 


1.0556 


3-1217 


1.0620 


2.9689 


^9 


*2 


1.0440 


3.4799 


1.0497 


3-2891 


1.0557 


3.II90 


1.0622 


2.9665 


18 


43 


1. 044 1 


3.4766 


1 .0498 


3.2861 


1.0558 


3.II63 


1.0623 


2.9641 


17 


H 


1.0442 


3.4732 


1.0499 


3-2831 


1-0559 


3.II37 


1.0624 


2.9617 


16 


15 


1.0443 


3-4698 


1.0500 


3.2801 


1.0560 


3. mo 


1.0625 


2.9593 


IS 


*6 


1.0444 


3-4665 


1.0501 


3-2772 


1.0561 


3.1083 


1.0626 


2.9569 


14 


*7 


1.0445 


3.4632 


1.0502 


3.2742 


1.0562 


3.1057 


1.0627 


2.9545 


13 


48 


1.0446 


3.4598 


1.0503 


3.2712 


1.0563 


3.1030 


1.0628 


2.9521 


12 


49 


1.0447 


3.4565 


1.0504 


3.2683 


1.056s 


3.1004 


1.0629 


2.9497 


II 


50 


1 .0448 


3.4532 


1.0505 


3.2653 


1.0566 


3.0977 


1.0630 


2.9474 


10 


51 


1 .0448 


3.4498 


1.0506 


3.2624 


1.0567 


3.0951 


1.0632 


2.9450 


9 


52 


1.0449 


3.4465 


1.0507 


3.2594 


1.0568 


3.0925 


1.0633 


2.9426 


8 


53 


1.0450 


3.4432 


1.0508 


3.2565 


1.0569 


3.0898 


1.0634 


2.9402 


7 


54 


1.0451 


3-4399 


1.0509 


3.2535 


1.0570 


3.0872 


1.0635 


2.9379 


6 


55 


1.0452 


3.4366 


1.0510 


3.2506 


1.0571 


3.0846 


1.0636 


2.935s 


S 


56 


1 .0453 


3-4334 


1.0511 


3.2477 


1.0572 


3.0820 


1.0637 


2.9332 


4 


57 


1.0454 


3-430I 


1.0512 


3.2448 


1.0573 


3.0793 


1.0638 


2.9308 


3 


58 


1.0455 


3.4268 


1-0513 


3.2419 


1.0574 


3.0767 


1.0639 


2.9285 


2 


59 


1.0456 


3-4236 


1.0514 


3-2390 


1.0575 


3.0741 


1. 0641 


2.9261 


I 


5o 


1.0457 


3-4203 


1.0515 


3.2361 


1.0576 


3.0715 


1.0642 


2.9238 





/ 


Co-sec. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


/ 




7J 


J° 


7". 


)o 


71 





7C 


)° 





NATURAL SECANTS AND CO-SECANTS 



873 





20° 


21° I 


22° 1 


23° 




t 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


/ 





1.0642 


2.9238 


1.0711 


2.7904 


1.0785 


2.6695 


1.0864 


2.5593 


60 


I 


1.0643 


2.9215 


1.0713 


2.7883 


1.0787 


2.6675 


1.0865 


2.5575 


59 


2 


1.0644 


2.9191 


1. 07 14 


2.7862 


1.0788 


2.6656 


1.0866 


2.5558 


58 


3 


1.0645 


2.9168 


1.0715 


2.7841 


1.0789 


2.6637 


1.0868 


2.5540 


57 


4 


1.0646 


2.9145 


1.0716 


2.7820 


1.0790 


2.6618 


1.0869 


2.5523 


56 


5 


1,0647 


2.9122 


1.0717 


2.7799 


1.0792 


2.6599 


1.0870 


2.5506 


55 


6 


1.0648 


2.9098 


1.0719 


2.7778 


1.0793 


2.6580 


1.0872 


2.5488 


54 


7 


1.0650 


2.9075 


1.0720 


2.7757 


1.0794 


2.6561 


1.0873 


2.5471 


53 


8 


1. 065 1 


2.9052 


1.0721 


2.7736 


1.0795 


2.6542 


1.0874 


2.5453 


52 


9 


1.0652 


2.9029 


1.0722 


2.7715 


1.0797 


2.6523 


1.0876 


2.5436 


51 


10 


1.0653 


2.9006 


1.0723 


2.7694 


1.0798 


2.6504 


1.0877 


2.5419 


50 


II 


1.0654 


2.8983 


1.0725 


2.7674 


1.0799 


2.6485 


1.0878 


2.5402 


49 


12 


1.0655 


2.8960 


1.0726 


2.7653 


1. 080 1 


2.6466 


1.0880 


2.5384 


48 


13 


1.0656 


2.8937 


1.0727 


2.7632 


1.0802 


2.6447 


1. 088 1 


2.5367 


47 


14 


1.0658 


2.8915 


1.0728 


2.7611 


1.0803 


2.6428 


1.0882 


2.5350 


46 


15 


1.0659 


2.8892 


1.0729 


2.7591 


1 .0804 


2.6410 


1.0884 


2.5333 


45 


16 


1 .0660 


2.8869 


1.0731 


2.7570 


1.0806 


2.6391 • 


1.0885 


2.5316 


44 


17 


1. 0661 


2.8846 


1.0732 


2.7550 


1.0807 


2.6372 


1.0886 


2.5299 


43 


18 


1.0662 


2.8824 


1.0733 


2.7529 


1.0808 


2.6353 


1.0888 


2.5281 


42 


19 


1.0663 


2.8801 


1.0734 


2.7509 


1. 0810 


2.6335 


1.0889 


2.5264 


41 


20 


1.0664 


2.8778 


1.0736 


2.7488 


1.0811 


2.6316 


1. 089 1 


2.5247 


40 


21 


1.0666 


2.8756 


1.0737 


2.7468 


1.0812 


2.6297 


1.0892 


2.5230 


39 


22 


1.0667 


2.8733 


1.0738 


2.7447 


1.0813 


2.6279 


1.0893 


2.5213 


38 


23 


1.0668 


2.8711 


1.0739 


2.7427 


1.0815 


2.6260 


1.0895 


2.5196 


37 


24 


1.0669 


2.8688 


1.0740 


2.7406 


1. 08 16 


2.6242 


1.0896 


2.5179 


36 


25 


1.0670 


2.8666 


1.0742 


2.7386 


1.0817 


2.6223 


1.0897 


2.5163 


35 


26 


1. 067 1 


2.8644 


1 .0743 


2.7366 


1.0819 


2.6205 


1.0899 


2.5146 


34 


27 


1.0673 


2.8621 


1.0744 


2.7346 


1.0820 


2.6186 


1.0900 


2.5129 


33 


28 


1.0674 


2.8599 


I.0745 


2.732s 


1. 082 1 


2.6168 


1.0902 


2.5112 


32 


29 


1.0675 


2.8577 


1.0747 


2.7305 


1.0823 


2.6150 


1.0903 


2.5095 


31 


30 


1.0676 


2.8554 


1.0748 


2.7285 


1.0824 


2.6131 


1.0904 


2.5078 


30 


31 


1.0677 


2.8532 


1.0749 


2.7265 


1.0825 


2.6113 


1.0906 


2.5062 


29 


32 


1.0678 


2.8510 


1.0750 


2.7245 


1.0826 


2.6095 


1.0907 


2.5045 


28 


33 


1.0679 


2.8488 


1.0751 


2.7225 


1.0828 


2.6076 


1.0908 


2.5028 


27 


34 


1. 068 1 


2.8466 


1.0753 


2.7205 


1.0829 


2.6058 


1. 0910 


2.5011 


26 


35 


1.0682 


2.8444 


1.0754 


2.7185 


1.0830 


2.6040 


1.0911 


2.4995 


25 


36 


1.0683 


2.8422 


1.0755 


2.7165 


1.0832 


2.6022 


1.0913 


2.4978 


24 


37 


1.0684 


2.8400 


1.0756 


2.7145 


1.0833 


2.6003 


1.0914 


2.4961 


23 


38 


1.0685 


2.8378 


1.0758 


2.7125 


1.0834 


2.5985 


1.0915 


2.4945 


22 


39 


1.0686 


2.8356 


I.0759 


2.7105 


1.0836 


2.5967 


1. 091 7 


2.4928 


21 


40 


1.0688 


2.8334 


1.0760 


2.7085 


1.0837 


2.5949 


1.0918 


2.4912 


20 


41 


1.0689 


2.8312 


1.0761 


2.7065 


1.0838 


2.5931 


1.0920 


2.4895 


19 


42 


1 .0690 


2.8290 


1.0763 


2.7045 


1 .0840 


2.5913 


1. 092 1 


2.4879 


18 


43 


1. 0691 


2.8269 


1.0764 


2.7026 


1. 0841 


2.5895 


1.0922 


2.4862 


17 


44 


1.0692 


2.8247 


1.0765 


2.7006 


1.0842 


2.5877 


1.0924 


2.4846 


16 


45 


1.0694 


2.8225 


1.0766 


2.6986 


1 .0844 


2.5859 


1.0925 


2.4829 


15 


46 


1.0695 


2.8204 


1.0768 


2.6967 


1.0845 


2.5841 


1.0927 


2.4813 


14 


47 


1.0696 


2.8182 


1.0769 


2.6947 


1.0846 


2.5823 


1.0928 


2.4797 


13 


48 


1.0697 


2.8160 


1.0770 


2.6927 


1.0847 


2.5805 


1.0929 


2.4780 


12 


49 


1.0698 


2.8139 


1.0771 


2.6908 


1.0849 


2.5787 


1. 093 1 


2.4764 


II 


50 


1.0699 


2.8117 


I-0773 


2.6888 


1.0850 


2.5770 


1.0932 


2.4748 


10 


51 


1. 0701 


2.8096 


1.0774 


2.6869 


1. 085 1 


2.5752 


1.0934 


2.4731 


9 


52 


1.0702 


2.8074 


1.0775 


2.6849 


1.0853 


2.5734 


1.0935 


2.4715 


8 


53 


1.0703 


2.8053 


1.0776 


2.6830 


1.0854 


2.5716 


1.0936 


2.4699 


7 


54 


1.0704 


2.8032 


1.0778 


2.6810 


1.0855 


2.5699 


1.0938 


2.4683 


6 


I55 


1.0705 


2.8010 


1.0779 


2.6791 


1.0857 


2.5681 


1.0939 


2.4666 


5 


56 


1.0707 


2.7989 


1.0780 


2.6772 


1.0858 


2.5663 


1. 0941 


2.4650 


4 


57 


1.0708 


2.7968 


1.0781 


2.6752 


1.0859 


2.5646 


1 .0942 


2.4634 


3 


58 


1.0709 


2.7947 


1.0783 


2.6733 


1. 086 1 


2.5628 


1.0943 


2.4618 


2 


59 


1.0710 


2.7925 


1.0784 


2.6714 


1.0862 


2.5610 


1.0945 


2.4602 


I 


|6o 


1.0711 


2.7904 


1.0785 


2.6695 


1.0864 


2.5593 


1.0946 


2.4586 





Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


r 


( 


6^ 


)° 


6J 


^° 


6' 


r° 


6( 


3° 





874 



GENERAL TABLES AND FORMULA 





24° 


25° 


26° 


27° 




/ 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


/ 


o 


1.0946 


2.4586 


1. 1034 


2.3662 


1.1126 


2.2812 


1. 1223 


2.2027 


60 


I 


1.0948 


2.4570 


1.1035 


2.3647 


1.1127 


2.2798 


1. 1225 


2.2014 




2 


1.0949 


2.4554 


1. 1037 


2.3632 


1.1129 


2.2784 


1. 1226 


2.2002 




3 


1. 095 1 


2.4538 


1. 1038 


2.3618 


1.1131 


2.2771 


1. 1228 


2.1989 


57 


4 


1.0952 


2.4522 


1. 1040 


2.3603 


1.1132 


2.2757 


1.1230 


2.1977 


56 


5 


1.0953 


2.4506 


1.1041 


2.3588 


1.1134 


2.2744 


1.1231 


2.1964 


5S 


6 


1 .0955 


2.4490 


1. 1043 


2.3574 


1.1135 


2.2730 


1.1233 


2.1952 


54 


7 


1.0956 


2.4474 


1. 1044 


2.3559 


1.1137 


2.2717 


I-I235 


2.1939 


53 


8 


1.0958 


2.4458 


1. 1046 


2.3544 


1.1139 


2.2703 


1.1237 


2.1927 


52 


9 


1.0959 


2.4442 


1. 1047 


2.3530 


1.1140 


2.2690 


1.1-38 


2.1914 


SI 


lO 


1. 096 1 


2.4426 


1. 1049 


2.3515 


1.1142 


2.2676 


1. 1240 


2.1902 


SO 


II 


1.0962 


2.44II 


1. 1050 


2.3501 


1.1143 


2.2663 


1.1242 


2.1889 


49 


12 


1.0963 


2.4395 


1. 1052 


2.3486 


1.1145 


2.2650 


1.1243 


2.1877 


48 


13 


1.0965 


2.4379 


1. 1053 


2.3472 


1.1147 


2.2636 


1. 1245 


2.1865 


47 


14 


1 .0966 


2.4363 


1.1055 


2.3457 


1.1148 


2 2623 


1. 1247 


2.1852 


46 


IS 


1.0968 


2.4347 


X.1056 


2.3443 


1.1150 


2.2610 


1. 1248 


2.1840 


45 


i6 


1 .0969 


2.4332 


1. 1058 


2.3428 


1.1151 


2.2596 


1. 1250 


2.1828 


44 


17 


1. 097 1 


2.4316 


1. 1059 


2.3414 


I-II53 


2.2583 


1. 1252 


2.1815 


43 


i8 


1.0972 


2.4300 


1.1061 


2.3399 


1.1155 


2.2570 


1.1253 


2.1803 


42 


19 


1.0973 


2.428s 


1. 1062 


2.3385 


1.1156 


2.2556 


1.1255 


2.1791 


41 


20 


1.0975 


2.4269 


1. 1064 


2.3371 


1.1158 


2.2543 


1.1257 


2.1778 


40 


21 


1.0976 


2.4254 


1. 1065 


2.3356 


1.1159 


2.2530 


1.1258 


2.1766 


35 


22 


1.0978 


2.4238 


1. 1067 


2.3342 


1.1161 


2.2517 


1. 1260 


2.1754 


38 


23 


1.0979 


2.4222 


1. 1068 


2.3328 


1.1163 


2.2503 


1. 1262 


2.1742 


37 


24 


1. 098 1 


2.4207 


1. 1070 


2.3313 


1.1164 


2.2490 


1. 1264 


2.1730 


36 


25 


1.0982 


2.4191 


1. 1072 


2.3299 


1.1166 


2.2477 


1. 1265 


2.1717 


35 


26 


1 .0984 


2.4176 


1.1073 


2.3285 


1.1167 


2.2464 


1. 1267 


2.1705 


34 


27 


1.0985 


2.4160 


I. 1075 


2.3271 


1.1169 


2.2451 


1. 1269 


2.1693 


33 


28 


1.0986 


2.4145 


1. 1076 


2.3256 


1.1171 


2.2438 


1. 1270 


2.1681 


32 


29 


1.0988 


2.4130 


I. 1078 


2.3242 


1.1172 


2.2425 


1. 1272 


2.1669 


51 


30 


1.0989 


2.4114 


1.1079 


2.3228 


1.1174 


2.2411 


1. 1274 


2.1657 


30 


31 


1. 0991 


2.4099 


1.1081 


2.3214 


1.1176 


2.2398 


1. 1275 


2.1645 


29 


32 


1.0992 


2.4083 


1. 1082 


2.3200 


1.1177 


2.2385 


1. 1277 


2.1633 


28 


33 


1.0994 


2.4068 


1. 1084 


2.3186 


1.1179 


2.2372 


1. 1279 


2.1620 


27 


34 


1.0995 


2.4053 


1. 1085 


2.3172 


1.1180 


2.2359 


1.1281 


2.1608 


26 


35 


1.0997 


2.4037 


1. 1087 


2.3158 


1.1182 


2.2346 


1.1282 


2.1596 


25 


36 


1.0998 


2.4022 


1. 1088 • 


2.3143 


1.1184 


2.2333 


1. 1284 


2.1584 


24 


37 


1. 1000 


2.4007 


1. 1090 


2.3129 


1.1185 


2.2320 


1.1286 


2.1572 


23 


38 


I.IOOI 


2.3992 


1. 1092 


2.3II5 


1.1187 


2.2307 


1.1287 


2.1560 


22 


39 


1. 1003 


2.3976 


1. 1093 


2.3IOI 


1.1189 


2.2294 


1. 1289 


2.1548 


21 


40 


1. 1004 


2.3961 


I. 1095 


2.3087 


1.1190 


2.2282 


1.1291 


2.1536 


20 


41 


1. 1005 


2.3946 


1. 1096 


2.3073 


1.1192 


2.2269 


1. 1293 


2.1525 


19 


42 


1. 1007 


2.3931 


1. 1098 


2.3059 


1.1193 


2.2256 


I. 1294 


2.1513 


18 


43 


1. 1008 


2.3916 


1. 1099 


2.3046 


1.1195 


2.2243 


1. 1296 


2.1501 


17 


44 


I.IOIO 


2.3901 


I.IIOI 


2.3032 


1.1197 


2.2230 


1. 1298 


2.1489 


16 


4| 


I. ion 


2.3886 


I.II02 


2.3018 


1.1198 


2.2217 


1. 1299 


2.1477 


IS 


46 


1.1013 


2.3871 


I.II04 


2.3004 


I. 1200 


2.2204 


1.1301 


2.1465 


14 


^^ 


1.1014 


2.3856 


I.II06 


2.2990 


I. 1202 


2.2192 


I. 1303 


2.1453 


13 


48 


1.1016 


2.3841 


I.IIO7 


2.2976 


I. 1203 


2.2179 


1.1305 


2.1441 


12 


49 


1.1017 


2.3826 


I.IIO9 


2.2962 


I. 1205 


2.2166 


1.1306 


2.1430 


II 


SO 


1.1019 


2.3811 


I.IIIO 


2.2949 


1. 1207 


2.2153 


1.1308 


2.1418 


10 


51 


1. 1020 


2.3796 


I.III2 


2.2935 


1.1208 


2.2141 


1.1310 


2.1406 


9 


52 


1. 1022 


2.3781 


I.III3 


2.2921 


1.1210 


2.2128 


1.1312 


2.1394 


8 


S3 


1.1023 


2.3766 


I.III5 


2.2907 


1.1212 


2.2115 


1-1313 


2.1382 


7 


54 


1. 1025 


2.3751 


I.III6 


2.2894 


1.1213 


2.2103 


1.1315 


2.1371 


6 


55 


1. 1026 


2.3736 


I.III8 


2.2880 


1.1215 


2.2090 


1.1317 


2.1359 


5 


S6 


1. 1028 


2.3721 


I.II20 


2.^866 


1.1217 


2.2077 


1.1319 


2.1347 


4 


^l 


1. 1029 


2.3706 


I.II2I 


2.2853 


1.1218 


2.2065 


1. 1320 


2'T^335 


3 


S8 


1-1031 


2.3691 


I.II23 


2.2839 


1. 1220 


2.2052 


1.1322 


2.1324 


a 


59 


1. 1032 


2.3677 


I.II24 


2.2825 


1. 1222 


2.2039 


1.1324 


2.1317 


I 


60 


1. 1034 


2.3662 


I.II26 


2.2812 


1. 1223 


2.2027 


1.1326 


2.1300 




4 


/ 


Co-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC 


Sec. 




e^ 


>° 


6^ 


6^ 


;° 


62 








NATURAL SECANTS AND CO-SECANTS 



875 





28^ 1 


29° 1 


30° 1 


31° 


/ 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 


Sec. 


Co-sec. 





1. 1326 


2.1300 


I-I433 


2.0627 


1. 1547 


2.0000 


1. 1666 


1. 9416 


I 


1.1327 


2.1289 


1.1435 


2.0616 


1. 1549 


1.9990 


1.1668 


1.9407 


2 


1-1329 


2.1277 


1-1437 


2.0605 


1.1551 


1.9980 


I. 1670 


1.9397 


3 


1.1331 


2.1266 


1.1439 


2.0594 


1.1553 


1.9970 


1. 1672 


1.9388 


4 


1.1333 


2.1254 


1.1441 


2.0583 


I-I555 


1.9960 


1.1674 


1.9378 


5 


1.1334 


2.1242 


1.1443 


2.0573 


I-I557 


1.9950 


1.1676 


1.9369 


6 


1.1336 


2.1231 


1-1445 


2.0562 


1. 1559 


1.9940 


1.1678 


1.9360 


7 


1.1338 


2.1219 


1. 1446 


2.0551 


1.1561 


1.9930 


1.1681 


1-9350 


8 


1. 1340 


2.1208 


1. 1448 


2.0540 


1.1562 


1.9920 


1.1683 


1-9341 


9 


1.1341 


2.1196 


1.1450 


2.0530 


1.1564 


1. 9910 


1.168s 


1.9332 


10 


1.1343 


2.1185 


1.1452 


2.0519 


1.1566 


1.9900 


1.1687 


1-9322 


II 


1.1345 


2.1173 


1-1454 


2.0508 


1.1568 


1.9890 


1.1689 


1-9313 


12 


1.1347 


2.1162 


1.1456 


2.0498 


1.1570 


1.9880 


1.1691 


1.9304 


13 


1.1349 


2.1150 


1.1458 


2.0487 


1. 1572 


1.9870 


1.1693 


1.9295 


14 


1.1350 


2.1139 


I.I459 


2.0476 


1.1574 


1.9860 


1.1695 


1.9285 


15 


1-1352 


2.1127 


1.1461 


2.0466 


1.1576 


1.9850 


1.1697 


1.9276 


16 


1.1354 


2.1116 


1.1463 


2.0455 


1.1578 


1 .9840 


1.1699 


1.9267 


17 


1-1356 


2.1104 


1.1465 


2.0444 


1.1580 


1.9830 


1.1701 


1.9258 


18 


1.1357 


2.1093 


1.1467 


2.0434 


1. 1582 


1.9820 


1.1703 


1.9248 


19 


I-I359 


2.1082 


1.1469 


2.0423 


1.1584 


1.9811 


1.1705 


1.9239 


20 


1.1361 


2.1070 


1-1471 


2.0413 


1.1586 


1. 980 1 


1.1707 


1.9230 


21 


1.1363 


2.1059 


1.1473 


2.0402 


1.1588 


1.9791 


1.1709 


1.9221 


22 


1.1365 


2.1048 


1. 1474 


2.0392 


1.1590 


1.9781 


1.1712 


1. 92 12 


23 


1.1366 


2.1036 


1.1476 


2.0381 


1.1592 


1-9771 


1.1714 


1.9203 


24 


1.1368 


2.1025 


1.1478 


2.0370 


1-1594 


1.9761 


1. 1716 


1.9193 


25 


1.1370 


2.1014 


1. 1480 


2.0360 


1. 1596 


1-9752 


1.1718 


1.9184 


26 


I-1372 


2.1002 


1.1482 


2.0349 


1.1598 


1.9742 


1. 1720 


1.9175 


27 


1.1373 


2.0991 


1. 1484 


2.0339 


1. 1600 


1.9732 


1.1722 


1.9166 


28 


I-I375 


2.0980 


1.1486 


2.0329 


1. 1602 


1.9722 


1. 1724 


1.9157 


29 


1.1377 


2.0969 


1.1488 


2.0318 


1. 1604 


1.9713 


1.1726 


1.9148 


30 


I-I379 


2.0957 


1.1489 


2.0308 


1.1606 


1.9703 


1. 1728 


1. 91 39 


31 


1.1381 


2.0946 


1.1491 


2.0297 


1.1608 


1.9693 


1.1730 


1. 9130 


32 


1. 1382 


2.0935 


I -1493 


2.0287 


1.1610 


1.9683 


1.1732 


1.9121 


33 


1.1384 


2.0924 


1. 1495 


2.0276 


1.1612 


1.9674 


1. 1734 


1.9112 


34 


1.1386 


2.0912 


1.1497 


2.0266 


1.1614 


1.9664 


1.1737 


1.9102 


35 


1.1388 


2.0901 


1. 1499 


2.0256 


1.1616 


1.9654 


1.1739 


1.9093 


36 


I. I 390 


2.0890 


1.1501 


2.0245 


1.1618 


1.9645 


1.1741 


1.9084 


37 


1.1391 


2.0879 


1. 1503 


2.0235 


1. 1620 


1.9635 


1-1743 


1.9075 


38 


1.1393 


2.0868 


1. 1505 


2.0224 


1. 1622 


1.9625 


1-1745 


1.9066 


39 


1.139s 


2.0857 


1.1507 


2.0214 


1. 1624 


1.9616 


1.1747 


1.9057 


40 


I-I397 


2.0846 


1.1508 


2.0204 


1.1626 


1.9606 


1. 1 749 


1.9048 


41 


I-1399 


2.0835 


1.1510 


2.0194 


1.1628 


1.9596 


1-1751 


1.9039 


42 


1.1401 


2.0824 


1.1512 


2.0183 


1. 1630 


1-9587 


I-I753 


1.9030 


43 


1. 1402 


2.0812 


1.1514 


2.0173 


1. 1632 


1-9577 


1.1756 


1. 902 1 


44 


1. 1404 


2.0801 


1.1516 


2.0163 


1.1634 


1-9568 


1.1758 


1.9013 


45 


1. 1406 


2.0790 


1.1518 


2.0152 


1.1636 


1-9558 


1. 1 760 


1.9004 


46 


1. 1408 


2.0779 


1.1520 


2.0142 


1.1638 


1-9549 


1. 1762 


1.8995 


47 


1.1410 


2.0768 


1.1522 


2.0132 


1. 1640 


1-9539 


1.1764 


1.8986 


48 


1.1411 


2.0757 


1.1524 


2.0122 


1. 1642 


1-9530 


1. 1766 


1.8977 


49 


1.1413 


2.0746 


1. 1526 


2.0111 


1. 1644 


1.9520 


1.1768 


1.8968 


50 


1.1415 


2.0735 


1.1528 


2.0101 


1. 1646 


1-9510 


1. 1770 


1.8959 


51 


1.1417 


2.072s 


1-1530 


2.0091 


1.1648 


1-9501 


1.1772 


1.8950 


52 


1.1419 


2.0714 


I-I53I 


2.0081 


1. 1650 


1. 9491 


1-1775 


1. 8941 


53 


1.1421 


2.0703 


1. 1533 


2.0071 


1. 1652 


1.9482 


1.1777 


1.8932 


54 


1. 1422 


2.0692 


1-1535 


2.0061 


1-1654 


1-9473 


1. 1779 


1.8924 


55 


1.1424 


2.0681 


I-I537 


2.0050 


1.1656 


1.9463 


1.1781 


1.8915 


56 


1. 1426 


2.0670 


I-I539 


2.0040 


1.1658 


1.9454 


1.1783 


1.8906 


^l 


1. 1428 


2.0659 


1.1541 


2.0030 


1. 1660 


1.9444 


1.1785 


1.8897 


58 


1.1430 


2.0648 


1.1543 


2.0020 


1.1662 


1.9435 


1.1787 


1.8888 


59 


1.1432 


2.0637 


1. 1545 


2.0010 


1. 1664 


1.9425 


1.1790 


1.8879 


60 


I-I433 


2.0627 


1-1547 


2.0000 


1. 1666 


1.9416 


1.1792 


1.8871 


/ 


Co-SEC. 


Sec. 


Cb-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-SEC. 


Sec. 




6] 


L^ 


6( 


r 


5^ 


r 


dl 


30 



876 



GENERAL TABLES AND FORMULA 





32** 1 


33° 1 


34° I 


35° 






/ 


Sec. 


Co-sec. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. Cc 


)-SEC. 


/ 





1.1792 


1.8871 


1.1924 


I.8361 


1.2062 


1.7883 


1.2208 1 


7434 


60 


X 


1.1794 


1.8862 


1. 1926 


1.8352 


1.2064 


1.7875 


1.2210 I 


7427 


59 


2 


1.1796 


1.8853 


1. 1928 


1.8344 


1.2067 


1.7867 


1.2213 I 


7420 


58 


3 


1.1798 


1.8844 


1. 1930 


1.8336 


1.2069 


1.7860 


1.2215 I 


7413 


57 


4 


1.1800 


1.8836 


I-I933 


1.8328 


1.2072 


1.7852 


1.2218 I 


740S 


56 


5 


I. 1802 


1.8827 


I-I935 


1.8320 


1.2074 


1.7844 


1.2220 1 


7598 


55 


6 


1.180S 


1.8818 


1.1937 


I.8311 


1.2076 


1-7837 


1.2223 1 


7391 


54 


7 


1.1807 


1.8809 


1. 1939 


1.8303 


1.2079 


1.7829 


1.2225 1 


7584 


53 


8 


1. 1809 


1. 880 1 


1.1942 


1.8295 


1.2081 


1.7821 


1.2228 1 


7377 


52 


9 


1.1811 


1.8792 


1.1944 


1.8287 


1.2083 


1.7814 


1.2250 I 


7369 


51 


10 


1.1813 


1.8783 


1. 1946 


1.8279 


1.2086 


1.7806 


1.2255 I 


7362 


50 


II 


1.1815 


1.8785 


1. 1948 


I.8271 


1.2088 


1-7798 


1.225s I 


7355 


49 


12 


1.1818 


1.8766 


1.1951 


1.8263 


1. 2091 


1.7791 


1.2258 1 


7348 


48 


13 


1. 1820 


1-8757 


1-1953 


1.8255 


1.2093 


1-7783 


1.2240 1 


7341 


47 


14 


1.1822 


1.8749 


1. 1955 


1.8246 


1.2095 


1.7776 


1.2245 I 


7334 


46 


15 


1. 1824 


1.8740 


1.1958 


1.8238 


1.2098 


1.7768 


1.224s I 


7327 


45 


16 


1. 1826 


1.8731 


1. 1960 


1.8230 


1.2100 


1.7760 


1.2248 1 


7319 


44 


17 


1.1828 


1.8723 


1. 1962 


1.8222 


1.2103 


1-7753 


1.2250 I 


7312 


43 


18 


1.1831 


1.8714 


1. 1964 


I.8214 


1.2105 


1.7745 


I.22S5 I 


7505 


42 


19 


1.1833 


1.8706 


1.1967 


1.8206 


1. 2107 


1.7758 


1.225s 1 


7298 


41 


20 


1.1835 


1.8697 


1. 1969 


1. 8198 


1.2110 


I-7730 


1.2258 1 


7291 


40 


21 


1.1837 


1.8688 


1.1971 


I.8190 


1.2112 


1.7725 


1.2260 1 


7284 


39 


22 


1.1839 


1.8680 


I. 1974 


I.8182 


1.2115 


1-7715 


1.2265 I 


7277 


38 


23 


1.1841 


1. 867 1 


1. 1976 


1. 81 74 


1.2117 


1.7708 


1.2265 I 


7270 


37 


24 


1. 1844 


1.8663 


1.1978 


I.8166 


1.2119 


1.7700 


1.2268 1 


7265 


36 


25 


1. 1846 


1.8654 


I. 1980 


I.8158 


1.2122 


1.7693 


1.2270 I 


7256 


35 


26 


1.1848 


1.8646 


1.1983 


I.8150 


1.2124 


1.7685 


1.2275 I 


7249 


34 


27 


1.1850 


1.8637 


1.1985 


I.8142 


1.2127 


1.7678 


1.2276 I 


7242 


33 


28 


1.1852 


1.8629 


1. 1987 


I.8134 


1.2129 


1.7670 


1.2278 1 


7254 


32 


29 


1-1855 


1.8620 


1. 1990 


I.8126 


1.2132 


1.7663 


1.2281 1 


7227 


31 


30 


1.1857 


1.8611 


1. 1992 


I.8118 


1.2154 


1.765s 


1.2285 I 


7220 


30 


31 


1.1859 


1.8603 


1. 1994 


I.8110 


1.2136 


1.7648 


1.2286 1 


7213 


29 


32 


1.1861 


1.8595 


1. 1997 


I.8102 


1-2159 


1.7640 


1.2288 1 


7206 


28 


33 


1.1863 


1.8586 


1. 1999 


1.8094 


1.2141 


1-7655 


1.2291 1 


7199 


27 


34 


1.1866 


1.8578 


1. 2001 


1.8086 


1.2144 


1.7625 


1.2295 I 


7192 


26 


35 


1.1868 


1.8569 


1.2004 


1.8078 


1.2146 


1.7618 


1.2296 I 


7185 


25 


36 


1. 1870 


1.8561 


1.2006 


1.8070 


1.2149 


1.7610 


1.2298 1 


7178 


24 


37 


1.1872 


1.8552 


1.2008 


1.8062 


1.2151 


1.7605 


1.2501 1 


7171 


23 


38 


1.1874 


1.8544 


1. 2010 


1.8054 


1-2153 


1-7596 


1.2504 1 


7164 


22 


39 


1.1877 


1.8535 


1.2013 


1 .8047 


1.2156 


1.7588 


1.2506 1 


7157 


21 


40 


1.1879 


1.8527 


1.2015 


1.8039 


1.2158 


1.7581 


1.2509 1 


7151 


20 


41 


1.1881 


1.8519 


1. 2017 


1. 803 1 


1.2161 


1.7573 


I.25II 1 


7144 


19 


42 


1.1883 


1. 85 10 


1.2020 


1.8023 


1.2163 


1.7566 


1.2514 1 


7137 


18 


43 


1.1886 


1.8502 


1.2022 


1. 801 5 


1.2166 


1.7559 


1.2316 1 


7130 


17 


44 


1.1888 


1.8493 


1.2024 


1.8007 


1.2168 


1-7551 


1.2319 I 


7123 


16 


45 


1. 1890 


1.8485 


1.2027 


1.7999 


1.2171 


1-7544 


1.2522 1 


7116 


15 


46 


1. 1892 


1.8477 


1.2029 


1.7992 


1.2173 


1-7537 


1.2524 1 


7109 


14 


47 


1.1894 


1.8468 


1.2031 


1.7984 


1.2175 


1.7529 


1.2527 1 


7102 


13 


48 


1.1897 


1.8460 


1.2034 


1.7976 


1.2178 


1-7522 


1.2529 1 


709s 


12 


49 


1.1899 


1.8452 


1.2036 


1.7968 


1.2180 


1-7514 


1.2552 1 


7088 


II 


50 


1.1901 


1.8443 


1.2039 


1.7960 


1.2183 


1.7507 


1.2535 I 


7081 


10 


51 


1. 1903 


1.8435 


1. 2041 


1-7553 


1.2185 


1.7500 


1-2557 I 


7075 


9 


52 


1.1906 


1.8427 


1.2043 


1-7945 


1.2188 


1.7493 


1.2540 I 


7068 


8 


53 


1. 1908 


1.8418 


1.2046 


1-7937 


1.2190 


1-7485 


1.2542 1 


7061 


7 


54 


1.1910 


1. 8410 


1.2048 


1.7929 


1-2193 


1.7478 


1.2545 I 


7054 


6 


55 


1.1912 


1.8402 


1.2050 


1.7921 


1.2195 


1.7471 


1.2548 1 


7047 


5 


56 


1.1915 


1.8394 


1.2053 


1.7914 


1.2198 


1.7465 


1.2550 1 


7040 


4 


57 


i.iqi7 


1.8385 


1.205s 


1.7906 


1.2200 


1.7456 


1.2553 I 


7053 


3 


58 


1.1919 


1.8377 


1.2057 


1.7898 


1.2203 


1.7449 


I-235S I 


7027 


2 


59 


1.1921 


1.8369 


.1.2060 


1.7891 


1.220s 


1.7442 


1.2558 1 


7020 


I 


60 


1. 1922 


1.8361 


1.2062 


1.7883 


1.2208 


1.7434 


1.2561 1 


7013 





/ 


Co-sec. 


Sec. 


Co-SEC. 


Sec 


Co-SEC. 


Sec. 


Co-SEC 


Sec. 


/ 




5 


7° 


5 


6° 


5 


5° 


54° 







NATURAL SECANTS AND CO-SECANTS 



877 



36 





37 





38 





39 







Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


Sec. 


Co-SEC. 


/ 


1.2361 


I.7013 


1.2521 


I.6616 


1.2690 


1.6243 


1.2867 


1.5890 


60 


1.2363 


1.7006 


1.2524 


1. 66 10 


1.2693 


1.6237 


1.2871 


1.5884 


59 


1.2366 


1.6999 


1.2527 


1.6603 


1.2696 


I.6231 


1.2874 


1.5879 


58 


1.2368 


1.6993 


1.2530 


1.6597 


1.2699 


1.6224 


1.2877 


I.5S73 


57 


1.2371 


1.6986 


1.2532 


1.6591 


1.2702 


I.6218 


1.2880 


1.5867 


56 


1-2374 


1.6979 


1.2535 


1.6584 


1.2705 


I.6212 


1.2883 


1.5862 


55 


1.2376 


1.6972 


1.2538 


1.6578 


1.2707 


1.6206 


1.2886 


1.5856 


54 


1.2379 


1.6965 


1. 2541 


1.6572 


1.2710 


1.6200 


1.2889 


1.5850 


S3 


1.2382 


1.6959 


1.2543 


1.6565 


1.2713 


1.6194 


1.2892 


1.5845 


52 


1.2384 


1.6952 


1.2546 


1.6559 


1. 2716 


I.6188 


1.2895 


1.5839 


51 


1.2387 


1.6945 


1.2549 


1.6552 


1.2719 


I.6182 


1.2898 


1.5833 


50 


1.2389 


1.6938 


1.2552 


1.6546 


1.2722 


1. 61 76 


1.2901 


1.5828 


49 


1.2392 


1.6932 


1.2554 


1.6540 


1.2725 


1. 61 70 


1.2904 


1.5822 


48 


1.239s 


1.6925 


1.2557 


1.6533 


1.2728 


1. 6164 


1.2907 


I.58I6 


47 


1.2397 


1. 6918 


1.2560 


1.6527 


1.2731 


I.6159 


1.2910 


I.58II 


46 


1.2400 


I.6912 


1.2563 


1.6521 


1.2734 


I.6153 


1.2913 


1.5805 


45 


1.2403 


1.6905 


1.2565 


1.6514 


1.2737 


I.6147 


1. 2916 


1.5799 


44 


1. 240s 


1.6898 


1.2568 


1.6508 


1.2739 


I.6141 


1.2919 


1.5794 


43 


1.2408 


1. 6891 


1.2571 


1.6502 


1.2742 


1.6135 


1.2922 


1.5788 


42 


1.2411 


1.6885 


1.2574 


1.6496 


1.2745 


I.6129 


1.2926 


1.5783 


41 


1.2413 


1.6878 


1.2577 


1.6489 


1.2748 


I.6123 


1.2929 


1.5777 


40 


1. 2416 


1. 687 1 


1.2579 


1.6483 


1.2751 


I.6117 


1.2932 


1.5771 


39 


1.2419 


1.6865 


1.2582 


1.6477 


1.2754 


I.611I 


1.2935 


1.5766 


38 


1.2421 


1.6858 


1.2585 


1.6470 


1.2757 


I.6105 


1.2938 


1.5760 


37 


1.2424 


1. 685 1 


1.2588 


1 .6464 


1.2760 


1.6099 


1.2941 


1.5755 


36 


1.2427 


1.6845 


1.2591 


1.6458 


1.2763 


1.6093 


1.2944 


1.5749 


35 


1.2429 


1.6838 


1.2593 


1.6452 


1.2766 


I.60S7 


1.2947 


1.5743 


34 


1.2432 


1. 683 1 


1.2596 


1.6445 


1.2769 


1. 608 1 


1.2950 


1.5738 


33 


1.2435 


1.6825 


1.2599 


1.6439 


1.2772 


1.6077 


1.2953 


1.5732 


32 


1.2437 


1. 68 18 


1.2602 


1.6433 


1.2775 


1.6070 


1.2956 


1.5727 


31 


1 .2440 


1.6812 


1.2605 


1.6427 


1.2778 


1.6064 


1.2960 


I.572I 


30 


1.2443 


1.6805 


1.2607 


1.6420 


1.2781 


1.6058 


1.2963 


1.5716 


29 


1.2445 


1.6798 


1.2610 


1. 6414 


1.2784 


1.6052 


1.2966 


1.5710 


28 


1.2448 


1.6792 


1.2613 


1.6408 


1.2787 


1.6046 


1.2969 


1.5705 


27 


1.2451 


1.6785 


1.2616 


1.6402 


1.2790 


1 .6040 


1.2972 


1.5699 


26 


1.2453 


1.6779 


1.2619 


1.6396 


1.2793 


1.6034 


1.2975 


1.5694 


25 


1.2456 


1.6772 


1.2622 


1.6389 


1.2795 


1.6029 


1.2978 


1.5688 


24 


I. 2459 


1.6766 


1.2624 


1.6383 


1.2798 


1.6023 


1.2981 


1.5683 


23 


I. 2461 


1.6759 


1.2627 


1.6377 


1.2801 


1. 601 7 


1.2985 


1.5677 


22 


1.2464 


1.6752 


1.2630 


1.6371 


1.2804 


1. 601 1 


1.2988 


1.5672 


21 


1.2467 


1.6746 


1.2633 


1.6365 


1.2807 


1.6005 


1.2991 


1.5666 


20 


1.2470 


1.6739 


1.2636 


1.6359 


1. 2810 


1.6000 


1.2994 


I.566I 


19 


1.2472 


1.6733 


1.2639 


1.6352 


1.2813 


1.5994 


1.2997 


1.5655 


18 


1.2475 


1.6726 


1. 2641 


1.6346 


1.2816 


1.5988 


1.3000 


1.5650 


17 


1.2478 


1.6720 


1.2644 


1.6340 


1.2819 


1.5982 


1.3003 


1.5644 


16 


1.2480 


1.6713 


1.2647 


1.6334 


1.2822 


1.5976 


1.3006 


1.5639 


IS 


1.2483 


1.6707 


1.2650 


1.6328 


1.2825 


1.5971 


1. 3010 


1.5633 


14 


1.2486 


1.6700 


1.2653 


1.6322 


1.2828 


1.5965 


1.3013 


1.5628 


13 


1.2488 


1.6694 


1.2656 


1.6316 


1.2831 


1.5959 


1.3016 


1.5622 


12 


1.2490 


1.6687 


1.2659 


1.6309 


1.2834 


1.5953 


1.3019 


1.5617 


II 


1.2494 


1. 6681 


1. 2661 


1.6303 


1.2837 


1.5947 


1.3022 


I.56II 


10 


1.2497 


1.6674 


1.2664 


1.6297 


1.2840 


1.5942 


1.302 s 


1.5606 


9 


1.2499 


1.6668 


1.2667 


1. 6291 


1.2843 


1.5936 


1.3029 


1.5600 


8 


1.2502 


1. 666 1 


1.2670 


1.6285 


1.2846 


1.5930 


1.3032 


1-5595 


7 


1.2505 


1.6655 


1.2673 


1.6279 


1.2849 


1.5924 


1.3035 


1.5590 


6 


1.2508 


1.6648 


1.2676 


1.6273 


1.2852 


1.5919 


1.3038 


1.5584 


5 


1.2510 


1.6642 


1.2679 


1.6267 


1.2855 


1.5913 


1. 3041 


1.5579 


4 


1.2513 


1.6636 


1. 2681 


1. 6261 


1.2858 


1.5907 


1.3044 


1.5573 


3 


1.2516 


1.6629 


1.2684 


1.6255 


1.2861 


1.5901 


1.3048 


1.5568 


2 


1.2519 


1.6623 


1.2687 


1.6249 


1.2864 


1.5896 


1.3051 


1.5563 


I 


1.2521 


1.6616 


1.2690 


1.6243 


1.2867 


1.5890 


1.3054 


1.5557 





Co-SEC. 


Sec. 


Co-sec. 


Sec. 


Co-SEC 


Sec. 


Co-SEC. 


Sec. 


/ 


5 


3° 


5 


2° 


5 


1° 


5 


0° 





878 



GENERAL TABLES AND FORMULA 



4C 


)° 


4] 





42° I 


43° 




Sec. 


Co-sec. 


Sec. 


Co-SEC. 


Sec 


Co-SEC 


Sec 


Co-SEC. 


/ 


1-3054 


1.5557 


1.3250 


1.5242 


1-3456 


1-4945 


1-3673 


1.4663 


6a 


1.3057 


1.5552 


1.3253 


1.5237 


1.3460 


1.4940 


1.3677 


1.4658 


59 


1.3060 


1.5546 


1.3257 


1.5232 


1-3463 


1.4935 


1.3681 


1.4654 


58 


1.3064 


1.5541 


1.3260 


1.5227 


1.3467 


1.4930 


1.3684 


1.4649 


57 


1.3067 


1.5536 


1.3263 


1.5222 


1.3470 


1.4925 


1.3688 


1.4644 


56 


1.3070 


1.5530 


1.3267 


I.52I7 


1.3474 


1.492 1 


1-3692 


1 .4640 


55 


1.3073 


1.5525 


1.3270 


I.52I2 


1.3477 


1.4916 


1-3695 


1-4635 


54 


1.3076 


1.5520 


1.3274 


1.5207 


1-3481 


1.4911 


1.3699 


1.4631 


53 


1.3080 


1.5514 


1.3277 


1.5202 


1-3485 


1.4906 


1.3703 


1.4626 


52 


1.3083 


1.5509 


1.3280 


I.5I97 


1-3488 


1. 490 1 


1.3707 


1.4622 


51 


1.3086 


1.5503 


1.3284 


I.5I92 


1.3492 


1.4897 


1.3710 


1. 461 7 


50 


1.3089 


1.5498 


1.3287 


I.5I87 


1.3495 


1.4892 


1.3714 


I.46I3 


49 


1.3092 


1-5493 


1.3290 


I.5I82 


1.3499 


1.4887 


1.3718 


1.4608 


48 


1.3096 


1.5487 


1.3294 


I.5I77 


1.3502 


1.4882 


1.3722 


1.4604 


47 


1.3099 


1.5482 


1.3297 


I.5I7I 


1.3506 


1.4877 


1.3725 


1.4599 


46 


1.3102 


1.5477 


1.3301 


I.5I66 


1.3509 


1.4873 


1.3729 


1.459s 


45 


1.3105 


1.5471 


1.3304 


I.5I6I 


1.3513 


1.4868 


1.3733 


1.4590 


44 


1.3109 


1.5466 


1.3307 


I.5I56 


1.3517 


1.4863 


1.3737 


1.4586 


43 


1.3112 


1.5461 


1.3311 


I-5I5I 


1.3520 


1.4858 


1.3740 


1.4581 


42 


1.3115 


1.5456 


1-3314 


1. 5 146 


1.3524 


1.4854 


1.3744 


1.4577 


41 


1.3118 


1.5450 


1.3318 


I.5I4I 


1.3527 


1.4849 


1-3748 


1.4572 


40 


1.3121 


1-5445 


1.3321 


I.5I36 


1.3531 


1.4844 


1-3752 


1.4568 


39 


1.312s 


1.5440 


1.3324 


1-5131 


1.3534 


1.4839 


1.3756 


1.4563 


38 


1.3128 


1.5434 


1.3328 


1. 5126 


1.3538 


1.4835 


1.3759 


1.4559 


37 


1.3131 


1.5429 


1.3331 


I.5I2I 


1.3542 


1.4830 


1.3763 


1-4554 


36 


1.3134 


1.5424 


1.3335 


I.5II6 


1.3545 


1.4825 


1.3767 


1-4550 


35 


1.3138 


1.5419 


1.3338 


I.5III 


1.3549 


1. 482 1 


1.3771 


1-4545 


34 


1.3141 


1.5413 


1.3342 


1. 5 106 


1.3552 


1.4816 


1.3774 


1-4541 


33 


1.3144 


1.5408 


1-3345 


I.5IOI 


1.3556 


1.4811 


1.3778 


1-4536 


33 


1.3148 


1.5403 


1-3348 


1.5096 


1.3560 


1:4806 


1.3782 


1-4532 


31 


1.3151 


1.5398 


1.3352 


1.5092 


1-3563 


1.4802 


1-3786 


1.4527 


30 


1.3154 


1-5392 


1.3355 


1.5087 


1.3567 


1-4797 


1.3790 


1.4523 


29 


1.3157 


1-5387 


1.3359 


1.5082 


1-3571 


1.4792 


1.3794 


1.4518 


28 


1.3161 


1.5382 


1.3362 


1.5077 


1.3574 


1.4788 


1.3797 


1-4514 


27 


1.3164 


1-5377 


1.3366 


1.5072 


1.3578 


1.4783 


1. 3801 


1.4510 


26 


1.3167 


1-5371 


1-3369 


1.5067 


1.3581 


1.4778 


1.380s 


1=4505 


25 


1.3170 


1.5366 


1.3372 


1.5062 


1.3585 


1.4774 


1.3809 


1-4501 


24 


1.3174 


1.5361 


1.3376 


z-5057 


1.3589 


1.4769 


1.3813 


1.4496 


23 


1.3177 


1.5356 


1.3379 


1.5052 


1.3592 


1.4764 


1.3816 


1.4492 


22 


1.3180 


1-5351 


1.3383 


1.5047 


1.3596 


1.4760 


1.3820 


1.4487 


21 


1.3184 


1.5345 


1.3386 


1.5042 


1.3600 


1.4755 


1.3824 


1.4483 


20 


1.3187 


1.5340 


1.3390 


1.5037 


1-3603 


1.4750 


1.3828 


1.4479 


19 


1.3190 


1.5335 


1.3393 


1.5032 


1.3607 


1.4746 


1.3832 


1.4474 


18 


1.3193 


1.5330 


1.3397 


1.5027 


1.3611 


1-4741 


1.3836 


1.4470 


17 


1.3197 


1.5325 


1.3400 


1*5022 


1.3614 


1-4736 


1.3839 


1.4465 


16 


1.3200 


1.5319 


1.3404 


I.50I8 


1. 36 1 8 


1-4732 


1.3843 


1.4461 


IS 


1.3203 


1-5314 


1.3407 


I.50I3 


1.3622 


1-4727 


1.3847 


1.4457 


14 


1.3207 


1-5309 


1.3411 


1.5008 


1.362s 


1-4723 


1.3851 


1.4452 


13 


1.3210 


1-5304 


1.3414 


1.5003 


1.3629 


1.4718 


1.3855 


1.4448 


12 


1.3213 


1.5299 


1.3418 


1.4998 


1.3633 


1.4713 


1.3859 


1.4443 


II 


1.3217 


1.5294 


1.3421 


1.4993 


1.3636 


1.4709 


1.3863 


1.4439 


10 


1.3220 


1.5289 


1.3425 


1.4988 


1-3640 


1.4704 


1.3867 


1-4435 


9 


1-3223 


1.5283 


1.3428 


1.4983 


1.3644 


1.4699 


1.3870 


1-4430 


8 


1.3227 


1.5278 


1.3432 


1.4979 


1.3647 


1-4695 


1.3874 


1.4426 


7 


1.3230 


1.5273 


1.3435 


1.4974 


1.3651 


1.4690 


1.3878 


1.4422 


6 


1.3233 


1.5268 


1.3439 


1.4969 


1-3655 


1.4686 


1.3882 


1.4417 


5 


1.3237 


1.5263 


1.3442 


1.4964 


1-3658 


1. 4681 


1.3886 


1.4413 


4 


1.3240 


1.5258 


1.3446 


1-4959 


1.3662 


1.4676 


1.3890 


1.4408 


3 


1.3243 


1.5253 


1.3449 


1.4954 


1.3666 


1.4672 


1.3894 


1.4404 


2 


1.3247 


1.5248 


1.3453 


1.4949 


1-3669 


1.4667 


1.3898 


1.4400 


I 


1.3250 


1.5242 


1.3456 


1.4945 


1.3673 


1-4663 


1.3902 


1.4395 





Co-sec. 


Sec. 


Co-SEC. 


Sec 


Co-SEC. 


Sec 


Co-SEC. 


Sec 


t 


4 


9^ 


4 


SO 


4' 


r° 


4 


[)° 





NATURAL SECANTS AND CO-SECANTS 



879 





440 




I 


440 






440 , 


$ 


Sec. 


Co-SEC. 




' 


Sec. 


Co-SEC. 


f 


/ 


Sec 


Co-SEC. 





1.3902 


1.4395 


60 


21 


1.3984 


1.4305 


39 


41 


1.4065 


1. 422 1 


I 


1-3905 


1-4391 


59 


22 


1.3988 


1. 430 1 


38 


42 


1.4069 


I.4217 


2 


1.3909 


1.4387 


58 


23 


1.3992 


1.4297 


37 


43 


1-4073 


I.4212 


3 


1-3913 


1.4382 


57 


24 


1.3996 


1.4292 


36 


44 


14077 


1.4208 


4 


1-3917 


1.4378 


56 


25 


1.4000 


1.4288 


35 


45 


1. 408 1 


1.4204 


5 


1. 392 1 


1.4374 


55 


26 


1.4004 


1.4284 


34 


46 


1.4085 


1.4200 


6 


1.3925 


1.4370 


54 


27 


1 .4008 


1.4280 


33 


47 


1.4089 


I.4196 


7 


1-3929 


1.4365 


53 


28 


1. 4012 


1.4276 


32 


48 


1.4093 


I.4192 


8 


1-3933 


1. 4361 


52 


29 


1. 4016 


I.427I 


31 


49 


1.4097 


I.4188 


9 


1.3937 


1-4357 


51 


30 


1.4020 


1.4267 


30 


50 


1.4101 


I.4183 


10 


I 3941 


1.4352 


50 


31 


1.4024 


1.4263 


29 


51 


1.4105 


I.4179 


11 


1.3945 


1.4348 


49 


32 


1.4028 


1.4259 


28 


52 


1.4109 


1-4175 


12 


1.3949 


1.4344 


48 


33 


1.4032 


1.4254 


27 


53 


1.4113 


I.4171 


13 


1-3953 


1.4339 


47 


34 


1.4036 


1.4250 


26 


54 


1.4117 


I.4167 


14 


1.3957 


1.4335 


46 


35 


1 .4040 


1.4246 


25 


55 


1.4122 


I.4163 


IS 


1-3960 


1.4331 


45 


36 


1.4044 


1.4242 


24 


56 


1.4126 


I.4159 


16 


1.3964 


1.4327 


44 


37 


1.4048 


1.4238 


23 


57 


1.4130 


I -41 54 


17 


1.3968 


1.4322 


43 


38 


1.4052 


1.4233 


22 


58 


1.4134 


I -41 50 


18 


1.3972 


1.4318 


42 


39 


1.4056 


1.4229 


21 


59 


1.4138 


1. 4146 


19 


1.3976 


I -43 14 


41 


40 


1.4060 


1.4225 


20 


60 


1.4142 


1.4142 


20 


1.3980 


1. 43 10 


40 
















/ 


CO-SEC. 


Sec. 


/ 


/ 


Co-SEC. 


Sec. 


/ 


/ 


Co-sec. 


Sec. 




4, 


5° 






4 


5° 






45*=> 1 



19 

18 

17 
16 
15 
14 
13 



88o 


GENERAL TABLES AND FORMULAE 
















Table 74 










N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


lOO 


000000 


0434 


0868 


1301 


1734 


2166 


2598 


3029 


3461 


3891 


432 


lOl 


4321 


4751 


5181 


5609 


6038 


6466 


6894 


7321 


7748 


8174 


428 


102 


8600 


9026 


9451 


9876 


*0300 


*0724 


*ii47 


♦1570 


*i993 


*24i5 


424 


103 


012837 


3259 


3680 


4100 


4521 


4940 


5360 


5779 


6197 


6616 


420 


104 


7033 


7451 


7868 


8284 


8700 


9116 


9532 


9947 


*036i 


*0775 416 1 


XO5 


021 189 


1603 


2016 


2428 


2841 


3252 




4075 


4486 


4896 


412 


Z06 


5306 


5715 


6125 


6533 


6942 


7350 


7757 


8164 


8571 


8978 


408 


107 


9384 


9789 


*oi95 


*o6oo 


*ioo4 


*i4o8 


*I8I2 


*22l6 


*26i9 


*302I 


404 


108 


033424 


3826 


4227 


4628 


5029 


5430 


5830 


6230 


6629 


7028 


400 


109 


7426 


7825 


8223 


8620 


9017 


9414 


9811 


♦0207 


*0602 


*0998 


397 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




434 


43 


?7 


130 


174 


217 


260 


304 


347 


391 


434 




433 


43 


87 


130 


173 


217 


260 


303 


346 




433 




432 


43 


86 


130 


173 


216 


259 


302 


346 


389 


432 




431 


43 


86 


129 


172 


216 


259 


302 


345 


388 


431 




430 


43 


86 


129 


172 


215 


258 


301 


344 


387 


430 




'^ 


43 


86 


129 


172 


215 


257 


300 


343 


386 


429 




43 


86 


128 


171 


214 


257 


300 


342 


3^5 


428 




427 


43 


S5 


128 


171 


214 


256 




342 


384 


427 




426 


43 


§5 


128 


170 


213 


256 


298 


341 


383 


426 




425 


43 


?5 


128 


170 


213 


255 


298 


340 


3?3 


425 




424 


42 


l^ 


127 


170 


212 


254 


297 




382 


424 




423 


42 


§5 


127 


169 


212 


254 


296 


338 


3?^ 


423 




422 


42 


?4 






211 


253 


295 


338 


380 


422 




421 


42 


?4 


126 


168 


211 


253 


295 


337 


379 


421 




420 


42 


84 


126 


168 


210 


252 


294 


336 


378 


420 


CO 


419 


42 


?4 


126 


168 


210 


251 


293 


335 


377 


419 
418 


< 
O4 


418 


42 


?4 


125 


167 


209 


251 


293 


334 


376 


417 


42 


83 


125 


167 




250 


292 


334 


375 


417 


416 


42 


§3 


125 


166 


208 


250 


291 


333 


374 


416 




415 


42 


?3 


125 


166 


208 


249 


291 


332 


374 


415 


iJ 


414 


41 


?3 


124 


166 


207 


248 




331 


373 


414 


< 


413 


41 


83 


124 


165 


207 


248 


289 


330 


372 


413 


2 


412 


41 


82 


124 


165 


206 


247 


288 


330 


371 


412 





411 


41 


82 


123 


164 


206 


247 


288 




370 


411 


H 


410 


41 


82 


123 


164 


205 


246 


287 


328 


369 


410 


(^ 


1^ 


41 


82 


123 


164 


205 


245 


286 


327 


368 


^ 


2 



41 


82 


122 


163 


204 


245 


286 


326 


367 


407 


41 


81 


122 


163 


204 


244 


285 


326 


366 


407 


406 


41 


81 


122 


162 


203 


244 


284 


325 


365 


406 


Oi 


405 


41 


81 


122 


162 


203 


243 


284 


324 


365 


405 




404 


40 


81 


121 


162 


202 


242 


283 


323 


364 


404 




403 


40 


81 


121 


161 


202 


242 


282 


322 


363 


403 




402 


40 


80 


121 


161 


201 


241 


281 


322 


362 


402 




401 


40 


80 


120 


160 


201 


241 


281 


321 


361 


401 




400 


40 


80 


120 


160 


200 


240 


280 


320 


360 


400 




398 


40 


80 


120 


160 


200 


239 


279 


319 

3^§ 


359 


iP 




40 


80 


119 


159 


199 


239 


279 


358 




397 


40 


79 


119 




199 


238 


278 


318 


357 


397 




396 


40 


79 


119 


158 


198 


238 


277 


317 


356 


396 




395 


40 


79 


119 


158 


198 


237 


277 


316 


356 


395 




394 


39 


79 


118 


158 


197 


236 


276 


315 


355 


394 j 




393 


39 


79 


118 


157 


197 


236 


275 


314 


354 


393 




392 


39 


^l 


118 


157 


196 


235 


274 


314 


353 


392 




391 


39 


7? 


117 


156 


196 


235 


274 


313 


■352 


391 




390 


39 


78 


117 


156 


195 


234 


273 


312 


351 


390 




ill 


39 


78 


117 


156 


195 


233 


272 


3" 


350 


iiij 




39 


78 


116 


155 


194 


233 


272 


310 


349 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




♦From 


Allen' 


s "Fie 


Id anc 


I Offic 


e Tab] 


les." C 


'opyrig 


ht, 190 


3, 1914. by 1 


c 


. P. AUe 


Q. 





















LOGARITHMS OF NUMBERS 



88 1 



, N. 





Z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


ZIO 


041393 


1787 


2182 


2576 


2969 


3362 


3755 


4148 


4540 


^11 


393 


III 


5323 


5714 


6105 


6495 


6885 


7275 


7664 


8053 


8442 




112 


9218 


9606 


9993 


*o38o 


*o766 


*ii53 


*I538 


*i924 


♦2309 


*2694 


386 


"3 


053078 


3463 


3846 


4230 


4613 


5378 


5760 


6142 


6524 


383 


114 


6905 


7286 


7666 


8046 


8426 


8805 


9185 


9563 


9942 


*0320 


379 


"5 


060698 


1075 


1452 


1829 


2206 


2582 


2958 


3333 


3709 


4083 


376 


116 


4458 


4832 


5206 


5580 


5953 


6326 


6699 


7071 


7443 


7815 


373 


117 


8186 


8557 


8928 




9668 


*oo38 


*0407 


*0776 


*ii45 


*I5I4 


370 


118 


071882 


2250 


2617 


2985 


3352 


3718 


4085 


4451 


4816 


5182 
8819 


366 


119 


5547 


5912 


6276 


6640 


7004 


7368 


7731 


8094 


8457 


363 


lao 


079181 


9543 


9904 


*0266 


*o626 


*0987 


*I347 


*I707 


*2o67 


♦2426 


360 


121 


082785 


3144 


3503 


3861 


4219 


4576 


4934 


5291 


5647 


6004 


357 


122 


6360 


6716 


7071 


7426 


7781 


8136 


8490 


8845 


9198 


^9552 


355 


123 


9905 


*0258 


*o6ii 


*0963 


*i3i5 


*i667 


*20l8 


*237o 


*272I 


*307i 


352 


124 


093422 


3772 


4122 


4471 


4820 


5169 


5518 


5866 


6215 


6562 


349 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




387 


39 


77 


116 


155 


194 


232 


271 


310 


348 


387 


( 


386 


39 


77 


116 


154 


193 


232 


270 


309 


347 


386 


j 


385 




77 


116 


154 


193 


231 


270 


308 


347 


3?5 




384 


38 


77 


"5 


154 


192 


230 




307 


346 


384 




383 


38 


77 


115 


153 


192 


230 


268 


306 


345 


383 




382 


3? 


76 


115 


153 


191 


229 


267 


306 


344 


382 




3?' 


38 


76 


114 


152 


191 




267 


305 


343 


35' 




380 


38 


76 


114 


152 


190 


266 


304 


342 


380 




i^l 


3? 


76 


114 


152 


Ifg 


227 


265 


303 


341 


P 




3? 


76 


"3 


151 


227 


265 


302 


340 




377 


38 


75 


"3 


151 


189 


226 


264 


302 


339 


377 




376 


3f 


75 


113 


150 


188 


226 


263 


301 




376 


1 GO 
J ^ 

< 


375 


38 


75 


"3 


150 


188 


225 


263 


300 


338 


375 


374 


37 


75 


112 


150 


187 


224 


262 


299 


337 


374 


373 


37 


75 


112 


149 


187 


224 


261 


298 


336 


373 


372 


37 


74 


112 


149 


186 


223 


260 


298 


335 


372 


371 


37 


74 


III 


148 


186 


223 


260 




334 


371 




370 


37 


74 


III 


148 


185 


222 


259 


296 


333 


370 


( J 
< 

. z 



•-• 


1 


37 


74 


III 


148 


'?5 


221 


258 


295 


332 


369 


37 


74 


no 


147 


184 


221 


258 


294 


331 


368 




37 


73 


no 


147 


184 


220 


257 


294 


330 


367 


366 


37 


73 


no 


146 


183 


220 


256 


293 


329 


366 


H 


365 


37 


73 


no 


146 


183 


219 


256 


292 


329 


365 


J (^ 


364 


36 


73 


109 


146 


182 


218 


255 


291 


328 


364 


2 



363 


36 


73 


109 


145 


182 


218 


254 


290 


327 


363 


362 


36 


72 




145 


181 


217 


253 




326 


362 


361 


36 


72 


108 


144 


181 


217 


253 


289 


325 


361 


! 0* 


360 


36 


72 


108 


144 


180 


216 


252 


288 


324 


360 




359 


36 


72 


108 


144 


180 


215 


251 


287 


323 


358 




358 


36 


72 


107 


143 


179 


215 


251 


286 


322 




357 


36 


71 


107 


143 


179 


214 


250 


286 


321 


357 




356 


36 


71 


107 


142 


'78 


214 


249 


^55 


320 


356 




355 


36 


71 


107 


142 


178 


213 


249 


284 


320 


355 




354 


35 


71 


106 


142 


177 


212 


248 


283 


319 


354 




353 


35 


71 


106 


141 


177 


212 


247 


282 


318 


353 




352 


35 


70 


106 


141 


176 


211 


246 


282 


317 


352 




351 


35 


70 


105 


140 


176 


211 


246 


281 


316 


351 


350 


35 


70 


105 


140 


175 


210 


245 


280 


315 


350 




349 


35 


70 


105 


140 


175 


209 


244 


279 


314 


iti 




348 


35 


70 


104 


139 


174 


l^ 


244 


278 


313 




347 


35 


69 


104 


139 


174 


243 


278 


312 347 


j 


Diff. 


Z 


2 


3 


4 


5 


6 


7 


8 


9 Diff. 



























GENERAL TABLES AND FORMULA 



N. 
125 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


096910 


7257 


7604 


7951 


8298 


8644 


8990 


9335 


9681 


*0026 


346 


126 


10037 I 


0715 


1059 


1403 


1747 


2091 


2434 


2777 


3119 


3462 


343 


127 


3804 


4146 


4487 


4828 


5169 


5510 


5851 


6191 


6531 


6871 


341 


128 


7210 


7549 


7888 


8227 


8565 


8903 


9241 


9579 


9916 


*o253 


338 


129 


I10590 


0926 


1263 


1599 


1934 


2270 


2605 


2940 


3275 


3609 


335 


130 


"3943 


4277 


461 1 


4944 


5278 


561 1 


5943 


6276 


6608 


6940 1 333 1 


131 


7271 


7603 


7934 


8265 




8926 


9256 


9586 


9915 


*0245 


' 330 


132 


120574 


0903 


1231 


1560 


1888 


2216 


2544 


2871 


3198 


3525 


328 


133 


3852 


4178 


4504 


4830 


5156 


5481 




6131 


6456 


6781 


325 


134 


7105 


7429 


7753 


8076 


8399 


8722 


9045 


9368 


9690 


*00I2 


323 


135 


130334 


0655 


0977 


1298 


1619 


1939 


2260 


2580 


2900 


3219 


321 


136 


3539 


3858 


4177 


4496 


4814 


5133 


5451 


5769 


6086 


6403 


318. 


137 


6721 


7037 


7354 


7671 


7987 


8303 


8618 


8934 


9249 


9564 


316 


138 


9879 


*oi94 


*05o8 


*0822 


*ii36 


♦1450 " 


'1763 


*2076 


*2389 


*2702 


314 


139 


143015 


3327 


3639 


3951 


4263 


4574 


4885 


5196 


5507 


5818 


311 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




347 


35 


69 


104 


139 


174 


208 


243 


278 


312 


347 




346 


35 


69 


104 


'38 


173 


208 


242 


277 


311 


346 




345 


35 


69 


104 


138 


173 


207 


242 


276 


311 


345 




344 


34 


69 


103 


138 


172 


206 


241 


275 


310 


344 




343 


34 


69 


103 


137 


172 


206 


240 


274 


309 


343 




342 


34 


68 


103 


137 


171 


205 


239 


274 


308 


342 




341 


34 


68 


102 


136 


171 


205 


239 


273 


307 


341 




340 


34 


68 


102 


136 


170 


204 


238 


272 


306 


340 




339 


34 


68 


102 


136 


170 


203 


237 


271 


305 


339 




338 


34 


68 


lOI 


135 


169 


203 


237 


270 


304 


338 




337 


34 


57 


lOI 


135 




202 


236 


270 


303 


337 




336 


34 


67 


lOI 


134 


168 


202 


235 


269 


302 


336 


03 


335 


34 


67 


lOI 


134 


168 


201 


235 


268 


302 


335 


h 


334 


33 


57 


100 


134 


167 


200 


234 


267 


301 


334 


Oi 


333 


33 


67 


100 


133 


167 


200 


233 


266 


300 


333 


< 


332 


33 


66 


100 


133 


166 


199 


232 


266 


299 


332 


Ck 


331 


33 


66 


99 


132 


166 




232 


265 


298 


331 


< 


330 


33 


66 


99 


132 


165 


198 


231 


264 


297 


330 


329 


33 


66 


99 


132 


165 


197 


230 


263 


296 


329 


z 


328 


33 


66 


98 


131 


164 


197 


230 


262 


295 


328 





327 


33 


65 


98 


131 


164 


196 


229 


262 


294 


327 





326 


33 


65 


98 


130 


163 


196 


228 


261 


293 


326 


325 


33 


55 


98 


130 


163 


195 


228 


260 


293 


325 


324 


32 


65 


97 


130 


162 


194 


227 


259 


292 


324 


s 


323 


32 


55 


97 


129 


162 


194 


226 


^5? 


291 


323 





322 


32 


64 


97 




161 


193 


225 


258 


290 


322 


(^ 


321 


32 


64 


96 


128 


161 


193 


225 


257 


289 


321 


p^ 


320 


32 


64 


96 


128 


160 


192 


224 


256 


288 


320 




319 


32 


64 


96 


128 


160 


191 


223 


255 


287 


319 




318 


32 


64 


95 


127 


159 


191 


223 


254 


286 


318 




317 


32 


63 


95 


127 


159 


190 


222 


254 


285 


317 




316 


32 


63 


95 


126 


158 


190 


221 


253 


284 


316 




315 


32 


63 


95 


126 


158 


189 


221 


252 


284 


315 




3M 


31 


63 


94 


126 


157 


188 


220 


251 


283 


314 




313 


31 


63 


94 


125 


157 


188 


219 


250 


282 


313 




312 


31 


62 


94 


125 


156 


187 


218 


250 


281 


312 




3" 


31 


62 


93 


124 


156 


187 


218 


249 


280 


311 




310 


31 


62 


93 


124 


155 


186 


217 


248 


279 


310 




309 


31 


62 


93 


124 


155 


185 


216 


247 


278 


P 




308 


31 


62 


92 


123 


154 


185 


216 


246 


277 




307 


31 


61 


92 


123 


154 


184 


215 


246 


276 


307 




Diflf. 


I 


2 


3 


4 


5 


^ 


7 


8 


9 


Diff. 









LOGARITHMS OF NUMBERS 






%^^ 


■ N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


140 


I46I28 


6438 


6748 


7058 


7367 


7676 


7985 


8294 


8603 


8911 


309 


141 


9219 


9527 


9835 


*0I42 


*0449 


*0756 


*io63 


*I370 


*i676 


*I982 


307 


142 


152288 


2594 


2900 


3205 


3510 


3815 


4120 


4424 


4728 


5032 


305 


143 


5336 


5640 


5943 


6246 


6549 


6852 


7154 


7457 


^7759 


8061 


303 


144 


8362 


8664 


8965 


9266 


9567 


9868 


*oi68 


*o469 


*0769 


*io68 


301 


145 


I6I368 


1667 


1967 


2266 


2564 


2863 


3161 


3460 


3758 


4055 


299 


146 


4353 


4650 


4947 


5244 


5541 


5838 


6134 


6430 


6726 


7022 


297 


147 


7317 


7613 


7908 


8203 


8497 


8792 


9086 


9380 


9674 


9968 


295 


148 


170262 


0555 


0848 


II4I 


1434 


1726 


2019 


2311 


2603 


2895 


293 


149 


3186 


3478 


3769 


4060 


4351 


4641 


4932 


5222 


5512 


5802 


291 


150 


176091 


6381 


6670 


6959 


7248 


7536 


7825 


8113 


8401 


8689 


289 


151 


8977 


9264 


9552 


9839 


*OI26 


*04i3 


*o699 


*0986 


*I272 


*I558 


287 


152 


181844 


2129 


2415 


2700 


2985 


3270 


3555 


3839 


4123 


4407 


285 


1 153 


4691 


4975 


5259 


5542 


5825 


6108 


6391 


6674 


6956 


7239 


283 


- 154 


7521 


7803 




8366 


8647 


8928 


9209 


9490 


9771 


*oo5i 


281 




190332 


0612 


0892 


II7I 


1451 


1730 


2010 


2289 


2567 


2846 


279 


~ 156 


3125 


3403 


3681 


3959 


4237 


4514 


4792 


5069 


5346 


5623 


278 


1 157 


5900 


6176 


6453 


6729 


7005 


7281 


7556 


7832 


8107 


8382 


276 


J158 


8657 


8932 


9206 


9481 


9755 


*0029 


*o303 


*0577 


*o85o 


^l^i 


274 


i 159 


201397 


1670 


1943 


2216 


2488 


2761 


3033 


3305 


3577 


3848 


272 


1 ^• 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




306 


3X 


61 


92 


122 


153 


184 


214 


245 


275 


306 


305 


31 


61 


92 


122 


153 


'^3 


214 


244 


275 


305 




304 


30 


61 


91 


122 


152 


182 


213 


243 


274 


304 


4-:-' 


303 


30 


61 


91 


121. 


152 


182 


212 


242 


273 


303 


1- ': 


302 


30 


60 


91 


121 


151 


181 


211 


242 


272 


302 


!,'> , ■ 


301 


30 


60 


90 


120 


151 


181 


211 


241 


271 


301 


r 


300 


30 


60 


90 


120 


150 


180 


210 


240 


270 


300 




299 


30 


60 


90 


120 


150 


179 


209 


239 


269 


299 




298 


30 


60 


89 


119 


149 


179 




238 


267 


298 




297 


30 


59 


119 


149 


178 




238 


297 


xn 


296 


30 


59 


89 


118 


148 


178 


207 


237 


266 


296 


295 


30 


59 


^9 


118 


148 


177 


207 


236 


266 


295 


294 


29 


59 


88 


118 


147 


176 


206 


235 


265 


294 


■' < 


293 


29 




88 


117 


147 


176 


205 


234 


264 


293 


&• 


292 


29 


58 


88 


117 


146 


175 


204 


234 


263 


292 


' < 


291 


29 


58 


87 


116 


146 


175 


204 


233 


262 


291 


290 


29 


58 


87 


116 


145 


174 


203 


232 


261 


290 


! 2 


289 


29 


58 


87 


116 


145 


173 


202 


231 


260 


289 


• 2 


288 


29 


58 


86 


115 


144 


173 


202 


230 


259 


288 


H 


^^ 


29 


57 


86 


115 


144 


172 


201 


230 


258 


287 


( ^ 


286 


29 


57 


86 


114 


143 


172 


200 




257 


286 


' 


^^5 


29 


57 


86 


114 


143 


171 


200 


228 


257 


285 


PL. 


284 


28 


57 


85 


114 


142 


170 


199 


227 


256 


284 





283 


28 


57 


85 


113 


142 


170 


198 


226 


255 


283 




282 


28 


56 


85 


113 


141 


169 


197 


226 


254 


282 


281 


28 


56 


84 


112 


141 




197 


225 


253 


281 




280 


28 


56 


84 


112 


140 


168 


196 


224 


252 


280 




279 


28 


56 


84 


112 


140 


167 


195 


223 


251 


%l 




278 


28 


56 


83 


III 


139 


167 


195 


222 


250 




277 


28 


55 


83 


III 


139 


166 


194 


222 


249 


277 




276 


28 


55 


83 


no 


138 


166 


193 


221 


248 


276 




275 


28 


55 


?3 


no 


138 


165 


193 


220 


248 


275 




274 


27 


55 


82 


no 


137 


164 


192 


219 


247 


274 




273 


27 


55 


82 


109 


137 


164 


191 


218 


246 


273 


i . 


272 


27 


54 


82 




136 


163 


190 


218 


245 


272 


1 


271 


27 


54 


81 


108 


136 


163 


190 


217 


244 


271 




Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



























884 


GENERAL TABLES AND FORMULA 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


160 


204120 


4391 


4663 


4934 


5204 


5475 


5746 


6016 


6286 


6556 


271 


161 


6826 


7096 


7365 


7634 


7904 


8173 


8441 


8710 


8979 


9247 


269 


162 


9515 


9783 


*005i 


*03i9 


*0586 


*o853 


*II2I 


*I388 


*i654 


*I92I 


267 


163 


2I2I88 


2454 


2720 


2986 


3252 


3518 


3783 


4049 


4314 


4579 


266 


164 


4844 


5109 


5373 


5638 


5902 


6166 


6430 


6694 


6957 


7221 


264 


165 


217484 


7747 


8010 


8273 


8536 


8798 


9060 


9323 


9585 


9846 


262 


166 


220108 


0370 


0631 


0892 


1 153 


1414 


1675 


1936 


2196 


2456 


261 


167 


2716 


2976 


3236 


3496 


3755 


4015 


4274 


4533 


4792 


5051 


259 


168 


5309 


5568 


5826 


6084 


6342 


6600 


6858 


7115 


7372 


7630 


258 


169 


7887 


8144 


8400 


8657 


8913 


9170 


9426 


9682 


9938 


*oi93 


256 


170 


230449 


0704 


0960 


1215 


1470 


1724 


1979 


2234 


2488 


2742 


255 


171 


2996 


3250 


3504 


3757 


401 1 


4264 


4517 


4770 


5023 


5276 


253 


172 


5528 


5781 




6285 


6537 


6789 


7041 


7292 


7544 


7795 


252 


173 


8046 


8297 


8548 


8799 


9049 


9299 


9550 


9800 


*oo5o 


*03oo 


250 


174 


240549 


0799 


1048 


1297 


1546 


1795 


2044 


2293 


2541 


2790 


249 


175 


243038 


3286 


3534 


3782 


4030 


4277 


4525 


4772 


5019 


5266 


248 


176 


5513 


5759 




6252 


6499 


6745 


6991 


7237 


7482 


7728 


246 


177 


7973 


8219 


8464 


8709 


8954 


9198 


9443 


9687 


9932 


*oi76 


245 


178 


250420 


0664 


0908 


1151 


1395 


1638 


1881 


2125 


2368 


2610 


243 


179 


2853 


3096 


3338 


3580 


3822 


4064 


4306 




4790 


5031 


242 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




273 


27 


54 


82 


109 


136 


163 


190 


218 


245 


273 




271 


27 


54 


81 


108 


136 


163 




217 


244 


271 1 




270 


27 


54 


81 


108 


135 


162 


189 


216 


243 


270 




lU 


27 


54 


81 


108 


135 


161 


188 


215 


242 


269 ^ 




27 


54 


80 


107 


134 


161 


188 


214 


241 


268 




267 


27 


53 


80 


107 


134 


160 


187 


214 


240 


267 




266 


27 


53 


80 


106 


133 


160 


186 


213 


239 


266 




265 


27 


53 


80 


106 


133 


159 


186 


212 


239 


265 




264 


26 


53 


79 


106 


132 


158 


185 


211 


238 


264 


FQ 


263 


26 


53 


79 


105 


132 


158 


184 


210 


237 


263 


H 


262 


26 


52 


79 


105 


131 


157 


'S^ 


210 


236 


262 


Ui 


26z 


26 


52 


78 


104 


131 


157 


183 


209 


235 


261 


< 


260 


26 


52 


78 


104 


130 


156 


182 


208 


234 


260 


< 
Z 




25! 


26 


52 


78 


104 


130 


155 


181 


207 


233 


259 


26 


52 


77 


103 


129 


155 


181 


206 


232 


258 


257 


26 


51 


77 


103 


129 


154 


180 


206 


231 


257 


256 


26 


51 


77 


102 


128 


154 


179 


205 


230 


256 


255 


26 


51 


77 


102 


128 


153 


179 


204 


230 


255 


H 


254 


25 


51 


76 


102 


127 


152 


-178 


203 


229 


254 






253 


25 


51 


76 


lOI 


127 


152 


177 


202 


228 


253 


252 


25 


50 


76 


lOI 


126 


151 


176 


202 


227 


252 


251 


25 


50 


75 


100 


126 


151 


176 


201 


226 


251 


Oi 


250 


25 


50 


75 


100 


125 


150 


175 


200 


225 


250 


Oi 


?ji 


25 


50 


75 


100 


125 


149 


174 


I^ 


224 


249 




25 


50 


74 


99 


124 


149 


174 


223 


248 




247 


25 


49 


74 




124 


148 


173 


198 


222 


247 J 




246 


25 


49 


74 


123 


148 


172 


197 


221 


246 




245 


25 


49 


74 


98 


123 


147 


172 


196 


221 


245 




244 


24 


49 


73 


98 


122 


146 


171 


195 


220 


244 




243 


24 


49 


73 


97 


122 


146 


170 


194 


219 


243 




242 


24 


4§ 


73 


97 


121 


145 


169 


194 


218 


242 ; 




241 


24 


48 


72 


96 


121 


145 




193 


217 


241 




240 


24 


48 


72 


96 


120 


144 


168 


192 


216 


240 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



























LOGARITHMS OF NUMBERS 



88s 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


180 


255273 


5514 
7918 


5755 


5996 


6237 


6477 


6718 


6958 


7198 


7439 


241 


181 


7679 


8158 


8398 


8637 


8877 


9116 


9355 


9594 


9833 


239 


182 


260071 


0310 


0548 


0787 


1025 


1263 


1501 


1739 


1976 


2214 


238 


183 


2451 


2688 


2925 


3162 


3399 


3636 


3873 


4109 


4346 


4582 


237 


184 


4818 


5054 


5290 


5525 


5761 


5996 


6232 


6467 


6702 


6937 


235 


lli 


267172 


7406 




7875 


8110 


8344 


8578 


8812 


9046 


9279 


234 


9513 


9746 


9980 


*02I3 


*0446 


*o679 


♦09x2 


*ii44 


*i377 


*i6o9 


233 


187 


271842 


2074 


2306 


2538 


2770 


3001 


3233 


3464 


3696 


3927 


232 


188 


4158 




6921 


4850 


5081 


5311 


5542 


5772 


6002 


6232 


230 


189 


6462 


6692 


7I5I 


7380 


7609 


7838 


8067 


8296 


8525 


229 


190 


278754 


8982 


9211 


9439 


9667 


9895 


*OI23 


*035i 


*0578 


*o8o6 


228 


191 


281033 


1261 


1488 


1715 


1942 


2169 


2396 


2622 


2849 


3075 


227 


192 


3301 


3527 


3753 


3979 
6232 


4205 


4431 


4656 


4882 


5107 


5332 


226 


193 


5557 


5782 


6007 


6456 


6681 


6905 


7130 


7354 


7578 


225 


194 


7802 


8026 


8249 


8473 


8696 


8920 


9143 


9366 


9589 


9812 


223 


?^ 


290035 


0257 


0480 


0702 


0925 


1 147 


1369 


1591 


1813 


2034 
4246 


222 


2256 


2478 


2699 


2920 


3141 


3363 


3584 




4025 


221 


197 


4466 


4687 


4907 


5127 


5347 


5567 


5787 


6226 


6446 


220 


198 


6665 


6884 


7104 


7323 


7542 


7761 


7979 


81^ 


8416 


8635 


219 


199 


8853 


9071 


9289 


9507 


9725 


9943 


*oi6i 


*0378 


*0595 


*o8i3 


218 


200 


301030 


1247 


1464 


1681 


1898 


2114 


2331 


2547 


2764 


2980 


217 


201 


3196 


3412 


3628 


3844 


4059 


4275 


4491 


&t 


4921 


5136 


216 


202 


5351 


5566 


5781 


5996 


6211 


6425 


6639 


7068 


7282 


215 


203 


7496 


7710 


7924 


8137 


8351 


8564 


8778 


8991 


9204 


9417 


213 


204 


9630 


9843 


*oo56 


*0268 


*048i 


*o693 


♦0906 


*iii8 


*i330 


*i542 


212 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 

lit 




239 


24 


48 


72 


96 


-120 


143 


167 


191 


215 




238 


24 


48 


71 


95 


119 


143 


'g 


190 


214 




237 


24 


47 


71 


95 


119 


142 


166 


190 


213 


237 




236 


24 


47 


71 


94 


118 


142 


165 


189 


212 


236 




235 


24 


47 


71 


94 


118 


141 


165 


188 


212 


235 




234 


23 


47 


70 


94 


117 


140 


164 


'S 


211 


234 




233 


23 


47 


70 


93 


117 


140 


163 


186 


210 


233 


00 


232 


23 


46 


70 


93 


116 


139 


162 


186 


209 


232 


i 


231 


23 


46 


69 


92 


116 


139 


162 


185 


208 


231 


230 


23 


46 


69 


92 


115 


138 


161 


184 


207 


230 


04 


229 


23 


46 


69 


92 


"5 


137 


160 


183 


206 


229 


^ 


228 


23 


46 


68 


91 


114 


137 


160 


182 


205 


228 


< 


227 


23 


45 


68 


91 


114 


136 


159 


182 


204 


227 


z 


226 


23 


45 


68 


90 


113 


136 


158 


181 


203 


226 





225 


23 


45 


68 


90 


"3 


135 


158 


180 


203 


225 


O4 


224 


22 


45 


67 




112 


134 


157 


179 


202 


224 


223 


22 


45 


67 


112 


134 


156 


178 


201 


223 





222 


22 


44 


67 


89 


III 


133 


155 


178 


200 


222 


04 


221 


22 


44 


66 


88 


III 


133 


155 


177 


199 


221 




Oh 


220 


22 


44 


66 


88 


no 


132 


154 


176 


198 


220 


219 


22 


44 


66 


88 


no 


131 


153 


175 


197 


219 
218 




218 


22 


44 


f5 


f7 


109 


131 


153 


174 


196 




217 


22 


43 


65 


87 




130 


152 


174 


195 


217 




216 


22 


43 


55 


86 


108 


130 


151 


173 


194 


216 




215 


22 


43 


f5 


86 


108 




151 


172 


194 


215 




214 


21 


43 


64 


86 


107 


128 


150 


171 


193 


214 




213 


21 


43 


64 


85 


107 


128 


149 


170 


192 


213 




212 


21 


42 


64 


85 


106 


127 


148 


170 


191 


212 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



886 


GENERAL TABLES AND FORMULA 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


205 


31 1754 


1966 


2177 


2389 


2600 


2812 


3023 


3234 


3445 


3656 


211 


206 


3867 


4078 


4289 


4499 


4710 


4920 


5130 


5340 


5551 


5760 


210 


207 


5970 


6180 


6390 


6599 


6809 


7018 


7227 


7436 


7646 


7854 


209 


208 


8063 


8272 


8481 


8689 


8898 


9106 


9314 


9522 


9730 


9938 


208 


209 


320146 


0354 


0562 


0769 


0977 


1 184 


1391 


1598 


1805 


2012 


207 


210 


322219 


2426 


2633 


2839 


3046 


3252 


3458 


3665 


3871 


4077 


206 


211 


4282 


4488 


4694 


4899 


5105 


5310 


5516 


5721 


5926 


61 3 1 


205 


212 


6336 


6541 


6745 


6950 


7155 


7359 


7563 


7767 


7972 


8176 


204 


213 


8380 


8583 


8787 


8991 


9194 


9398 




9805 


*ooo8 


*02II 


203 


214 


330414 


0617 


0819 


1022 


1225 


1427 


1630 


1832 


2034 


2236 


202 


215 


332438 


2640 


2842 


3044 


3246 


3447 


3649 


3850 




4253 


202 


216 


4454 


4655 


4856 


5057 


5257 


5458 


5658 


5859 


6059 


6260 


201 


217 


6460 


6660 


6860 


7060 


7260 


7459 


7659 


7858 


8058 


8257 


200 


218 


8456 


8656 


8855 


9054 


9253 


9451 


9650 


9849 


*0047 


*0246 


199 


219 


340444 


0642 


0841 


1039 


1237 


1435 


1632 


1830 


2028 


2225 


198 


220 


342423 


2620 


2817 


3014 


3212 


3409 


3606 


3802 


3999 


4196 


197 


221 


4392 


4589 


4785 


4981 


5178 


5374 


5570 


5766 


5962 


6157 


196 


222 


6353 


6549 


6744 


6939 


7135 


7330 


7525 


7720 


7915 


8110 


195 


223 


8305 


8500 


8694 


8889 


9083 


9278 


9472 


9666 


9860 


*oo54 


194 


224 


350248 


0442 


0636 


0829 


1023 


1216 


1410 


1603 


1796 


1989 


193 


225 


352183 


2375 


2568 


2761 


2954 


3147 


3339 


3532 


3724 


3916 


193 


226 


4108 


4301 


4493 


4685 


4876 




5260 


5452 


5643 


5834 


192 


227 


6026 


6217 


6408 


6599 


6790 


6981 


7172 


7363 


7554 


7744 


191 


228 


7935 


8125 


8316 


8506 


8696 


8886 


9076 


9266 


9456 


9646 




229 


9835 


*0025 


*02I5 


♦0404 


*0593 


*0783 


*0972 


*ii6i 


*I350 


*i539 


189 


230 


361728 


I9I7 


2105 


2294 


2482 


2671 


2859 


3048 


3236 


3424 


188 


231 


3612 


3800 


3988 


4176 


4363 


4551 


4739 


4926 


5113 


5301 


188 


232 


5488 


5675 


5862 


6049 


6236 


6423 


6610 


6796 




7169 


^^ol 


233 


7356 


7542 


7729 


7915 


8101 


8287 


373 


8659 


8845 


9030 


186 


234 


9216 


9401 


9587 


9772 


9958 


*oi43 


*0328 


*05i3 


*o698 


*o883 


185 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




212 


21 


42 


64 


85 


106 


127 


148 


170 


191 


212 




211 


21 


42 


63 


84 


106 


127 


148 






211 




210 


21 


42 


63 


84 


105 


126 


147 


168 


189 


210 




209 


21 


42 


63 


84 


105 


125 


146 


167 


188 


209 


CO 


208 


21 


42 


62 


83 


104 


125 


146 


166 


187 


208 


207 


21 


41 


62 


83 


104 


124 


145 


166 


186 


207 


pti 


206 


21 


41 


62 


82 


103 


124 


144 


165 


185 


206 


< 


205 


21 


41 


62 


82 


103 


123 


144 


164 


'?5 


205 


Pa 


204 


20 


41 


61 


82 


102 


122 


143 


163 


184 


204 


J 


203 


20 


41 


61 


81 


102 


122 


142 


162 


183 


203 


<j 


202 


20 


40 


61 


81 


lOI 


121 


141 


162 


182 


202 


^ 


201 


20 


40 


60 


80 


lOI 


121 


141 


161 


181 


201 





200 


20 


40 


60 


80 


100 


120 


140 


160 


180 


200 


H 


199 


20 


40 


60 


80 


100 


119 


139 


159 


179 


199 


(^ 


198 


20 


40 


59 


79 


99 


119 


139 


158 


178 


198 





197 


20 


39 


59 


79 




118 


138 


158 


177 


197 


Pa 


ft, 


196 


20 


39 


59 


78 


98 


118 


137 


157 


176 


196 


195 


20 


39 


59 


7f 


98 


117 


137 


156 


176 


195 


194 


19 


39 


5§ 


78 


97 


116 


136 


155 


175 


194 




193 


19 


39 


5? 


77 


97 


116 


135 


154 


174 


193 




192 


19 


3? 


58 


77 


96 


115 


134 


154 


173 


192 




191 


19 


3? 


57 


76 


96 


115 


134 


153 


172 


191 




190 


19 


38 


57 


76 


95 


114 


133 


152 


171 


190 




'fi 


19 


38 


57 


76 


95 


113 


132 


151 


170 


\^ 




188 


19 


38 


56 


75 


94 


113 


132 


150 


169 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



887 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


235 


371068 


1253 


1437 


1622 


1806 


1991 


2175 


2360 


2544 


2728 


184 


236 


2912 


3280 


3464 


3647 


3831 


4015 


4198 


4382 


4565 


184 


237 


4748 


4932 


5115 


5298 


5481 


5664 


5846 


6029 


6212 


6394 


^?3 


238 


6577 


6759 


6942 


7124 


7306 


7488 


7670 


7852 


8034 


8216 


182 


239 


8398 


8580 


8761 


8943 


9124 


9306 


9487 


9668 


9849 


*oo30 


181 


240 


3802 I I 


0392 


0573 


0754 


0934 


1115 


1296 


1476 


1656 


1837 


181 


241 


2017 


2197 


2377 


2557 


2737 


2917 


3097 


3277 


3456 


3636 


180 


242 


3815 


3995 


4174 


4353 


4533 


4712 


4891 


5070 


5249 


5428 


179 


243 


5606 


5785 


5964 


6142 


6321 


6499 


6677 


6856 


lo^ 


7212 


^7? 


244 


7390 


7568 


7746 


7923 


8101 


8279 


8456 


8634 


88II 


8989 


178 


245 


389166 


9343 


9520 


9698 


9875 


*oo5i 


*0228 


*0405 


*0582 


*0759 


177 


246 


390935 


1112 


1288 


1464 


1641 


1817 


1993 


2169 


2345 


2521 


176 


247 


2697 


2873 


3048 


3224 


3400 


3575 


3751 


3926 


4101 


4277 


176 


248 


4452 


4627 


4802 


4977 


5152 


5326 


5501 


5676 


5850 


6025 


175 


249 


6199 


6374 


6548 


6722 




7071 


7245 


7419 


7592 


7766 


174 


250 


397940 


8114 


8287 


8461 


8634 


8808 


8981 


9154 


9328 


9501 


173 


251 


9674 


9847 


*0020 


*0I92 


=^0365 


*0538 


*07ii 


*o883 


*io56 


*I228 


173 


252 


401401 


1573 


1745 


I9I7 


2089 


2261 


2433 


2605 


2777 


2949 


172 


253 


3121 


3292 


3464 


3635 


3807 


3978 


4149 


4320 


4492 


4663 


171 


254 


4834 


5005 


5176 


5346 


5517 


5688 


5858 


6029 


6199 


6370 


171 


255 


406540 


6710 


6881 


7051 


7221 


7391 


7561 


7731 


7901 


8070 


170 


236 


8240 


8410 


8579 


8749 


8918 


9087 


9257 


9426 


9595 


9764 


169 


257 


9933 


*0I02 


*027I 


*o440 


*o6o9 


*0777 


*0946 


*iii4 


*I283 


'^1451 




258 


41 1620 


1788 


1956 


2124 


2293 


2461 


2629 


2796 


2964 


3132 


168 


259 


3300 


34^7 


3635 


3803 


3970 


4137 


4305 


4472 


4639 


4806 


167 


260 


414973 


5140 


5307 


5474 


5641 


5808 


5974 


6141 


6308 


6474 


167 


261 


6641 


6807 


6973 




7306 


7472 


7638 


7804 


7970 


8135 


166 


262 


8301 


8467 


8633 


8798 


8964 


9129 


9295 


9460 


9625 


9791 


165 


263 


9956 


*0I2I 


*0286 


*045i 


*o6i6 


*o78i 


*0945 


*IIIO 


*I275 


*i439 


165 


264 


421604 


1768 


1933 


2097 


2261 


2426 


2590 


2754 


2918 


3082 


164 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




^ll 


19 


37 


5^ 


75 


94 


112 


13T 


150 


168 


187 




186 


19 


37 


55 


74 


93 


112 


130 


149 


167 


186 




185 


19 


37 


56 


74 


93 


III 


130 


148 


167 


185 




184 


18 


37 


55 


74 


92 


no 


129 


147 


166 


184 




183 


18 


37 


55 


73 


92 


no 


128 


146 


165 


183 


09 


182 


18 


3$ 


55 


73 


91 


109 


127 


146 


164 


182 


H 


181 


18 


36 


54 


72 


91 




127 


145 


163 


i8i 


Oi 


180 


18 


36 


54 


72 


90 


108 


126 


144 


162 


180 


< 


179 


18 


3f 


54 


72 


90 


107 


125 


143 


161 


lit 




178 


18 


36 


53 


71 


89 


107 


125 


142 


160 


w) 


177 


18 


35 


53 


71 


89 


106 


124 


142 


159 


177 


< 


176 


18 


35 


53 


70 


88 


106 


123 


141 


158 


176 


Z 


175 


18 


35 


53 


70 


88 


105 


123 


140 


158 


175 





174 


17 


35 


52 




?7 


104 


122 


139 


157 


174 


H 


173 


17 


35 


52 


69 


S 


104 


121 


138 


156 


173 


(^ 


172 


17 


34 


52 


69 


86 


103 


120 


138 


155 


172 





171 


17 


34 


51 


68 


86 


103 


120 


137 


154 


171 





170 


17 


34 


51 


68 


85 


102 


119 


136 


153 


170 


'!i 


17 


34 


51 


68 


85 


lOI 


118 


135 


^52 


i6g 


Pk 


168 


17 


34 


50 


67 


^4 


lOI 


118 


134 


151 


168 




167 


17 


33 


50 




84 


100 


117 


134 


150 


167 




166 


17 


33 


50 


66 


83 


100 


116 


133 


149 


166 




165 


17 


33 


50 


66 


83 


99 


116 


132 


149 


165 




164 


16 


33 


49 


66 


82 


98 


115 


131 


148 


164 


Diff. 


Z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



888 



GENERAL TABLES AND FORMULA 



N. 





z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


265 


423246 


3410 


3574 


3737 


3901 


4065 


4228 


4392 


4555 


4718 


164 


266 


4882 


5045 


5208 


5371 


5534 


5697 


5860 


6023 


6186 


6349 


163 


267 


651 1 


6674 


6836 




7161 


7324 


7486 


7648 


7811 


7973 


162 


268 


8135 


8297 


8459 


8621 


8783 


8944 


9106 


9268 


9429 


^9591 


162 


269 


9752 


9914 


*oo75 


*0236 


*0398 


*0559 


*0720 


*o88i 


*I042 


*I203 


i6i 


270 


431364 


1525 


1685 


1846 


2007 


2167 


2328 


2488 


2649 


2809 


161 


271 


2969 


3130 


3290 


3450 


3610 


3770 


3930 


4090 


4249 


4409 


160 


272 


tin 


4729 


4888 


5048 


5207 


5367 


5526 


5685 


5844 


6004 


159 


273 


6322 


6481 


6640 


6799 


6957 


7II6 


7275 


7433 


7592 


159 


274 


7751 


7909 


8067 


8226 


8384 


8542 


8701 


8859 


9017 


9175 


158 


275 


439333 


9491 


9648 


9806 


9964 


*0I22 


*0279 


*0437 


*0594 


*0752 


158 


276 


440909 


1066 


1224 


1381 


1538 


1695 


1852 




2166 


2323 


157 


277 


2480 


2637 


2793 


2950 


3106 


3263 


3419 


3576 


3732 




157 


278 


4045 


4201 


4357 


4513 


4669 


4825 


4981 


5137 


5293 


5449 


156 


279 


5604 


5760 


5915 


6071 


6226 


6382 


6537 


6692 


6848 


7003 


155 


280 


447158 


7313 


7468 


7623 


7778 


7933 


8088 


8242 


8397 


8552 


155 


281 


8706 


8861 


9015 


9170 


9324 


9478 


9633 


9787 


9941 


*0095 


154 


282 


450249 


0403 


0557 


071 1 


0865 


1018 


1 172 


1326 


1479 


1633 


154 


283 


1786 


1940 


2093 


2247 


2400 


2553 


2706 


2859 


3012 


3165 


153 


284 


3318 


3471 


3624 


3777 


3930 


4082 


4235 


4387 


4540 


4692 


153 


285 


454845 


4997 


5150 


5302 


5454 


5606 


5758 


5910 


6062 


6214 


152 


286 


6366 


6518 


6670 


6821 


6973 


7125 




7428 


7579 


7731 


152 


287 


7882 


8033 


8184 


8336 


8487 


8638 


8789 


8940 


9091 


9242 


151 


288 


9392 


9543 


9694 


9845 


9995 


*oi46 


*0296 


*0447 


*o597 


*0748 


151 


289 


460898 


1048 


1 198 


1348 


1499 


1649 


1799 


1948 


2098 


2248 


150 


290 


462398 


2548 


2697 


2847 


2997 


3146 


3296 


3445 


3594 


3744 


150 


291 


3893 


4042 


4191 


4340 


4490 


4639 


4788 


4936 


5085 


5234 
6719 


149 


292 


5383 


5532 


5680 


5829 


5977 


6126 


6274 
7756 


6423 


6571 


149 


393 


6868 


7016 


7164 


7312 
8790 


7460 


7608 


7904 


8052 


8200 


148 


294 


8347 


8495 


8643 


8938 


9085 


9233 


9380 


9527 


9675 


148 


295 


469822 


9969 


*oii6 


*0263 


*04io 


*0557 


*0704 


*o85i 


*0998 


*ii45 


147 


296 


471292 


1438 


1585 


1732 


1878 


2025 


2171 


2318 


2464 


2610 


146 


297 


2756 


2903 


3049 


3195 


3341 


3487 


3633 


3779 


3925 


4071 


146 


298 


4216 


4362 


4508 


4653 


4799 


4944 


5090 
6542 






5526 


146 


299 


5671 


5816 


5962 


6107 


6252 


6397 


6687 


6832 


6976 


145 


N. 


Diff. 


Z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




164 


16 


33 


49 


66 


82 


98 


"5 


131 


148 


164 




163 


16 


33 


49 


65 


82 


98 


114 


130 


147 


163 




162 


16 


32 


49 


65 


81 


97 


113 


130 


146 


162 




161 


16 


32 


48 


64 


81 


97 


113 


129 


145 


161 


CO 

H 


160 


16 


32 


48 


64 


80 


96 


112 


128 


144 


160 


158 


16 


32 


48 


64 


80 


95 


III 


127 


143 


JP 


< 


16 


32 


47 


f3 


79 


95 


III 


126 


142 


(U 


157 


16 


31 


47 


63 


79 


94 


no 


126 


141 


157 


^3 


156 


16 


31 


47 


62 


78 


94 


109 


125 


140 


156 


< 


155 


16 


31 


^I 


62 


78 


93 


109 


124 


140 


155 


z 


154 


15 


31 


46 


62 


77 


92 


108 


123 


139 


154 





153 


15 


31 


46 


61 


77 


92 


107 


122 


138 


153 




152 


15 


30 


46 


61 


76 


91 


106 


122 


137 


152 


151 


15 


30 


45 


60 


76 


91 


106 


121 


136 


151 


9 


150 


15 


30 


45 


60 


75 


90 


105 


120 


135 


150 


i 


Jii 


15 


30 


45 


60 


75 


89 


104 


119 


134 


149 


15 


30 


44 


59 


74 




104 


118 


133 


148 


147 


15 


29 


44 




74 


80 


103 


118 


132 


147 




146 


15 


29 


44 


58 


73 


88 


102 


117 


131 


146 




145 


15 


29 


44 


5? 


73 


ll 


102 


116 


131 


145 




144 


14 


29 


43 


58 


72 


86 


101 


115 


130 


144 




143 


14 


29 


43 


57 


72 


86 


100 


114 


129 


143 




Diflf. 


I 


2 


1 3 


1 "^ 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



889 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


300 


477I2I 


7266 


7411 


7555 


7700 


7844 


7989 


8133 


8278 


8422 


145 


301 


8566 


8711 


8855 


8999 


9143 


9287 


^i¥ 


9575 


9719 


9863 


144 


302 


480007 


0151 


0294 


0438 


0582 


0725 


0869 


1012 


1156 


1299 


144 


303 


1443 


1586 


1729 


1872 


2016 


2159 


2302 


2445 


2588 


2731 


143 


304 


2874 


3016 


3159 


3302 


3445 


3587 


3730 


3872 


4015 


4157 


143 




484300 


4442 


4585 


4727 


4869 


501 1 


5153 


5295 


5437 


5579 


142 


306 


5721 


5863 


6005 


6147 


6289 


6430 


6572 


6714 




6997 


142 


IS 


7138 


7280 


7421 


7563 


7704 


7845 


7986 


8127 


8269 


8410 


141 


8551 


8692 


8833 


8974 


9114 


9255 


9396 


9537 


9677 


9818 


141 


309 


9958 


*oo99 


*o239 


*038o 


*0520 


*o66i 


*o8oi 


*094i 


*io8i 


*I222 


140 


310 


491362 


1502 


1642 


1782 


1922 


2062 


2201 


2341 


2481 


2621 


140 


3H 


2760 


2900 


3040 


3179 


3319 


3458 


3597 


3737 


3876 


4015 


139 


313 


4155 


4294 


4433 


4572 


47II 


4850 




5128 


5267 


5406 


139 


313 




5683 


5822 


5960 


6099 


6238 


6376 


6515 


6653 


6791 




314 


6930 


7068 


7206 


7344 


7483 


7621 


7759 


7897 


8035 


8173 


138 


315 


4983II 


8448 


8586 


8724 


8862 


8999 


9137 


9275 


9412 


^9550 


138 


316 


9687 


9824 


9962 


*oo99 


*0236 


*0374 


*05ii 


*o648 


*o785 


*0922 


137 


317 


501059 


1196 


1333 


1470 


1607 


1744 


1880 


2017 


2154 


2291 


137 


318 


2427 


2564 


2700 


2837 


2973 


3109 


3246 


3382 


3518 


3655 


'^i 


319 


3791 


3927 


4063 


4199 


4335 


4471 


4607 


4743 


4878 


5014 


136 


320 


505150 


5286 


5421 


5557 


5693 


5828 


5964 


6099 


6234 


6370 


136 


321 


6505 


6640 


6776 


6911 


7046 


7181 


7316 


7451 


7586 


7721 


135 


322 


7856 


7991 


8126 


8260 


8395 


8530 


8664 


8799 


8934 


9068 


135 


323 


9203 


9337 


9471 


9606 


9740 


9874 


*ooo9 


*oi43 


*0277 


*04ii 


134 


324 


510545 


0679 


0813 


0947 


1081 


1215 


1349 


1482 


1616 


1750 


134 


325 


5II883 


2017 


2151 


2284 


2418 


2551 




2818 


2951 


3084 


133 


326 


3218 


3351 


3484 


3617 


3750 


3883 


4016 


4149 


4282 


4415 


133 


327 


4548 


4681 


4813 


4946 


5079 


5211 


5344 


5476 


5609 


5741 


133 


328 


7196 


6006 


6139 


6271 


6403 


6535 


6668 


6800 


6932 


7064 


132 


329 


7328 


7460 


7592 


7724 


7855 


7987 


8119 


8251 


8382 


132 


330 


5I85I4 


8646 


8777 


8909 


9040 


9171 


9303 


9434 


9566 


9697 


131 


331 


9828 


9959 


*oo9o 


*022I 


*0353 


*o484 


*o6i5 


*0745 


*o876 


*ioo7 


131 


332 


521 138 


1269 


1400 


1530 


1661 


1792 


1922 


2053 


2183 


3616 


131 


333 


2444 
3746 


2575 


2705 


2835 


2966 


3096 


3226 


3356 


3486 


130 


334 


3876 


4006 


4136 


4266 


4396 


4526 


4656 




4915 
6210 


130 


335 


525045 


5174 


5304 


5434 


5563 


5693 


5822 


5951 


6081 


129 


336 


6339 


6469 


6598 


5727 


6856 


6985 


7114 


7243 


7372 


7501 


129 


337 


7630 


7759 


7888 


8016 


8145 


8274 


8402 


8531 


8660 




129 


338 


8917 


9045 


9174 


9302 


9430 


9559 


9687 


9815 


9943 


*0072 


128 


339 


530200 


0328 


0456 


0584 


0712 


0840 


0968 


1096 


1223 


I35I 


128 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




142 


14 


28 


43 


57 


71 


?5 


99 


114 


. 128 


142 


CO 


141 


14 


28 


42 


5$ 


71 


85 




113 


127 


141 


§ 


140 


14 


28 


42 


56 


70 


84 


98 


112 


126 


140 


139 


14 


28 


42 


56 


70 


83 


97 


III 


125 


138 


0* 


138 


14 


28 


41 


55 


69 


?3 


97 


no 


124 


< 
Z 




137 


14 


27 


41 


55 


69 


82 


96 


no 


123 


137 


136 


14 


27 


41 


54 


68 


82 


95 


109 


122 


136 


135 


14 


27 


41 


54 


68 


81 


95 


108 


122 


135 


134 


13 


27 


40 


54 


67 


80 


94 


107 


•121 


134 


r* 


133 


13 


27 


40 


53 


67 


80 


93 


106 


120 


133 


H 

2 


132 


13 


26 


40 


53 


66 


79 


92 


106 


119 


132 


131 


13 


26 


39 


52 


66 


79 


92 


105 


118 


131 


130 


13 


26 


39 


52 


65 


78 


91 


104 


117 


130 





Hi 


13 


26 


39 


52 


f5 


77 


90 


103 


116 


!,1 


Oi 


13 


26 


38 


51 


64 


77 


90 


102 


115 


Pk 


127 


13 


25 


38 


51 


64 


76 


89 


102 


114 


127 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



890 



GENERAL TABLES AND FORMULA 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


- ■ 1 
Diff. 


340 


531479 


^^7 


1734 


1862 


1990 


2117 


2245 


2372 


2500 


2627 


128 


341 


2754 


2882 


3009 


3136 


3264 


3391 


3518 


3645 


3772 


3899 


127 


342 


4026 


4153 


4280 


4407 


4534 


4661 


4787 


4914 


5041 




127 


343 


5294 


5421 


5547 


5674 


5800 


5927 


6053 


6i8:> 


6306 


62 


126 


344 


6558 


6685 


681 1 


6937 


7063 


7189 


7315 


7441 


7567 


7693 


126 


345 


537819 


7945 


8071 


8197 


8322 


8448 


8574 




8825 


8951 


126 


346 


9076 


9202 


9327 


9452 


9578 


9703 


9829 


9904 


*oo79 


*0204 


125 


347 


540329 


0455 


0580 


0705 


0830 


0955 


1080 


1205 


1330 


1454 


125 


348 


1579 


1704 


1829 


1953 


2078 


2203 


2327 


2452 


2576 


2701 


125 


349 


2825 


2950 


3074 


3199 


3323 


3447 


3571 


3696 


3820 


3944 


124 


350 


544068 


4192 


4316 


4440 


4564 


4688 


4812 


4936 


5060 


5183 


124 


351 


5307 


5431 


5555 


5678 


5802 


5925 


6049 


6172 


6296 


6419 


124 


352 


6543 


6666 


6789 


6913 


7036 


7159 


7282 
8512 


7405 


7529 


7652 


123 


353 


7775 


7898 


8021 


8144 


8267 


8389 


8635 


8758 


8881 


123 


354 


9003 


9126 


9249 


9371 


9494 


9616 


9739 


9861 


9984 


*oio6 


123 


355 


550228 


0351 


0473 


0595 


0717 


0840 


0962 


1084 


1206 


1328 


122 


356 


1450 


1572 


1694 


1816 


1938 


2060 


2181 


2303 


2425 


2547 


122 


357 


2668 


2790 


291 1 


3033 


3155 


3276 


3398 


3519 


3640 


3762 


121 


358 


3883 


4004 


4126 


4247 


4368 


4489 


4610 


4731 


4852 


4973 


121 


359 


5094 


5215 


5336 


5457 


5578 


5699 


5820 


5940 


6061 


6182 


121 


360 


556303 


6423 


6544 


6664 


6785 


6905 


7026 


7146 


7267 


7387 


120 


361 


7507 


7627 


7748 


7868 


7988 


8108 


8228 


8349 


8469 


8589 


120 


362 


8709 


8829 


8948 


9068 


9188 


9308 


9428 


9548 


9667 


9787 


120 


363 


9907 


*0026 


*oi46 


♦0265 


*o385 


*o504 


*o624 


*0743 
1936 


*o863 


♦0982 


119 


364 


561 lOI 


I22I 


1340 


1459 


1578 


1698 


1817 


2055 


2174 


119 


365 


562293 


2412 


2531 


2650 


2769 


2887 


3006 


3125 


3244 


3362 


119 


366 


3481 


3600 


3718 


3837 


3955 


4074 


4192 


4311 


4429 


4548 


119 


367 


4666 


4784 


4903 


5021 


5139 


5257 


5376 


5494 


5612 


5730 


118 


368 


5848 


5966 


6084 


6202 


6320 


6437 


6555 


6673 


6791 


6909 


iiS 


369 


7026 


7144 


7262 


7379 


7497 


7614 


7732 


7849 


7967 


8084 


118 


370 


568202 


8319 


8436 


8554 


8671 


8788 


8905 


9023 


9140 


9257 


117 


371 


9374 


9491 


9608 


9725 


9842 


9959 


♦0076 


*oi93 


*0309 


*0426 


117 


372 


570543 


0660 


0776 




lOIO 


1126 


1243 


1359 


1476 


1592 


117 


373 


1709 


1825 


1942 


2058 


2174 


2291 


2407 


2523 


2639 


2755 


116 


374 


2872 


2988 


3104 


3220 


3336 


3452 


3568 


3684 


3800 


3915 


116 


375 


574031 


4147 


4263 


4379 


4494 


4610 


4726 


4841 


4957 


5072 


116 


376 


5188 


5303 


5419 


5534 


5650 


5765 


5880 


5996 


6111 


6226 


115 


377 


6341 


6457 


6572 


6687 




6917 


7032 


7147 
8295 


7262 


7377 


115 


378 


7492 


7607 


7722 


7836 


7951 


8066 


8i8i 


8410 


8525 


115 


379 


8639 


8754 




8983 


9097 


9212 


9326 


9441 


9555 


9669 


114 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




128 


13 


26 


38 


51 


64 


77 


90 


102 


"5 


128 




127 


13 


25 


38 


51 


64 


76 


89 


102 


114 


127 


e 


126 


13 


25 


38 


50 


63 


76 


88 


lOI 


113 


126 


125 


13 


25 


38 


50 


53 


75 


88 


100 


113 


125 


< 


124 


12 


25 


37 


50 


62 


74 


?J 


99 


112 


124 


2 


123 


12 


25 


37 


49 


62 


74 


86 


98 


III 


123 




?22 


12 


24 


37 


49 


61 


73 


?5 


98 


no 


122 


p^ 


121 


12 


24 


36 


48 


61 


73 


85 


97 


109 


121 


2 


120 


12 


24 


36 


48 


60 


72 


84 


96 


108 


120 


Ah 


iig 


12 


24 


36 


48 


60 


71 


?3 


95 


107 


III 




118 


12 


24 


35 


47 


59 


71 


^3 


94 


106 




117 


12 


23 


35 


47 


59 


70 


82 


94 


105 


117 




116 


12 


23 


35 


46 


58 


70 


81 


93 


104 


116 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 









LOGARITHMS OF NUMBERS 




891 


N. 


G 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


380 


579784 


9898 


*OOI2 


*OI26 


*024I 


*0355 


*0469 


*0583 


*o697 


*o8ii 


114 


381 


580925 


. 1039 


1 153 


1267 


I38I 


1495 


1608 


1722 


1836 


1950 


114 


382 


2063 


2177 


2291 


2404 


2518 


2631 


2745 


2858 


2972 


3085 


114 


383 


3199 


3312 


3426 


3539 


3652 


3765 


3879 


3992 


4105 


4218 


113 


384 


4331 


4444 


4557 


4670 


4783 


4896 


5009 


5122 


5235 


5348 


113 


385 


585461 


5574 


5686 


5799 


5912 


6024 


6137 


6250 


6362 


6475 


113 


386 


6587 


6700 


68 12 


6925 


7037 


7149 


7262 


7374 


7486 


7599 


112 


387 


771 1 


7823 


7935 


8047 


8160 


8272 


8384 




8608 


8720 


112 


388 


8832 


8944 


9056 


9167 


9279 


9391 


9503 


9615 


9726 


9838 


112 


389 


9950 


*oo6i 


*oi73 


*o284 


*0396 


*0507 


*o6i9 


*0730 


*o842 


*0953 


112 


390 


591065 


1 176 


1287 


1399 


1510 


1621 


1732 


1843 


1955 


2066 


III 


391 


2177 


2288 


2399 


2510 


2621 


2732 


2843 


2954 




3175 


III 


392 


3286 


3397 


3508 


3618 


3729 


3840 


3950 


4061 


4x71 


4282 


III 


393 


4393 


4503 


4614 


4724 


4834 


4945 


5055 


5165 


5276 


5386 


IIO 


394 


5496 


5606 


5717 


5827 


5937 


6047 


6157 


6267 


6377 


6487 


IIO 


395 


596597 


6707 


6817 


6927 


7037 


7146 


7256 


7366 


7476 


7586 


IIO 


396 




7805 


7914 


8024 


8134 


8243 


8353 


8462 


8572 


8681 


IIO 




8791 


8900 


9009 


9119 


9228 


9337 


9446 


.9556 


9665 


9774 


109 


398 


9883 


9992 


*OIOI 


*02I0 


*03i9 


*0428 


*o537 


*o646 


*0755 


*o864 


109 


399 


600973 


1082 


1191 


1299 


1408 


1517 


1625 


1734 


1843 


1951 


109 


400 


602060 


2169 


2277 


2386 


2494 


2603 


2711 


2819 


2928 


3036 


108 


401 


3144 


3253 


3361 


3469 


3577 


3686 


3794 


3902 


4010 


4118 


108 


402 


4226 


4334 


4442 


4550 


4658 


4766 


4874 


4982 


5089 


5197 


108 


' 403 


5305 


5413 


5521 


5628 


5736 


5844 


5951 


6059 


6166 


6274 


108 


404 


6381 


6489 




6704 


6811 


6919 


7026 


7133 


7241 


7348 


107 


405 


607455 


7562 


7669 


7777 


7884 


7991 


8098 


8205 


8312 


8419 


107 


406 


8526 


8633 


8740 


8847 


8954 


9061 


9167 


9274 


9381 


9488 


107 


407 


9594 


9701 


9808 


9914 


*002I 


*OI28 


*o234 


*034i 


*0447 


*0554 


107 


408 


610660 


0767 


0873 


0979 


1086 


1192 


1298 


1405 


15H 


1617 


106 


1 409 


1723 


1829 


1936 


2042 


2148 


2254 


2360 


2466 


2572 


2678 


106 


; 410 


612784 


2890 


2996 


3102 


3207 


3313 


3419 


3525 


3630 


3736 


106 


411 


3842 


3947 


4053 


4159 


4264 


4370 


4475 


4581 


4686 


4792 


106 


412 


4897 


5003 


5108 


5213 


5319 


5424 


5529 


5634 


5740 


5845 


105 


413 


5950 


6055 


6160 


6265 


6370 


6476 


6581 


6686 


6790 


6895 


105 


414 


7000 


7105 


7210 


7315 


7420 


7525 


7629 


7734 


7839 


7943 


105. 


415 


618048 


8153 


8257 


8362 


8466 


8571 


8676 


8780 


8884 


8989 


105 


416 


9093 


9198 


9302 


9406 


95II 


9615 


9719 


9824 


9928 


*0032 


104 


417 


620136 


0240 


0344 


0448 


0552 


0656 


0760 


0864 


0968 


1072 


104 


418 


1 176 


1280 


1384 


1488 


1592 


1695 


1799 


1903 


2007 


2110 


104 


419 


2214 


2318 


2421 


2525 


2628 


2732 


2835 


2939 


3042 


3146 


104 


1 N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


1 


115 


12 


23 


35 


46 


58 


69 


81 


92 


104 


"5 




114 


II 


23 


34 


46 


57 


68 


80 


91 


103 


114 


CO 


"3 


II 


23 


34 


45 


57 


68 


79 


90 


102 


"3 


: < 


112 


II 


22 


34 


45 


56 


67 


78 




lOI 


112 


III 


II 


22 


33 


44 


56 


67 


78 


89 


100 


III 


no 


II 


22 


33 


44 


55 


66 


77 


88 


99 


no 


'1 




'x^i 


II 


22 


33 


44 


55 


65 


76 


§7 


98 


U 


II 


22 


32 


43 


54 


65 


76 


86 


97 


107 


II 


21 


32 


43 


54 


64 


75 


86 


96 


107 


106 


II 


21 


32 


42 


53 


64 


74 


?5 


95 


106 


' 


105 


II 


21 


32 


42 


53 


63 


74 


84 


95 


105 




104 


10 


21 


31 


42 


52 


62 


73 


!3 


94 


104 




103 


ID 


21 


31 


41 


52 


62 


72 


82 


93 


103 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



























89^ 


} 


GENERAL TABLES AND FORMULA 






N. 





z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


4ao 


623249 


3353 


3456 


3559 


3663 


3766 


3869 


3973 


4076 


4179 


103 


421 


4282 


4385 


4488 


4591 


4695 


4798 


4901 


5004 


5107 


5210 


103 


422 


5312 


5415 


5518 


5621 


5724 


5827 


5929 


6032 


6135 


6238 


103 


423 


6340 


6443 


6546 


6648 


6751 


6853 




7058 


7161 


7263 


103 


424 


7366 


7468 


7571 


7673 


7775 


7878 


7980 


8082 


8185 


8287 


102 


425 


628389 


8491 


8593 


8695 


8797 


8900 


9002 


9104 


9206 


9308 


102 


426 


9410 


9512 


9613 


9715 


9817 


9919 


*oo2r 


*OI23 


*0224 


♦0326 


102 


427 


630428 


0530 


0631 


0733 


0835 


0936 


1038 


II39 


I24I 


1342 


102 


428 


1444 


1545 


1647 


1748 


1849 


1951 


2052 


2153 


2255 


2356 


lOI 


429 


2457 


2559 


2660 


2761 


2862 


2963 


3064 


3165 


3266 


3367 


lOI 


430 


633468 


3569 


3670 


3771 


3872 


3973 


4074 


4175 


4276 


4376 


lOI 


431 


4477 


4578 


4679 


4779 


4880 


4981 




5182 




5383 


10 1 


432 






5685 


5785 


5886 




6087 


6187 


6287 


6388 


100 


433 


6488 


6588 


6688 


6789 


6889 


6989 


7089 


7189 


7290 


7390 
8389 


100 


434 


7490 


7590 


7690 


7790 


7890 


7990 


8090 


8190 


8290 


100 


435 


638489 


8589 


8689 


8789 


8888 


8988 


9088 


9188 


9287 


9387 


100 


436 


9486 


9586 


9686 


9785 


9885 


9984 


*oo84 


*oi83 


♦0283 


♦0382 


99 


437 


640481 


0581 


0680 


0779 


0879 


0978 


1077 


1177 


1276 


1375 


99 


438 


1474 


1573 


1672 


1771 


1871 


1970 


2069 


2168 


2267 


2366 


99 


439 


2465 


2563 


2662 


2761 


2860 


2959 


3058 


3156 


3255 


3354 


99 


440 


643453 


3551 


3650 


3749 


3847 


3946 


4044 


4143 


4242 


4340 


98 


441 


4439 


4537 


4636 


4734 


4832 


4931 


5029 


5127 


5226 


5324 


98 


442 


5422 


5521 


5619 


5717 


5815 


5913 


601 1 


6110 


6208 


6306 


98 


443 


6404 


6502 


6600 


6698 


6796 


6894 


6992 


7089 


7187 
8165 


8262 


98 


444 


7383 


7481 


7579 


7676 


7774 


7872 




8067 


98 


445 


648360 


8458 


8555 


8653 


8750 


8848 


8945 


9043 


9140 


9237 


97 


446 


9335 


9432 


9530 


9627 


9724 


9821 


9919 


*ooi6 


*oii3 


*02I0 


97 


447 


650308 


0405 


0502 


0599 




0793 


0890 


0987 


1084 


II8I 


97 


448 


1278 


1375 


1472 


1569 


1666 


1762 


'?5? 


1956 


2053 


2150 


97 


449 


2246 


2343 


2440 


2536 


2633 


2730 


2826 


2923 


3019 


31 16 


97 


450 


653213 


3309 


3405 


3502 


3598 


3695 


3791 


3888 


3984 


4080 


96 


451 


4177 


4273 


4369 


4465 


4562 


4658 


4754 


4850 


4946 


5042 


96 


452 


5138 


5235 


5331 


5427 


5523 


5619 


5715 


5810 




6002 96 1 


453 


6098 


6194 


6290 


6386 


6482 


6577 


6673 


6769 


6864 


6960 


96 


454 


7056 


7152 


7247 


7343 


7438 


7534 


7629 


7725 


7820 


7916 


96 


455 


6580 I I 


8107 


8202 


8298 


8393 


8488 


8584 


8679 


8774 


8870 


95 


456 


8965 


9060 


9155 


9250 


9346 


9441 


9536 


9631 


9726 


9821 


95 


457 


9916 


*OOII 


*oio6 


*020I 


♦0296 


*039i 


*0486 


*058i 


♦0676 


♦0771 


95 


458 


660865 


0960 


1055 


1 150 


1245 


1339 


1434 


1529 


1623 


I718 


95 


459 


1813 


1907 


2002 


2096 


2191 


2286 


2380 


2475 


2569 


2663 


95 


460 


662758 


2852 


2947 


3041 


3135 


3230 


3324 


3418 


3512 


3607 


94 


461 


3701 


3795 


3889 


3983 


4078 


4172 


4266 


4360 


4454 


4548 


94 


462 


4642 


4736 4830 


4924 


5018 


5112 


5206 


5299 


5393 


5487 


94 


463 


5581 


5675 1 5769 


5862 


5956 


6050 


6143 


6237 


6331 


6424 


94 


464 


6518 


6612 1 6705 


6799 


6892 


6986 


7079 


7173 


7266 


7360 


94 


N. 


Diff. 


Z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




104 


ID 


21 


31 


42 


52 


62 


73 


83 


94 


104 


CO 


103 


10 


21 


31 


41 


52 


62 


72 


82 


93 


103 


S 


102 


10 


20 


31 


41 


51 


61 


71 


82 


92 


102 


< 


101 


10 


20 


30 


40 


51 


61 


71 


81 


91 


lOX 


a* 


zoo 


10 


20 


30 


40 


50 


60 


70 


80 


90 


100 


(C 


p 


10 


20 


30 


40 


50 


59 


69 


79 


89 


P 





10 


20 


29 


39 


49 


59 




78 


88 


(^ 


97 


10 


19 


29 


39 


49 


58 


68 


78 


87 


97 


(^ 


96 


10 


19 


29 


38 


48 


58 


67 


77 


86 


96 




95 


10 


19 


29 


38 


48 


57 


67 


76 


86 


95 




Diff. 


Z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



























LOGARITHMS OF NUMBERS 



893 





N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




465 


667453 


7546 


7640 


7733 


7826 


7920 


8013 


8106 


8199 


8293 


93 




466 


8386 


8479 


8572 


8665 


8759 


8852 


8945 


9038 


9131 


9224 


93 






9317 


9410 


9503 


9596 


9689 


9782 


9875 


9967 


*oo6o 


*oi53 


93 




468 


670246 


0339 


0431 


0524 


0617 


0710 


0802 


0895 


0988 


1080 


93 




469 


1 173 


1265 


1358 


1451 


1543 


1636 


1728 


1821 


1913 


2005 


93 




470 


672098 


2190 


2283 


2375 


2467 


2560 


2652 


^la 


2836 


2929 


92 




471 


3021 


3113 


3205 


3297 


3390 


3482 


3574 


3666 


3758 


3850 


92 




473 


3942 


4034 


4126 


4218 


4310 


4402 


4494 


4586 


4677 


4769 


92 




473 


4861 


4953 


5045 


5137 


5228 


5320 


5412 


5503 


5595 


5687 


92 




t74 


5778 




5962 


6053 


6145 


6236 


6328 


6419 


6511 


6602 


92 




475 


676694 


6785 


6876 


6968 


7059 


7151 


7242 


7333 


Iti 


7516 


91 




476 


7607 


7698 


7789 


7881 




8063 


8154 


8245 


8427 


91 




477 


8518 


8609 


8700 


8791 


8882 


8973 


9064 


9155 


9246 


9337 


91 




478 


.o942f 


9519 


9610 


9700 


9791 


9882 


9973 


*oo63 


*oi54 


*0245 


91 




479 


680336 


0426 


0517 


0607 


0698 


0789 


0879 


0970 


1060 


I151 


91 




480 


681 241 


1332 


1422 


1513 


1603 


1693 


1784 


1874 


1964 


2055 


90 




481 


2145 


2235 


2326 


2416 


2506 


2596 


2686 


2777 


2867 


2957 


90 




482 


3047 


3137 


3227 


3317 


3407 


3497 


3587 


3677 


3767 


3857 


90 




483 


3947 


4037 


4127 


4217 


4307 


4396 


4486 


4576 


4666 


4756 


90 




484 


^4845 


4935 


5025 


5114 


5204 




5383 


5473 


5563 


5652 






4?l 


685742 


5831 


5921 


6010 


6100 


6189 


6279 


6368 


6458 


6547 


89 




486 


6636 


6726 


6815 


6904 


6994 


7083 


7172 


7261 


7351 


7440 


89 




487 


7529 


7618 


7707 


7796 


7886 


7975 


8064 


■8153 


8242 


8331 


89 




488 


8420 


8509 


8598 


8687 


8776 


8865 


8953 


9042 


9131 


9220 


89 


1 


489 


9309 


9398 


9486 


9575 


9664 


9753 


9841 


9930 


*ooi9 


*oio7 


89 




490 


690196 


0285 


0373 


0462 


0550 


0639 


0728 


0816 


0905 


0993 


89 


' 


491 


1081 


1170 1258 


1347 


1435 


1524 


1612 


1700 


1789 


1877 


88 




492 


1965 


2053 


2142 


2230 


2318 


2406 


2494 


2583 


2671 


2759 


88 




493 


2847 


2935 


3023 


3111 


3199 


3287 


3375 


3463 


3551 


3639 


88 




494 


, 3727 


3815 


3903 


3991 


4078 


4166 


4254 


4342 


4430 


4517 


88 


1 




694605 


4693 


4781 


4868 


4956 


5044 


5131 


5219 




5394 


88 


\ 


496 


5482 


5569 


5657 


5744 


5832 


5919 


6007 


6094 


6182 


6269 


87 




497 


6356 


6444 


6531 


6618 


6706 


-6793 


6880 


6968 


7055 


7142 


87 




498 


7229 


7317 


7404 


7491 


7578 


7665 


7752 


7839 




8014 


§7 




499 


8101 


8188 


8275 


8362 


8449 


8535 


8622 


8709 


8796 


8883 


87 


1 


500 


698970 


9057 


9144 


9231 


9317 


9404 


9491 


9578 


9664 


^9751 


?7 




501 


9838 


9924 


*OOII 


*oo98 


*oi84 


*027I 


*0358 


*0444 


*053i 


*o6i7 


SJ 




502 


700704 


0790 


0877 


0963 


1050 


1 136 


1222 


1309 


1395 


1482 


86 




503 


1568 


1654 


1741 


1827 


1913 


1999 


2086 


2172 


2258 


2344 


86 


1 


504 


2431 


2517 


2603 


2689 


2775 


2861 


2947 


3033 


3119 


3205 


86 




505 


703291 


3377 


3463 


3549 


3635 


3721 


3807 


3893 


3979 


4065 


86 




506 


4151 


4236 


4322 


4408 


4494 


4579 


4665 


4751 


4837 


4922 


86 




507 


5008 


5094 


5179 


5265 


5350 


5436 


5522 


5607 


5693 


5778 


86 




508 


5864 


5949 


6035 


6120 


6206 


6291 


6376 


6462 


6547 




|5 


! 


509 


6718 


6803 


6888 


6974 


7059 


7144 


7229 


7315 


7400 


7485 


85 


J 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


I 




94 


9 


19 


28 


38 


47 


5$ 


66 


75 


!5 


94 


( 


CO 

H 


93 


9 


19 


28 


37 


47 


56 


65 


74 


84 


93 


1 


92 


9 


18 


28 


37 


46 


55 


64 


74 


^3 


92 


i 


< 


91 


9 


18 


27 


36 


46 


55 


64 


73 


82 


91 


1 


s 


90 


9 


18 


27 


36 


45 


54 


63 


72 


81 


90 


( 


cC 


8g 


9 


18 


27 


36 


45 


53 


62 


71 


80 


is 


1 





88 


9 


18 


26 


35 


44 


53 


62 


70 


^i 


* 


(^ 


87 


9 


17 


26 


35 


44 


52 


6i 




78 


tl 


1 


cu 


86 


9 


17 


26 


34 


43 


52 


60 


69 


77 


86 


( 




85 


9 


17 


26 


34 


43 


51 


60 


68 


77 


85 


1 




Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



894 




GENERAL TABLES AND FORMULA 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


510 


707570 


7655 


7740 


7826 


791 1 


7996 


8081 


8166 


8251 


8336 


85 


5" 


8421 


8506 


8591 


8676 


8761 


8846 


8931 


9015 


9100 


9185 


85 


512 


9270 


9355 


9440 


9524 


9609 


9694 


9779 


9863 


9948 


*oo33 


85 


513 


7IOII7 


0202 


0287 


0371 


0456 


0540 


0625 


0710 


0794 


0879 


85 


514 


0963 


1048 


I132 


1217 


1301 


1385 


1470 


1554 


1639 


1723 


84 


515 


7II807 


1892 


1976 


2060 


2144 


2229 


2313 


2397 


2481 


2566 


84 


516 


2650 


2734 


2818 


2902 


2986 


3070 


3154 


3238 


.3323 


3407 


84 


5'7 


3491 


3575 


3659 


3742 


3826 


3910 


3994 


4078 


4162 


4246 


84 


518 


4330 


4414 


4497 


4581 


4665 


4749 


4833 


4916 


5000 


5084 


84 


519 


5167 


5251 


5335 


5418 


5502 


5586 


5669 


5753 


5836 


5920 


84 


520 


716003 


6087 


6170 


6254 


6337 


6421 


6504 


6588 


6671 


6754 


83 


521 


6838 


6921 


7004 


7088 


7171 


7254 


7338 


7421 


7504 


7587 


83 


522 


7671 


7754 


7837 


7920 


8003 


8086 


8169 


8253 


8336 


8419 


83 


523 


8502 


8585 


8668 


8751 


8834 


8917 


9000- 


9083 


9165 


9248 


!^ 


524 


9331 


9414 


9497 


9580 


9663 


9745 


9828 


991 1 


9994 


*oo77 


?3 


525 


720159 


0242 


0325 


0407 


0490 


0573 


0655 


0738 


0821 


0903 


83 


526 


0986 


1068 


1151 


1233 


1316 


1398 


1481 


1563 


1646 


1728. 


82 


527 


I8II 


1893 


1975 




2140 


2222 


2305 


2387 


2469 


2552 


82 


528 


2634 


2716 


2798 


2881 


2963 


3045 


3127 


3209 


3291 


3374 


82 


529 


3456 


3538 


3620 


3702 


3784 


3866 


3948 


4030 


4112 


4194 


82 


530 


724276 


4358 


4440 


4522 


4604 


4685 


4767 


4849 


4931 


5013 


82 


531 


5095 


5176 


5258 


5340 


5422 


5503 


5585 


5667 


5748 


5830 


82 


532 


5912 




6075 


6156 


6238 


6320 


6401 


6483 


6564 


6646 


82 


533 


6727 


6809 


6890 


6972 


7053 


7134 


7216 


7297 


7379 


7460 


81 


534 


7541 


7623 


7704 


7785 


7866 


7948 


8029 


8110 


8191 


8273 


81 


535 


728354 


8435 


8516 


8597 


8678 


8759 


8841 


8922 


9003 


9084 


8i 


536 


9165 


9246 


9327 


9408 


9489 


9570 


9651 


9732 


9813 


9893 


81 


537 


9974 


*oo55 


*oi36 


*02I7 


*o298 


*0378 


*0459 


*054o 


*062I 


*0702 


81 


538 


730782 


0863 


0944 


1024 


1 105 


1 186 


1266 


1347 


1428 


1508 


81 


539 


1589 


1669 


1750 


1830 


19H 


1991 


2072 


2152 


2233 


2313 


81 


540 


732394 


2474 


2555 


2635 


2715 


2796 


2876 


2956 


3037 


3II7 


80 


541 


3197 


3278 


3358 


3438 


3518 


3598 


3679 


3759 


3839 


3919 


80 


542 


3999 


4079 


4160 


4240 


4320 


4400 


4480 


4560 


4640 


4720 


80 


543 


4800 


4880 


4960 


5040 


5120 


5200 


5279 


5359 


5439 


5519 


80 


544 


5599 


5679 


5759 


5838 


5918 


5998 


6078 


6157 


6237 


6317 


80 


545 


736397 


6476 


6556 


6635 


6715 


6795 


6874 


6954 


7034 


7II3 


80 


546 


7193 


7272 


7352 


7431 


7511 


7590 


7670 


7749 


7829 


7908 


79 


547 




8067 


8146 


8225 


8305 


8384 


8463 


8543 


8622 


8701 


79 


548 


8781 


8860 


8939 


9018 




9177 


9256 


9335 


9414 


9493 


79 


549 


9572 


9651 


9731 


9810 


9889 




*oo47 


*OI26 


*0205 


*0284 


79 


550 


740363 


0442 


0521 


0600 


0678 


0757 


0836 


0915 


0994 


1073 


79 


551 


1 152 


1230 


1309 


1388 


1467 


1546 


1624 


1703 


1782 


i860 


79 


552 


1939 


2018 


2096 


2175 


2254 


2332 


241 1 


2489 


2568 


2647 


79 


553 


2725 


2804 


2882 


2961 


3039 


3118 


3196 


3275 


3353 


3431 


78 


554 


3510 


3588 


3667 


3745 


3823 


3902 


3980 


4058 


4136 


4215 


78 


N. 


Diflf. 


I 


2 


3 


4 


5 


6 


' 


8 


9 


Diff. 


CO 


86 


9 


17 


26 


34 


43 


52 


60 


69 


77 


86 


(^ 


85 




17 


26 


34 


43 


51 


60 


68 


77 


?5 


< 


84 


8 


17 


25 


34 


42 


50 


59 


67 


76 


84 


Oi 


83 


8 


^l 


25 


33 


42 


50 


58 


66 


75 


?3 


. 


82 


8 


16 


25 


33 


41 


49 


57 


66 


74 


82 


cu 


81 


8 


16 


24 


32 


41 


49 


57 


65 


73 


81 




0^ 


80 


8 


16 


24 


32 


40 


48 


56 


64 


72 


80 


cu 


79 


8 


16 


24 


32 


40 


47 


55 


63 


71 


79 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



























LOGARITHMS OF NUMBERS 



89s 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


744293 


4371 


4449 


4528 


4606 


4684 


4762 


4840 


4919 


4997 


7? 


556 


5075 


5153 


5231 


5309 


5387 


5465 


5543 


5621 


5699 


57 yy 


7? 


557 


5855 


5933 


601 1 


6089 


6167 


6245 


6323 


6401 


6479 


6556 


78 


558 


6634 


6712 


6790 


6868 


6945 


7023 


7101 


7179 


7256 


7334 


78 


559 


7412 


7489 


7567 


7645 


7722 


7800 


7878 


7955 


8033 


8110 


78 


560 


748188 


8266 


8343 


8421 


8498 


8576 


8653 


8731 


8808 


8885 


77 


561 


8963 


9040 


9118 


9195 


9272 


9350 


9427 


9504 


,9582 


9659 


77 


562 


9736 


9814 


9891 


9968 


*oo45 


*OI23 


*0200 


*0277 


*0354 


*043i 


77 


563 


750508 


0586 


0663 


0740 


0817 


0894 


0971 


1048 


1125 


1202 


77 


564 


1279 


1356 


1433 


1510 


1587 


1664 


I74I 


18 18 


1895 


1972 


77 


5^1 


752048 


2125 


2202 


2279 


2356 


2433 


2509 


2586 


2663 


2740 


77 


566 


2816 


2893 


2970 


3047 


3123 


3200 


3277 


3353 


3430 


3506 


77 


567 


3583 


3660 


3736 


3813 


3889 


3966 


4042 


4119 


4195 


4272 


77 


568 


4348 


4425 


4501 


4578 


4654 


4730 


4807 


4883 


4960 


5036 


76 


569 


51 12 


5189 


5265 


5341 


5417 


5494 


5570 


5646 


5722 


5799 


76 


570 


755875 


5951 


6027 


6103 


6180 


6256 


6332 


6408 


6484 


6560 


76 


571 


6636 


6712 


6788 


6864 


6940 


7016 


7092 


7168 


7244 


7320 


76 


572 


7396 


7472 


7548 


7624 


7700 


7775 


7851 


7927 


8003 


8079 


76 


573 


8155 


8230 


8306 


8382 


8458 


8533 


8609 


8685 


8761 


8836 


76 


574 


8912 


8988 


9063 


9139 


9214 


9290 


9366 


9441 


9517 


9592 


76 


575 


759668 


9743 


9819 


9894 


9970 


*oo45 


*OI2I 


*oi96 


*0272 


*0347 


75 


576 


760422 


0498 


0573 


0649 


0724 


0799 


0875 


0950 


1025 


IIOI 


75 


577 


1176 


1251 


1326 


1402 


1477 


1552 


1627 


1702 


1778 


1853 


75 


578 


1928 


2003 


2078 


2153 


2228 


2303 


2378 


2453 


2529 


2604 


75 


579 


2679 


2754 


2829 


2904 


2978 


3053 


3128 


3203 


3278 


3353 


75 


580 


763428 


3503 


3578 


3653 


3727 


3802 


3877 


3952 


4027 


4101 


75 


5?^ 


4176 


4251 


4326 


4400 


4475 


4550 


4624 


4699 


4774 


4848 


75 


582 


4923 


4998 


5072 


5147 


5221 


5296 


5370 


5445 


5520 


5594 


75 


5^3 




5743 


5818 


5892 


5966 


6041 


6115 


6190 


6264 


6338 


74 


584 


6413 


6487 


6562 


6636 


6710 


6785 


6859 


6933 


7007 


7082 


74 


5^5 


767156 


7230 


7304 


7379 


7453 


7527 


7601 


7675 


7749 


7823 


74 


586 


7898 


7972 


8046 


8120 


8194 


8268 


8342 


8416 


8490 


8564 


74 




8638 


8712 


8786 


8860 


8934 


9008 


9082 


9156 


9230 


9303 


74 


588 


9377 


9451 


9525 


9599 


9673 


9746 


9820 


9894 


9968 


*0042 


74 


589 


770115 


0189 


0263 


0336 


0410 


0484 


0557 


0631 


0705 


0778 


74 


590 


770852 


0926 


0999 


1073 


1 146 


1220 


1293 


1367 


1440 


I5I4 


74 


591 


1587 


1661 


1734 


1808 


1881 


1955 


2028 


2102 


2175 


2248 


73 


592 


2322 


2395 


2468 


2542 


2615 


2688 


2762 


2835 


2908 


2981 


73 


593 


3055 


3128 


3201 


3274 


3348 


3421 


3494 


3567 


3640 


3713 


73 


594 


3786 


3860 


3933 


4006 


4079 


4152 


4225 


4298 


4371 


4444 


73 


595 


774517 


4590 


4663 


4736 


4809 


4882 


4955 


5028 


5100 


5173 


73 


596 


5246 


5319 


5392 


5465 


5538 


5610 




5756 


5829 


5902 


73 


597 


5974 


6047 


6120 


6193 


6265 


6338 


641 1 


6483 


6556 


6629 


73 


598 


6701 


6774 


6846 


6919 


6992 


7064 


7137 


7209 


7282 


7354 


73 


599 


7427 


7499 


7572 


7644 


7717 


7789 


7862 


7934 


8006 


8079 


72 


N. 


Diff. 


I 


234 


5 


6 


7 


8 


9 


Diff. 


H 


78 


8 


16 


23 


31 


39 


47 


55 


62 


70 


78 


C^ 


77 


8 


15 


23 


31 


39 


46 


54 


62 


69 


77 


< 


76 


8 


15 


23 


30 


38 


46 


53 


61 


68 


76 


Oi 


75 


8 


15 


23 


30 


38 


45 


53 


60 


68 


75 


6 


74 


7 


15 


22 


30 


37 


44 


52 


59 


67 


74 


73 


7 


15 


22 


29 


37 


44 


51 


58 


66 


73 


£ 


72 


7 


14 


22 


29 


36 


43 


« 50 


58 


65 


72 
Diff. 




Diff. 


I 


234 


5 


6 


7 


8 


9 



896 



GENERAL TABLES AND FORMULA 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


600 


778151 


8224 


8296 


8368 


8441 


8513 


8585 


8658 


8730 


8802 


72 


601 


8874 


8947 


9019 


9091 


9163 


9236 


9308 


9380 


9452 


^9524 


72 


602 


9596 


9669 


9741 


9813 


9885 




*0029 


*0I0I 


*oi73 




72 


603 


780317 


0389 


0461 


0533 


0605 


0677 


0749 


0821 


0893 


0965 


72 


604 


1037 


1 109 


1181 


1253 


1324 


1396 


1468 


1540 


1612 


1684 


72 


605 


781755 


1827 


1899 


197 1 


2042 


2114 


2186 


2258 


2329 


2401 


72 


606 


2473 


2544 


2616 


2688 


2759 


2831 


2902 


2974 


3046 


3117 


72 


^0 


3189 


3260 


3332 


3403 


3475 


3546 


3618 


3689 


3761 


3832 


71 


608 


3904 


3975 


4046 


4118 


4189 


4261 


4332 


4403 


4475 


4546 


71 


6og 


4617 


4689 


4760 


4831 


4902 


4974 


5045 


5II6 


5187 


5259 


71 


610 


785330 


5401 


5472 


5543 


5615 


5686 


5757 


5828 


5899 


5970 


71 


611 


6041 


6lI2 


6183 


6254 


6325 


6396 


6467 


6538 


6609 


6680 


71 


612 


6751 


6822 


6893 


6964 


7035 


7106 


7177 


7248 


7319 


7390 


71 


613 


7460 


7531 


7602 


7673 


7744 


7815 




7956 


8027 




71 


614 


8168 


8239 


8310 


8381 


8451 


8522 


8593 


8663 


8734 


8804 


71 


615 


788875 


8946 


9016 


9087 


9157 


9228 


9299 


9369 


9440 


9510 


71 


616 


9581 


9651 


9722 


9792 


9863 


9933 


*ooo4 


*oo74 


*oi44 


*02I5 


70 


617 


790285 


0356 


0426 


0496 


0567 


0637 


0707 


0778 


0848 


0918 


70 


618 




1059 


1129 


1 199 


1269 


1340 


1410 


1480 


1550 


1620 


70 


6ig 


1691 


1761 


1831 


1901 


1971 


2041 


2111 


2181 


2252 


2322 


70 


620 


792392 


2462 


2532 


2602 


2672 


2742 


2812 


2882 


2952 


3022 


70 


621 


3092 


^o^^ 


3231 


3301 


3371 


3441 


351 1 


3581 


3651 


3721 


70 


622 


3790 


3860 


3930 


4000 


4070 


4139 


4209 


4279 


4349 


4418 


70 


623 


4488 


4558 


4627 


4697 


4767 


4836 


4906 


4976 


5045 


5i^5 


70 


624 


5185 


5254 


5324 




5463 


5532 


5602 


5672 


5741 


581 1 


70 


625 


795880 


5949 


6019 


6088 


6158 


6227 


6297 


6366 


6436 


6505 


69 


626 


6574 


6644 


6713 


6782 


6852 


6921 


6990 


7060 


7129 


7198 


69 


^n 


7268 


7337 


7406 


7475 


7545 


7614 


7683 


7752 


7821 




69 


628 


7960 


8029 


8098 


8167 


8236 


8305 


8374 


8443 


8513 


8582 


69 


629 


8651 


8720 


8789 


8858 


8927 


8996 


9065 


9134 


9203 


9272 


69 


630 


799341 


9409 


9478 


9547 


9616 


9685 


9754 


9823 


9892 


9961 


'69 


631 


800029 


0098 


0167 


0236 


0305 


0373 


0442 


051 1 


0580 


0648 


69 


632 


0717 


0786 


0854 


0923 


0992 


1061 


1129 


1 198 


1266 


1335 


69 


633 


1404 


1472 


1541 


1609 


1678 


1747 


1815 


1884 


1952 


2021 




634 


2089 


2158 


2226 


2295 


2363 


2432 


2500 


2568 


2637 


2705 


68 


635 


802774 


2842 


2910 


2979 


3047 


3116 


3184 


3252 


3321 


3389 


68 


636 


3457 


3525 


3594 


3662 


3730 


3798 


3867 


3935 


4003 


4071 


68 


537 


4139 


4208 


4276 


4344 


4412 


4480 


4548 


4616 


4685 


4753 


68 


638 


4821 


4889 


4957 


5025 


5093 


5161 


5229 


5297 


5365 


5433 


68 


639 


5501 


5569 


5637 


5705 


5773 


5841 


5908 


5976 


6044 


6112 


68 


640 


806180 


6248 


6316 


6384 


6451 


6519 


6587 


6655 


6723 


6790 


68 


641 


6858 


6926 


6994 


7061 


7129 


7197 


7264 


7332 


7400 


7467 


68 


642 


7535 


7603 


7670 


7738 


7806 


7873 


7941 




8076 


8143 


68 


643 


8211 


8279 


8346 


8414 


8481 


8549 


8616 


8684 


8751 


8818 


67 


644 


8886 


8953 


9021 


9088 


9156 


9223 


9290 


9358 


9425 


9492 


67 


645 


809560 


9627 


9694 


9762 


9829 


9896 


9964 


*oo3i 


*0098 


*oi65 


67 


646 


810233 


0300 


0367 


0434 


0501 


0569 


0636 


0703 


0770 


0837 


^7 


H 


0904 


0971 


1039 


1 106 


1 173 


1240 


1307 


1374 


1441 


1508 


67 


648 


1575 


1642 


1709 


1776 


1843 


1910 


1977 


2044 


2111 


2178 


$7 


649 


2245 


2312 


2379 


2445 


2512 


2579 


2646 


2713 


2780 


2847 


67 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


CO 


73 


7 


15 


22 


29 


37 


44 


51 


58 


66 


73 


H 


72 


7 


14 


22 




35 


43 


50 


58 


f5 


72 


Q< 


71 


7 


14 


21 


28 


36 


43 


50 


57 


64 


71 




70 


7 


14 


21 


28 


35 


42 


49 


56 


63 


70 


6 


U 


7 


14 


21 


28 


35 


41 


48 


55 


62 


?? 


di 


7 


14 


20 


27 


34 


41 


48 


54 


61 


68 




Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



897 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


650 


812913 


2980 


3047 


3114 


3181 


3247 


3314 


3381 


3448 


3514 


67 


651 


3581 


3648 


3714 


3781 


3848 


3914 


3981 


4048 


4114 


4181 


^7 


652 


4248 


4314 


4381 


4447 


4514 


4581 


4647 


4714 


4780 


4847 


67 


653 


4913 


4980 


5046 


5113 


5179 


5246 


5312 


5378 


5445 


5511 


66 


654 


5578 


5644 


5711 


5777 


5843 


5910 


5976 


6042 


6109 


6175 


66 


655 


816241 


6308 


6374 


6440 


6506 


6573 


6639 


6705 


6771 


6838 


66 


656 


6904 


6970 


7036 


7102 


7169 


7235 


7301 


7367 


7433 


7499 


66 


657 


7565 


7631 


7698 


7764 


7830 


7896 




8028 


8094 


8160 


66 


658 


8226 


8292 


8358 


8424 


8490 


8556 


8622 


8688 


8754 


8820 


66 


659 


8885 


8951 


9017 


9083 


9149 


9215 


9281 


9346 


9412 


9478 


66 


660 


819544 


9610 


9676 


9741 


9807 


9873 


9939 


*ooo4 


*oo7o 


*oi36 


66 


661 


820201 


0267 


0333 


0399 


0464 


0530 


0595 


0661 


0727 


0792 


66 


662 


0858 


0924 


0989 


1055 


1120 


1186 


1251 


1317 


1382 


1448 


66 


663 


1514 


1579 


1645 


1710 


1775 


1841 


1906 


1972 


2037 


2103 


65 


664 


2168 


2233 


2299 


2364 


2430 


2495 


2560 


2626 


2691 


2756 


55 


665 


822822 


2887 


2952 


3018 


3083 


3148 


3213 


3279 


3344 


3409 


65 


666 


3474 


3539 


3605 


3670 


3735 


3800 


3865 


3930 


3996 


4061 


65 


667 


4126 


4191 


4256 


4321 


4386 


4451 


4516 


4581 


4646 


4711 


65 


668 


4776 


4841 


4906 


4971 


5036 


5101 


5166 


5231 


5296 


5361 


65 


669 


5426 


5491 


5556 


5621 


5686 


5751 


5815 


5880 


5945 


6010 


65 


670 


826075 


6140 


6204 


6269 


6334 


6399 


6464 


6528 


6593 


6658 


65 


671 


6723 


6787 


6852 


6917 


6981 


7046 


7111 


7175 


7240 


7305 


65 


672 


7369 


7434 


7499 


7563 


7628 


7692 


7757 


7821 
8467 


7886 


7951 


65 


673 


8015 


8080 


8144 


8209 


8273 


8338 


8402 


8531 


8595 


64 


674 


8660 


8724 


8789 


8853 


8918 


8982 


9046 


9111 


9175 


9239 


64 


675 


829304 


9368 


9432 


9497 


9561 


9625 


9690 


9754 


9818 


9882 


64 


676 


9947 


*OOII 


*oo75 


*oi39 


*0204 


*o268 


*0332 


*0396 


♦0460 


*0525 


64 


677 


830589 


0653 


0717 


0781 


0845 


0909 


0973 


1037 


1102 


1166 


64 


678 


1230 


1294 


1358 


1422 


i486 


1550 


1614 


1678 


1742 


1806 


64 


679 


1870 


1934 


1998 


2062 


2126 


2189 


2253 


2317 


2381 


2445 


64 


680 


832509 


2573 


2637 


2700 


2764 


2828 


2892 


2956 


3020 


3083 


64 


68i 


3147 


3211 


3275 


3338 


3402 


3466 


3530 


3593 


3657 


3721 


64 


682 


3784 


3848 


3912 


3975 


4039 


4103 


4166 


4230 


4294 


4357 


64 


f?3 


4421 


4484 


4548 


461 1 


4675 


4739 


4802 


4866 


4929 


4993 


64 


684 


5056 


5120 


5183 


5247 


5310 


5373 


5437 


5500 


5564 


5627 


63 


685 


835691 


5754 


5817 


5881 


r5944 


6007 


6071 


6134 


6197 


6261 


63 


686 


6324 


6387 


6451 


6514 


6577 


6641 


6704 


6767 


6830 


6894 


63 


687 


6957 


7020 


7083 


7146 


7210 


7273 


7336 


7399 


7462 


7525 


63 


688 


7588 


7652 


7715 


7778 


7841 


7904 


7967 


8030 


8093 


8156 


63 


68g 


8219 


8282 


8345 


8408 


8471 


8534 


8597 


8660 


8723 


8786 


63 


690 


838849 


8912 


8975 


9038 


9101 


9164 


9227 


9289 


9352 


9415 


63 


691 


9478 


9541 


9604 




9729 


9792 


9855 


9918 


9981 


*oo43 


f3 


692 


840106 


0169 


0232 


0294 


0357 


0420 


0482 


0545 


0608 


0671 


63 


693 


0733 


0796 


0859 


0921 




1046 


1 109 


1 172 


1234 


1297 


63 


694 


1359 


1422 


1485 


1547 


1610 


1672 


1735 


1797 


i860 


1922 


$3 


695 


841985 


2047 


2110 


2172 


2235 


2297 


2360 


2422 


2484 


2547 


62 


696 


2609 


2672 


2734 


2796 


2859 


2921 


2983 


3046 


3108 


3170 


62 


697 


3233 


3295 


3357 


3420 


3482. 


3544 


3606 


3669 


3731 


3793 


62 


698 


3855 


3918 


3980 


4042 


4104 


4166 


4229 


4291 


4353 


4415 


62 


699 


4477 


4539 


4601 


4664 


4726 


4788 


4850 


4912 


4974 


5036 


62 


N. 


DiflF. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




67 


7 


13 


20 


27 


34 


40 


47 


54 


60 


67 


Oi 


66 


7 


13 


20 


26 


33 


40 


46 


53 


59 


66 




55 


7 


13 


20 


26 


33 


39 


46 


52 


59 


65 


6 


64 


6 


13 


19 


26 


32 


38 


45 


51 


58 


64 




63 


6 


13 


19 


25 


32 


38 


44 


50 


57 


63 


62 


6 


12 


19 


25 


31 


37 


43 


50 


56 


62 




DiflF. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



898 



GENERAL TABLES AND FORMULA 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 
62 


700 


845098 


5160 


5222 


5284 


5346 


5408 


5470 


5532 


5594 


5656 


701 


5718 


5780 


5842 


5904 


5966 


6028 


6090 


6151 


6213 


6275 


62 


702 


6337 


6399 


6461 


6523 


6585 


6646 


6708 


^779 


6832 


6894 


62 


703 


6955 


7017 


7079 


7I4I 


7202 


7264 


7326 


7388 


7449 


751 1 


62 


704 


7573 


7634 


7696 


7758 


7819 


7881 


7943 


8004 


8066 


8128 


62 


705 


848189 


8251 


8312 


8374 


8435 


8497 


8559 


8620 


8682 


8743 


62 


706 


8805 


8866 


8928 


8989 


9051 


9112 


9174 


9235 


9297 


9358 


61 


707 


9419 


9481 


9542 


9604 


9665 


9726 


9788 


9849 


991 1 


9972 


61 


708 


850033 


0095 


0156 


0217 


0279 


0340 


0401 


0462 


0524 
1136 


0585 


61 


709 


0646 


0707 


0769 


0830 


0891 


0952 


1014 


1075 


1 197 


6i 


710 


851258 


1320 


1381 


1442 


1503 


1564 


1625 


1686 


1747 


1809 


61 


711 


1870 


193 1 


1992 


2053 


2114 


2175 


2236 


2297 


2358 


2419 


61 


712 


2480 


2541 


2602 


2663 


2724 


2785 


2846 


2907 


2968 


3029 


61 


713 


3090 


3150 


3211 


3272 


3333 


3394 


3455 


3516 


3577 


3637 


61 


714 


3698 


3759 


3820 


3881 


3941 


4002 


4063 


4124 


4185 


4245 


61 


715 


854306 


4367 


4428 


4488 


4549 


4610 


4670 


4731 


4792 


4852 


61 


7r6 


4913 


4974 


5034 


5095 


5156 


5216 


5277 


5337 


5398 


5459 


61 


717 


5519 


5580 


5640 


5701 


5761 


5822 




5943 


6003 


6064 


61 


718 


6124 


6185 


6245 


6306 


6366 


6427 


6487 


6548 


6608 


6668 


60 


719 


6729 


6789 


6850 


6910 


6970 


7031 


7091 


7152 


7212 


7272 


60 


720 


857332 


7393 


7453 


7513 


7574 


7634 


7694 


7755 


7815 


7875 


60 


721 


7935 


7995 


8056 


8II6 


8176 


8236 


8297 


8357 


8417 


8477 


60 


722 


8537 


8597 


8657 


8718 


8778 


8838 


8898 


8958 


9018 


9078 


60 


723 


9138 


9198 


9258 


9318 


9379 


9439 


9499 


^9559 


9619 


9679 


60 


724 


9739 


9799 


9859 


9918 


9978 


*oo38 


♦0098 


*oi58 


*02l8 


*0278 


60 


725 


860338 


0398 


0458 


0518 


0578 


0637 


0697 


0757 


0817 


0877 


60 


726 


0937 


0996 


1056 


III6 


1 176 


1236 


1295 


1355 


I4I5 


1475 


60 


727 


1534 


1594 


1654 


I7I4 


1773 


1833 


1893 


1952 


2012 


2072 


60 


728 


2131 


2191 


2251 


2310 


2370 


2430 


2489 


2549 


2608 


2668 


60 


729 


2728 


2787 


2847 


2906 


2966 


3025 


3085 


3144 


3204 


3263 


60 


730 


863323 


3382 


3442 


3501 


3561 


3620 


3680 


3739 


3799 


3858 


59 


731 


3917 


3977 


4036 


4096 


4155 


4214 


4274 


4333 


4392 


4452 


59 


732 


451 1 


4570 


4630 


4689 


4748 


4808 


.4867 


4926 


4985 


5045 


59 


733 


5104 


5163 


5222 


5282 


5341 


5400 


5459 


5519 


5578 


5637 


59 


734 


5696 


5755 


5814 


5874 


5933 


5992 


6051 


6110 


6169 


6228 


59 


735 


866287 


6346 




6465 


6524 


6583 


6642 


6701 


6760 


6819 


59 


736 


6878 


6937 


6996 


7055 


71 14 


7173 


7232 


7291 


7350 


7409 


59 


737 


7467 


7526 


7585 


7644 7703 


7762 


7821 




7939 


7998 


59 


738 


8056 


8115 


8174 


8233 


8292 


8350 


8409 


8468 


8527 


8586 


59 


739 


8644 


8703 


8762 


8821 


8879 


8938 


8997 


9056 


9114 


9173 


59 


740 


869232 


9290 


9349 


9408 


9466 


9525 


9584 


9642 


9701 


9760 


59 


741 


9818 


9877 


9935 


9994 


*oo53 


*OIII 


*oi7o 


*0228 


*o287 


*0345 




742 


870404 


0462 


0521 


0579^ 


0638 


0696 


0755 


0813 


0872 


0930 


58 


743 


0989 


1047 


1106 


1 164 


1223 


1 281 


1339 


1398 


1456 


1515 


58 


744 


1573 


1631 


1690 


1748 


1806 


1865 


1923 


198 1 


2040 




58 


745 


872156 


2215 


2273 


2331 


2389 


2448 


2506 


2564 


2622 


2681 


58 


746 


2739 


2797 


2855 


2913 


2972 


3030 


3088 


3146 


3204 


3262 


5? 


747 


3321 


3379 


3437 


3495 


3553 


3611 


3669 


3727 


3785 


3844 


58 


748 


3902 


3960 


4018 


4076 


4134 


4192 


4250 




4366 


4424 


5? 


749 


4482 


4540 


4598 


4656 


4714 


4772 


4830 


4888 


4945 


5003 


58 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 




62 


6 


12 


• 19 


25 


31 


37 


43 


50 


56 


62 


^ 


61 


6 


12 


18 


24 


31 


37 


43 


49 


55 


61 




60 


6 


12 


18 


24 


30 


36 


42 


48 


54 


60 


d 


59 


6 


12 


18 


24 


30 


35 


41 


47 


53 


59 




58 


6 


12 


17 


23 


29 


35 


41 


46 


52 


58 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



899 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


DiflT. 


750 


875061 


5119 


5177 


5235 


5293 


5351 


5409 


5466 


5524 


|5?' 


58 


751 


5640 




5756 


5813 


5871 


5929 


5987 


6045 


6102 


6160 


^l 


752 


6218 


6276 


6333 


6391 




6507 


6564 


6622 


6680 


6737 


5? 


753 


6795 


6853 


6910 


6968 


7026 


7083 


7141 


7199 


7256 


7314 


5^ 


754 


7371 


7429 


7487 


7544 


7602 


7659 


7717 


7774 


7832 


7889 


58 




877947 


8004 


8062 


8119 


8177 


8234 


8292 


8349 


8407 


8464 


57 


756 


8522 


8579 


8637 


8694 


8752 


8809 


8866 


8924 


8981 


9039 


57 


757 


9096 


9153 


9211 


9268 


9325 


9383 


9440 


9497 


9555 


9612 


57 


758 


9669 


9726 


9784 


9841 


9898 


9956 


*ooi3 


*oo7o 


*OI27 


*oi85 


57 


759 


880242 


0299 


0356 


0413 


0471 


0528 


0585 


0642 


0699 


0756 


57 


760 


880814 


0871 


0928 


0985 


1042 


1099 


1156 


1213 


1271 


1328 


57 


761 


1385 


1442 


1499 


1556 


1613 


1670 


1727 


1784 


1841 


1898 


57 


762 


1955 


2012 




2126 


2183 


2240 


2297 


2354 


241 1 


2468 


57 


763 


2525 


2581 


2638 


2695 


2752 


2809 


2866 


2923 


2980 


3037 


57 


764 


3093 


3150 3207 


3264 


3321 


3377 


3434 


3491 


3548 


3605 


57 


765 


883661 


3718 3775 


3832 


3888 


3945 


4002 


4059 


4"5 


4172 


57 


766 


4229 


4285 4342 


4399 


4455 


4512 


4569 


4625 


4682 


4739 


57 


767 


4795 


4852 4909 


4965 


5022 


5078 


5135 


5192 


5248 


5305 


57 


768 


5361 


5418 


5474 


5531 


5587 


5644 


5700 


5757 


5813 


5870 


57 


769 


5926 


5983 


6039 


6096 


6152 


6209 


6265 


6321 


6378 


6434 


56 


770 


886491 . 6547 I 


6604 


6660 


6716 


6773 


6829 


6885 


6942 


6998 


5f 


771 


7054 


7111 


7167 


7223 


7280 


7336 


7392 


7449 


7505 


7561 


5^ 


772 


7617 


7674 


7730 


7786 


7842 


7898 


7955 


801 1 


8067 


8123 


56 


773 


8179 


8236 


8292 


8348 


8404 


8460 


8516 


8573 


8629 


8685 


55 


774 


8741 


8797 


8853 


8909 


8965 


9021 


9077 


9134 


9190 


9246 


56 


775 


889302 


9358 


9414 


9470 


9526 9582 


9638 


9694 


9750 


9806 


55 


776 


9862 


9918 


9974 


*oo30 


*oo86 


*oi4i 


*oi97 


*0253 


*0309 


*0365 


5? 


777 


890421 


0477 


0533 


0589 


0645 


0700 


0756 


0812 


0868 


0924 


55 


778 


0980 


1035 


1091 


1147 


1203 


1259 


1314 


1370 


1426 


1482 


5? 


779 


1537 


1593 


1649 


1705 


1760 


1816 


1872 


1928 


1983 


2039 


56 


780 


892095 


2150 


2206 


2262 


2317 


2373 


2429 


2484 


2540 


2595 


56 


7?^ 


2651 


2707 


2762 


2818 


2873 


2929 


2985 


3040 


3096 


3151 


5^ 


782 


3207 


3262 


3318 


3373 


3429 


3484 


3540 


3595 


3651 


3706 


56 


783 


3762 


3817 


3873 


3928 


3984 


4039 




4150 


4205 


4261 


55 


784 


4316 


4371 


4427 


4482 


4538^ 


4593 


4648 


4704 


4759 


4814 


55 


785 


894870 


4925 


4980 


5036 


5091 


5146 


5201 


5257 


5312 


5367 


55 


786 


5423 


5478 


5533 




5644 


5699 


5754 


5809 


5864 


5920 


55 


787 


5975 


6030 




6140 


6195 


6251 


6306 


6361 


6416 


6471 


55 


788 


6526 


6581 


6636 


6692 


6747 


6802 


6857 


6912 


6967 


7022 


55 


789 


7077 


7132 


7187 


7242 


7297 


7352 


7407 


7462 


7517 


7572 


55 


790 


897627 


7682 


7737 


7792 


7847 


7902 


7957 


8012 


8067 


8122 


55 


791 


8176 


8231 


8286 


8341 


8396 


8451 


8506 


8561 


8615 


8670 


55 


792 


8725 


8780 


8835 


8890 


8944 


8999 


9054 


9109 


9164 


9218 


55 


793 


9273 


9328 


9383 


9437 


9492 


9547 


9602 


9656 


9711 


9766 


55 


794 


9821 


9875 


9930 




*oo39 


*oo94 


*oi49 


*0203 


*0258 


*03I2 


55 


795 


900367 


0422 


0476 


0531 


0586 


0640 


0695 


0749 


0804 


0859 


55 


796 


0913 


0968 


1022 


1077 


1131 


1186 


1240 


1295 


1349 


1404 


55 


797 


1458 


1513 


1567 


1622 


1676 


1731 


1785 


1840 




1948 


54 


798 


2003 


2057 


2112 


2166 


2221 


2275 


2329 


2384 


2438 


2492 


54 


799 


2547 


2601 


2655 


2710 


2764 


2818 


2873 


2927 


2981 


3036 


54 


N. 


Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diflf. 




^l 


6 


II 


17 


23 


29 


34 


40 


46 


51 


57 


a< 


56 


6 


II 


17 


22 


28 


34 


39 


45 


50 


56 




55 


6 


II 


17 


22 


28 


33 


39 


44 


. 50 


55 


54 


5 


II 


16 


22 


27 


32 


38 


43 


49 


54 




Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diflf. 



900 



GENERAL TABLES AND FORMULA 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


800 


903090 


3144 


3199 


3253 


3307 


3361 


3416 


3470 


3524 


3578 


54 


801 


3633 


3687 


3741 


3795 


3849 


3904 


3958 


4012 


4066 


4120 


54 


802 


4174 


4229 


4283 


4337 


4391 


4445 


4499 


4553 


4607 


4661 


54 


803 


4716 


4770 


4824 


4878 


4932 


4986 


5040 


5094 


5148 


5202 


54 


804 


5256 


5310 


5364 


5418 


5472 


5526 


5580 


5634 


5688 


5742 


54 


805 


905796 


5850 


5904 


5958 


6012 


6066 


6119 


6173 


6227 


6281 


54 


806 


6335 


6389 


6443 


6497 


6551 


6604 


6658 


6712 


6766 


6820 


54 


H 


6874 


6927 


6981 


7035 


7089 


7143 


7196 


7250 


7304 


7358 


54 


808 


74II 


7465 


7519 


7573 


7626 


7680 


7734 


7787 


7841 


7895 


54 


809 


7949 


8002 


8056 


8110 


8163 


8217 


8270 


8324 


8378 


8431 


54 


810 


908485 


8539 


8592 


8646 


8699 


8753 


8807 


8860 


8914 


8967 


54 


811 


9021 


9074 


9128 


9181 


9235 


9289 


9342 


9396 


9449 


9503 


54 


812 


9556 


9610 


9663 


9716 


9770 


9823 


9877 


9930 


9984 


*oo37 


53 


813 


910091 


0144 


0197 


0251 


0304 


0358 


041 1 


0464 


0518 


0571 


53 


814 


0624 


0678 


0731 


0784 


0838 




0944 


0998 


1051 


1 104 


53 


815 


911158 


1211 


1264 


1317 


1371 


1424 


1477 


1530 


1584 


1637 


53 


816 


1690 


1743 


1797 


1850 


1903 


1956 


2009 


2063 


2116 


2169 


53 


2'Z 


2222 


2275 


2328 


2381 


2435 


2488 


2541 


2594 


2647 


2700 


53 


818 


2753 


2806 


2859 


2913 


2966 


3019 


3072 


3125 


3178 


3231 


53 


819 


3284 


3337 


3390 


3443 


3496 


3549 


3602 


3655 


3708 


3761 


53 


820 


913814 


3867 


3920 


3973 


4026 


4079 


4132 


4184 


4237 


4290 


53 


821 


4343 


4396 


4449 


4502 


4555 


4608 


4660 


4713 


4766 


4819 


53 


822 


4872 


4925 


4977 


5030 


5083 


5136 


5189 


5241 


5294 


5347 


53 


823 


5400 


5453 


5505 


5558 


561 1 




5716 


5769 


5822 


5875 


53 


824 


5927 


5980 


6033 


6085 


6138 


6191 


6243 


6296 


6349 


6401 


53 


?l 


916454 


6507 


6559 


6612 


6664 


6717 


6770 


6822 


6875 


6927 


53 


826 


6980 


7033 


7085 


7138 


7190 


7243 


7295 


7348 


7400 


7453 


53 


in 


7506 


7558 


761 1 


7663 


7716 


7768 


7820 


7873 


7925 


7978 


52 


828 


8030 


8083 


8135 


8188 


8240 


8293 


8345 


8397 


8450 


8502 


52 


829 


8555 


8607 


8659 


8712 


8764 


8816 


8869 


8921 


8973 


9026 


52 


830 


919078 


9130 


9183 


9235 


9287 


9340 


9392 


9444 


9496 


9549 


52 


?3^ 


9601 


9653 


9706 


9758 


9810 


9862 


9914 


9967 


*ooi9 


*oo7i 


52 


832 


920123 


0176 


0228 


0280 


0332 


0384 


0436 


0489 


0541 


0593 


52 


833 


0645 


0697 


0749 


0801 


0853 


0906 


0958 


1010 


1062 


1114 


52 


834 


1 166 


1218 


1270 


1322 


1374 


1426 


1478 


1530 


1582 


1634 


52 


835 


921686 


1738 


1790 


1842 


1894 


1946 


1998 


2050 


2102 


2154 


52 


s 


2206 


2258 


2310 


2362 


2414 


2466 


2518 


2570 


2622 


2674 


52 


2725 


2777 


2829 


2881 


2933 


2985 


3037 


3089 


3140 


3192 


52 


838 


3244 


3296 


3348 


3399 


3451 


3503 


3555 


3607 


3658 


3710 


52 


839 


3762 


3814 


3865 


3917 


3969 


4021 


4072 


4124 


4176 


4228 


52 


840 


924279 


4331 


4383 


4434 


4486 


4538 


4589 


4641 


4693 


4744 


52 


841 


4796 


4848 


4899 


4951 


5003 


5054 


5106 


5157 


5209 


5261 


52 


842 


5312 


5364 


5415 


5467 


5518 


5570 


5621 


5673 


5725 


5776 


52 


843 


5828 


5879 


5931 


5982 


6034 


6085 


6137 


6188 


6240 


6291 


51 


844 


6342 


6394 


6445 


6497 


6548 


6600 


6651 


6702 


6754 


6805 


51 


845 


926857 


6908 


6959 


7011 


7062 


71U 


7165 


7216 


7268 


7319 


51 


846 


7370 


7422 


7473 


7524 


7576 7627 


7678 


7730 


7781 


7832 


51 


847 


7883 


7935 




8037 


8088 


8140 


8191 


8242 


8293 


8345 


51 


848 


8396 


8447 


8498 


8549 


8601 


8652 


8703 


8754 


8805 


8857 


51 


849 


8908 


8959 


9010 


9061 


9112 


9163 


9215 


9266 


9317 


9368 


5^ 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


CO 

H 


55 


6 


II 


17 


22 


28 


33 


39 


44 


50 


55 


04 


54 


5 


II 


16 


22 


27 


32 


38 


43 


49 


54 




53 


5 


II 


16 


21 


27 


32 


37 


42 


48 


53 


52 


5 


10 


16 


21 


26 


31 


36 


42 


47 


52 




Diflf. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



901 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


850 


929419 


9470 


9521 


9572 


9623 


9674 


9725 


9776 


9827 


^9879 


51 


851 


9930 


9981 


*0032 


*oo83 


*oi34 


*oi85 


*0236 


*0287 


*0338 




51 


852 


930440 


0491 


0542 


0592 


0643 


0694 


0745 


0796 


0847 


0898 


51 


853 


0949 


1000 


I05I 


1102 


1 153 


1204 


1254 


1305 


1356 


1407 


51 


854 


1458 


1509 


1560 


1610 


1661 


1712 


1763 


1814 


1865 


1915 


51 


855 


931966 


2017 


2068 


2118 


2169 


2220 


2271 


2322 


2372 


2423 


51 


856 


2474 


2524 


2575 


2626 


2677 


2727 


2778 


2829 


2879 


2930 


51 




2981 


3031 


3082 


3133 


3183 


3234 


3285 


3335 


3386 


3437 


51 


858 


3487 


3538 


3589 


3639 


3690 


3740 


3791 


3841 


3892 


3943 


51 


859 


3993 


4044 


4094 


4145 


4195 


4246 


4296 


4347 


4397 


4448 


51 


860 


934498 


4549 


4599 


4650 


4700 


4751 


4801 


4852 


4902 


4953 


50 


86i 


5003 


5054 


5104 


5154 


5205 


5255 


5306 


5356 


5406 


5457 


50 


863 


5507 


5558 


5608 


5658 


5709 


5759 


5809 


5860 


5910 




50 


863 


601 1 




6111 


6162 


6212 


6262 


6313 


6363 


6413 


6463 


50 


864 


6514 


6564 


6614 


6665 


6715 


6765 


6815 


6865 


6916 


6966 


50 


865 


937016 


7066 


7117 


7167 


7217 


7267 


7317 


7367 


7418 


7468 


50 


866 


7518 
8019 


7568 


7618 


7668 


7718 


7769 


7819 


7869 


7919 


7969 


50 


867 


8069 


8119 


8169 


8219 


8269 


8320 


8370 


8420 


8470 


50 


868 


8520 


8570 


8620 


8670 


8720 


8770 


8820 


8870 


8920 


8970 


50 


869 


9020 


9070 


9120 


9170 


9220 


9270 


9320 


9369 


9419 


9469 


50 


870 


939519 


9569 


9619 


9669 


9719 


9769 


9819 


9869 


9918 


9968 


50 


871 


940018 


0068 


0118 


0168 


0218 


0267 


0317 


0367 


0417 


0467 


50 


872 


0516 


0566 


0616 


0666 


0716 


0765 


0815 


0865 


0915 


0964 


50 


873 


1014 


1064 


1114 


1 163 


1213 


1263 


1313 


1362 


1412 


1462 


50 


874 


1511 


1561 


1611 


1660 


1710 


1760 


1809 


1859 


1909 


1958 


50 


875 


942008 


2058 


2107 


2157 


2207 


2256 


2306 


2355 


2405 


2455 


50 


876 


2504 


2554 


2603 


2653 


2702 


2752 


2801 


2851 


2901 


2950 


50 


?77 


3000 


3049 


3099 


3148 


3198 


3247 


3297 


3346 


3396 


3445 


49 


878 


3495 


3544 


3593 


3643 


3692 


3742 


3791 


3841 


3890 


3939 


49 


879 


3989 


4038 


4088 


4137 


4186 


4236 


4285 


4335 


4384 


4433 


49 


880 


944483 


4532 


4581 


4631 


4680 


4729 


4779 


4828 


4877 


4927 


49 


881 


4976 


5025 


5074 


5124 


5173 


5222 


5272 


5321 


5370 


5419 


49 


882 


5469 


5518 


5567 


5616 


5665 


5715 


5764 


5813 


5862 


5912 


49 


883 


5961 


6010 


6059 


6108 


6157 6207 


6256 


6305 


6354 


6403 


49 


884 


6452 


6501 


6551 


6600 


6649 


6698 


6747 


6796 


6845 




49 


885 


946943 


6992 


7041 


7090 


7140 


7189 


7238 


7287 


7336 


7385 


49 


886 


7434 


7483 


7532 


7581 


7630 


7679 


7728 


7777 


7826 


7875 


49 


887 


7924 


7973 


8022 


8070 


8119 


8168 


8217 


8266 


8315 


8364 


49 


888 


8413 


8462 


8511 


8560 


8609 


8657 


8706 


8755 


8804 


8853 


49 


889 


8902 


8951 


8999 


9048 


9097 


9146 


9195 


9244 


9292 


9341 


49 


890 


949390 


9439 


9488 


9536 


9585 


9634 


9683 


9731 


9780 


9829 


49 


891 


9878 


9926 


9975 


*0O24 


*oo73 


*OI2I 


*oi7o 


*02I9 


*0267 


*o3i6 


49 


892 


950365 


0414 


0462 


051 1 


0560 


0608 


0657 


0706 


0754 


0803 


49 


893 


0851 


0900 


0949 


0997 


1046 


1095 


1143 


II92 


1240 


1289 


49 


894 


1338 


1386 


1435 


1483 


1532 


1580 


1629 


1677 


1726 


1775 


49 




951823 


1872 


1920 


1969 


2017 


2066 


2114 


2163 


2211 


2260 


48 


896 


2308 


2356 


2405 


2453 


2502 


2550 


2599 


2647 


2696 


2744 


48 


897 


2792 


2841 


2889 


2938 


2986 


3034 


3083 


3I3I 


3180 


3228 


48 


898 


3276 


3325 


3373 


3421 


3470 


3518 


3566 


3615 


3663 


3711 


48 


899 


3760 


3808 


3856 


3905 


3953 


4001 


4049 


4098 


4146 


4194 


48 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


04 


51 


5 


10 


15 


20 


26 


31 


36 


41 


46 


51 


50 


5 


10 


15 


20 


25 


30 


35 


40 


45 


50 




% 


5 


10 


15 


20 


25 


29 


34 


3? 


44 


^i 


5 


10 


14 


19 


24 


29 


34 


38 


43 


48 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



902 



GENERAL TABLES AND FORMULAE 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


900 


954243 


4291 


4339 


4387 


4435 


4484 


4532 


4580 


4628 


4677 


48 


901 


4725 


4773 


4821 


4869 


4918 


4966 


5014 


5062 


5110 


5158 


4? 


902 


5207 


5255 


5303 


5351 


5399 


5447 


5495 


5543 


5592 


5640 


48 


903 


5688 


5736 


5784 


5832 




5928 


5976 


6024 


6072 


6120 


48 


904 


6168 


6216 


6265 


6313 


636? 


6409 


6457 


6505 


6553 


6601 


48 


905 


956649 


6697 


6745 


6793 


6840 


6888 


6936 


6984 


7032 


7080 


48 


906 


7128 


7176 


7224 


7272 


7320 


7368 


7416 


7464 


7512 


7559 


'^g 


907 


7607 


7655 


7703 


7751 


7799 


7847 


7894 


7942 


7990 


8038 


48 


908 


8086 


8134 


8181 


8229 


8277 


8325 


8373 


8421 


8468 


8516 


48 


909 


8564 


8612 


8659 


8707 


8755 


8803 


8850 


8898 


8946 


8994 


48 


910 


959041 


9089 


9137 


9185 


9232 


9280 


9328 


9375 


9423 


9471 


4? 


911 


9518 


9566 


9614 


9661 


9709 


9757 


9804 


9852 


9900 


9947 


48 


912 


9995 


*0042 


*oo90 


*oi38 


*oi85 


*0233 


*0280 


*0328 


*o376 


*0423 


4^ 


913 


960471 


0518 


0566 


0613 


0661 


0709 


0756 


0804 


0851 


0899 


48 


914 


0946 


0994 


104 1 


1089 


1 136 


1 184 


I23I 


1279 


1326 


1374 


48 


915 


961421 


1469 


1516 


1563 


1611 


1658 


1706 


1753 


1801 


1848 


47 


916 


1895 


1943 


1990 


2038 


2085 


2132 


2180 


2227 


2275 


2322 


47 


917 


2369 


2417 


2464 


2511 


2559 


2606 


2653 


2701 


2748 


2795 


47 


918 


2843 


2890 


2937 


2985 


3032 


3079 


3126 


3174 


3221 


3268 


47 


919 


3316 


3363 


3410 


3457 


3504 


3552 


3599 


3646 


3693 


3741 


47 


920 


963788 


3835 


3882 


3929- 


3977 


4024 


4071 


4118 


4165 


4212 


47 


921 


4260 


4307 


4354 


4401 


4448 


4495 


4542 


4590 


4637 


4684 


47 


922 


4731 


4778 


4825 


4872 


4919 


4966 


5013 


5061 


5108 


5155 


47 


923 


5202 


5249 


5296 


5343 


5390 


5437 


5484 


5531 


5578 


5625 


47 


924 


5672 


5719 


5766 


5813 


5860 


5907 


5954 


6001 


6048 




47 


925 


966142 


6189 


6236 


6283 


6329 


6376 


6423 


6470 


6517 


6564 


47 


926 


6611 


6658 


6705 


6752 


6799 


6845 


6892 


6939 


6986 


7033 


47 


927 


7080 


7127 


7173 


7220 


7267 


73H 


7361 


7408 


7454 


7501 


47 


928 


7548 


7595 


7642 


7688 


7735 


7782 


7829 


7875 


7922 


7969 


47 


929 


8016 


8062 


8109 


8156 


8203 


8249 


8296 


8343 


8390 


8436 


47 


930 


968483 


8530 


8576 


8623 


8670 


8716 


8763 


8810 


8856 


8903 


47 


931 


8950 


8996 


9043 


9090 


9136 


9183 


9229 


9276 


9323 


9369 


47 


932 


9416 


9463 


9509 


9556 


9602 


9649 


9695 


9742 


9789 


9835 


47 


933 


9882 


9928 


9975 


*002I 


*oo68 


*oii4 


*oi6i 


*0207 


*0254 


*0300 


47 


934 


970347 


0393 


0440 


0486 


0533 


0579 


0626 


0672 


0719 


0765 


46 




970812 


0858 


0904 


0951 


0997 


1044 


1090 


II37 


1 183 


1229 


46 


936 


1276 


1322 


1369 


I415 


1461 


1508 


1554 


I60I 


1647 


1693 


46 


937 


1740 


1786 


1832 


1879 


1925 


1971 


2018 


2064 


21 10 


2157 


46 


938 


2203 


2249 


2295 


2342 


2388 


2434 


2481 


2527 


2573 


2619 


46 


939 


2666 


2712 


2758 


2804 


2851 


2897 


2943 


2989 


3035 


3082 


46 


940 


973128 


3174 


3220 


3266 


3313 


3359 


3405 


3451 


3497 


3543 


46 


941 


3590 


3636 


3682 


3728 


3774 


3820 


3866 


3913 


3959 


4005 


46 


942 


4051 


4097 


4143 


4189 


4235 


4281 


4327 


4374 


4420 


4466 


46 


943 


4512 


4558 


4604 


4650 


4696 


4742 


4788 


4834 


4880 


4926 


46 


944 


4972 


5018 


5064 


5IIO 


5156 


5202 


5248 


5294 


5340 


5386 


46 


945 


975432 


5478 


5524 


5570 


5616 


5662 


5707 


5753 


5799 


5845 


46 


946 


5891 


5937 


5983 


6029 


6075 


6121 


6167 


6212 


6258 


6304 


46 


947 


6350 


6396 


6442 


6488 


6533 


6579 


6625 


6671 


6717 


6763 


46 


948 


6808 


6854 


6900 


6946 


6992 


7037 


7083 


7129 


7175 


7220 


46 


949 


7266 


7312 


7358 


7403 


7449 


7495 


7541 


7586 


7632 


7678 


46 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


H 


49 


5 


10 


15 


20 


25 


29 


34 


39 


44 


1i 


Ph 


48 


5 


10 


14 


19 


24 


29 


34 


38 


43 


, 


47 


5 


9 


14 


19 


24 


28 


33 


38 


42 


47 


¥ 
tk 


46 


5 


9 


14 


18 


23 


28 


32 


37 


41 


46 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



LOGARITHMS OF NUMBERS 



903 



N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


950 


977724 


7769 


7815 


7861 


7906 


7952 


7998 


8043 


8089 


8135 


46 


951 


8181 


8226 


8272 


8317 


8363 


8409 


8454 


8500 


8546 


8591 


46 


952 


8637 


8683 


8728 


8774 


8819 


8865 


8911 


8956 


9002 


9047 


46 


953 


9093 


9138 


9184 


9230 


275 


9321 


9366 


9412 


9457 


9503 


46 


954 


9548 


9594 


9639 


9685 


9730 


9776 


9821 


9867 


9912 


9958 


46 


955 


980003 


0049 0094 


0140 


0185 


0231 


0276 


0322 


0367 


0412 


45 


956 


0458 


0503 


0549 


0594 


0640 


0685 


0730 


0776 


0821 


0867 


45 


957 


0912 


0957 


1003 


1048 


1093 


1139 


1 184 


1229 


1275 


1320 


45 


958 


1366 


1411 


1456 


1 501 


1547 


1592 


1637 


1683 


1728 


1773 


45 


959 


1819 


1864 


1909 


1954 


2000 


2045 


2090 


2135 


2181 


2226 


45 


960 


982271 


2316 


2362 


2407 


2452 


2497 


2543 


2588 


2633 


2678 


45 


961 


2723 


2769 


2814 


2859 


2904 


2949 


2994 


3040 


3085 


3130 


45 


962 


3175 


3220 


3265 


3310 


3356 


3401 


3446 


3491 


3536 


3581 


45 


963 


3626 


3671 


3716 


3762 


3807 


3852 


3897 


3942 


3987 


4032 


45 


964 


4077 


4122 


4167 


4212 


4257 


4302 


4347 


4392 


4437 


4482 


45 


965 


984527 


4572 


4617 


4662 


4707 


4752 


4797 


4842 


4887 


4932 


45 


966 


4977 


5022 


5067 


5112 


5157 


5202 


5247 


5292 


5337 


5382 


45 


967 


5426 


5471 


5516 


5561 


5606 


5651 


5696 


5741 


5786 


5830 


• 45 


968 


5875 


5920 


5965 


6010 


6055 


6100 


6144 


6189 


6234 


6279 


45 


969 


6324 


6369 


6413 


6458 


6503 


6548 


6593 


6637 


6682 


6727 


45 


970 


986772 


6817 


6861 


6906 


6951 


6996 


7040 


7085 


7130 


7175 


45 


971 


7219 


7264 


7309 


7353 


7398 


7443 


7488 


7532 


7577 


7622 


45 


972 


7666 


7711 


7756 


7800 


7845 


7890 


7934 


7979 


8024 


8068 


45 


973 


8113 


8157 


8202 


8247 


8291 


8336 


^J^l 


8425 


8470 


8514 


45 


974 


8559 


8604 


8648 


8693 


8737 


8782 


8826 


8871 


8916 


8960 


45 


975 


989005 


9049 


9094 


9138 


9183 


9227 


9272 


9316 


9361 


9405 


45 


976 


9450 


9494 


9539 


9583 


9628 


9672 


^9717 


9761 


9806 


9850 


44 


977 


9895 


9939 


9983 


*0028 


*0072 


*oii7 


*oi6i 


*0206 


*0250 


*0294 


44 


978 


990339 


0383 


0428 


0472 


0516 


0561 


0605 


0650 


0694 


0738 


44 


979 


0783 


0827 


0871 


0916 


0960 


1004 


1049 


1093 


II37 


1 182 


44 


980 


991226 


1270 


1315 


1359 


1403 


1448 


1492 


1536 


1580 


1625 


44 


98X 


1669 


1713 


1758 


1802 


1846 


1890 


1935 


1979 


2023 


2067 


44 


982 


2111 


2156 


2200 


2244 


2288 


2333 


2377 


2421 


2465 


2509 


44 


983 


2554 


2598 


2642 


2686 


2730 


2774 


2819 


2863 


2907 


2951 


44 


984 


2995 


3039 


3083 


3127 


3172 


3216 


3260 


3304 


3348 


3392 


44 




993436 


3480 


3524 


3568 


3613 


3657 


3701 


3745 


3789 


3833 


44 


986 


3877 3921 


3965 


4009 


4053 ' 4097 


4141 


4185 


4229 


4273 


44 


987 


4317 


4361 


4405 


4449 


4493 


4537 


4581 


4625 


4669 


4713 


44 


988 


4757 


4801 


4845 


4889 


4933 


4977 


5021 


5065 


5108 


5152 


44 


989 


5196 


5240 


5284 


5328 


5372 


5416 


5460 


5504 


5547 


5591 


44 


990 


995635 


5679 


5723 


5767 


5811 


5854 


5898 


5942 


5986 


6030 


44 


991 


6074 


6117 


6161 


6205 


6249 


6293 


6337 


6380 


6424 


6468 


44 


992 


6512 


6555 


6599 


6643 


6687 


6731 


6774 


6818 


6862 


6906 


44 


993 


6949 


6993 


7037 


7080 


7124 


7168 


7212 


7255 


7299 


7343 


44 


994 


7386 


7430 


7474 


7517 


7561 


7605 


7648 


7692 


7736 


7779 


44 


995 


997823 


7867 
8303 


7910 


7954 


7998 


8041 


8085 


8129 


8172 


8216 


44 


I 996 


8259 


8347 


8390 


8434 


.8477 


8521 


8564 


8608 


8652 


44 


997 


8695 


8739 


8782 


8826 


8S69 


8913 


8956 


9000 


9043 


9087 


44 


998 


9131 


9174 


9218 


9261 


9305 


9348 


9392 


9435 


9479 


9522 


44 


999 




9609 


9652 


9696 


9739 


9783 


9826 


9870 


9913 


9957 


43 


N. 


Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


1 CO 


46 


5 


9 


14 


18 


23 


28 


32 


37 


41 


46 


a< 


45 1 5 


9 


14 


18 


23 


27 


32 


36 


41 


45 


\ i 


44 


4 


9 


13 


18 


22 


26 


31 


35 


40 


44 


43 


4 


9 


13 


17 


22 


26 


30 


34 


39 


43 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 



























904 




GENERAL TABLES AND FORMULA 






N. 





I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. 


lOOO 


000000 


0043 


0087 


0130 


0174 


0217 


0260 


0304 


0347 


0391 


43 1 


lOOI 


0434 


0477 


0521 


0564 


0608 


0651 


0694 


0738 


0781 




43 ! 


1002 


0868 


0911 


0954 


0998 


1041 


1084 


1128 


1171 


1214 


1258 


43 i 


1003 


1301 


1344 




143 1 


1474 


1517 


1561 


1604 


1647 


1690 


43 ' 


1004 


1734 


1777 


1820 


1863 


1907 


1950 


1993 


2036 


2080 


2123 


43 


1005 


002166 


2209 


2252 


2296 


2339 


2382 


2425 


2468 


2512 


2555 


43 


1006 


2598 


2641 


2684 


2727 


2771 


2814 


""^11 


2900 


2943 


2986 


43 « 


1007 


3029 


3073 


3I16 


3159 


3202 


3245 


3288 


3331 


3374 


^i^l 


43 


1008 


3461 


3504 


3547 


3590 


3633 


3676 


3719 


3762 


3805 


3848 


43 


1009 


3891 


3934 


3977 


4020 


4063 


4106 


4149 


4192 


4235 


4278 


43 


loio 


004321 


4364 


4407 


4450 


4493 


4536 


4579 


4622 


4665 


4708 


43 


101 1 


4751 


4794 


4837 


4880 


4923 


4966 


5009 


5052 


5095 


5138 


43 


IOI2 


5181 


5223 


5266 


5309 


5352 


5395 


5438 


5481 


5524 


5567 


43 


IOI3 




5652 


5695 


5738 


5781 


5824 


5867 


5909 


5952 


5995 


43 


ZOI4 


6038 


6081 


6124 


6166 


6209 


6252 


6295 


6338 


6380 


6423 


43 


IOI5 


006466 


6509 


6552 


6594 


6637 


6680 


6723 


6765 


6808 


6851 


43 


IOI6 


6894 


6936 


6979 


7022 


7065 


7107 


7150 


7193 


7236 


7278 


43. 


IOI7 


7321 


7364 


7406 


7449 


7492 


7534 


7577 


7620 


7662 


7705 


43 


IO18 


7748 


7790 


7833 


7876 


7918 


7961 


8004 


8046 


8089 


8132 


43 


IOI9 


8174 


8217 


8259 


8302 


8345 


8387 


8430 


8472 


8515 


8558 


43 


loao 


008600 


8643 


8685 


8728 


8770 


8813 


8856 


8898 


8941 


8983 


43 


102 1 


9026 


9068 


9111 


9153 


9196 


9|38 


9281 


9323 


9366 


9408 


42 


1022 


9451 


9493 


9536 


^9578 


9621 




9706 


9748 


9791 


9833 


42 


1023 


9876 


9918 


9961 


*ooo3 


*oo45 


*oo88 


*oi30 


*oi73 


*02I5 


*0258 


42 


1024 


010300 


0342 


0385 


0427 


0470 


0512 


0554 


0597 


0639 


0681 


42 


1025 


010724 


0766 




0851 


0893 


0936 


0978 


1020 


1063 


1 105 


42 


1026 


1 147 


1190 


1232 


1274 


1317 


1359 


1401 


1444 


i486 


1528 


42 


1027 


1570 


1613 


1655 


1697 


1740 


1782 


1824 


1866 


1909 


1951 


42 


1028 


1993 


2035 


2078 


2120 


2162 


2204 


2247 


2289 


2331 


2373 


42 


1029 


2415 


2458 


2500 


2542 


2584 


2626 


2669 


2711 


2753 


2795 


42 


1030 


012837 


2879 


2922 


2964 


3006 


3048 


3090 


3132 


3174 


3217 


42 


1031 


3259 


3301 


3343 


3385 


3427 


3469 


3511 


3553 


3596 


3638 


42 


1032 




3722 


3764 


3806 


3848 


3890 


3932 


3974 


4016 


4058 


42 


1033 


4100 


4142 


4184 


4226 


4268 


4310 


4353 


4395 


4437 


4479 


42 


1034 


4521 


4563 


4605 


4647 


4689 


4730 


4772 


4814 


4856 


4898 


42 


1035 


014940 


4982 


5024 


5066 


5108 


5150 


5192 


5234 


5276 


5318 


42 


1036 


5360 


5402 


5444 


5485 


5527 


5569 


561 1 


5653 


5695 


5737 


42 


1037 


5779 


5821 


5863 


5904 


5946 


5988 


6030 


6072 


6114 


6156 


42 


1038 


6197 


6239 


6281 


6323 


6365 


6407 


6448 


6490 


6532 


6574 


42 


1039 


6616 


6657 


6699 


6741 


6783 


6824 


6866 


6908 


6950 


6992 


42 


1040 


017033 


7075 


7117 


7159 


7200 


7242 


7284 


7326 


7367 


7409 


42 


1041 


7451 


7492 


7534 


7576 


7618 


7659 


7701 


7743 


7784 


7826 


42 


Z042 


7868 
8284 


7909 


7951 


7993 


8034 


8076 


8118 


8159 


8201 


8243 


42 


1043 


8326 


8368 


8409 




8492 


8534 


8576 


8617 


8659 


42 


1044 


8700 


8742 


8784 


8825 


8867 


8908 


8950 


8992 


9033 


9075 


42 


1045 


019116 


9158 


9199 


9241 


9282 


9324 


9366 


9407 


9449 


9490 


42 


1046 


9532 


9573 


9615 


9656 


9698 


9739 


9781 


9822 


9864 


9905 


41 


1047 


9947 


9988 


*oo30 


*oo7i 


*oii3 


*oi54 


*oi95 


*0237 


*0278 


*0320 


41 


1048 


020361 


0403 


0444 


0486 


0527 


0568 


0610 


0651 


0693 


0734 


41 


1049 


0775 


0817 


0858 


0900 


0941 


0982 


1024 


1065 


1 107 


1 148 


41 


1050 


021189 


1231 


1272 


1313 


1355 


1396 


1437 


M79 


1520 


I56I 


41 


N. 


Diff. 


Z 


2 


3 


4 


5 


6 


7 


8 


9 


Diff.' 




44 


4 


9 


13 


18 


22 


26 


31 


35 


40 


44 1 


43 


4 




13 


17 


22 


26 


30 


34 


39 


43 


pi 


42 


4 


8 


13 


17 


21 


25 


29 


34 


38 


42 ;| 


41 


4 


8 


12 


16 


21 


25 


29 


33 


37 


41 1 




Diff. 


I 


2 


3 


4 


5 


6 


7 


8 


9 


Diff. ^ 
























Of 



O^ LOGARITHMIC SIN., COS., TAN. AND COT.* 179° 
Table 75 



M. Sin. D. 1''. Cos. D. i''. Tan. D. i". Cot. 



6.463726 
.764756 
.940847 
7.065786 
7.162696 
.241877 
.308824 
.366816 
.417968 

7-463726 
.505118 
.542906 
.577668 
.609853 

7.639816 
.667845 
.694173 
.718997 
.742478 

7-764754 
.785943 
.806146 

.825451 
.843934 
7,861662 
.878695 
.895085 
.910879 
.926119 

7.940842 
.955082 
.968870 
.982233 
.995198 

8.007787 
.020021 
.031919 
.043501 
.054781 

8.065776 
.076500 
.086965 
.097183 
.107167 

8. 1 16926 
.126471 
.135810 
.144953 
.153907 

8.162681 
.171280 
.179713 
.187985 
.196102 

8.204070 
.211895 
.219581 
.227134 

.234557 
8.241855 



Cos. 



5017.17 
2934-85 
2082.32 
1615.17 
1319-68 
1115.78 
966.53 
852.53 
762.63 

689.87 
629.80 
579-37 
536.42 
499.38 

467-15 
438.80 

413.73 
391.35 
371.27 

353.15 
336.72 
321.75 
308.05 

295-47 
283.88 
273.17 
263.23 
254-00 
245.38 

237.33 
229.80 
222.72 
216.08 
209.82 
203.90 
198-30 
193.03 
188.00 
183.25 

178.73 
174.42 
170.30 
166.40 
162.65 
159.08 
155-65 
152.38 
149.23 
146.23 

143.32 
140.55 
137.87 
135.28 
132.80 
130.42 
128.10 
125.88 
123.72 
121.63 



D. I" 



10.000000 
.000000 
.000000 
.000000 
.000000 

10.000000 

9-999999 
.999999 

.999999 
.999999 

9.999998 
.999998 
.999997 
.999997 
.999996 

9.999996 
.999995 
.999995 
.999994 
.999993 

9.999993 
.999992 
.999991 
.999990 
.999989 

9.999989 
.999988 
.999987 
.999986 
.999985 

9-999983 
.999982 
.999981 
.999980 
.999979 

9-999977 
.999976 
.999975 
.999973 
.999972 

9.999971 
.999969 



.999966 

-999964 

9.999963 

.999961 

-999959 
.999958 
.999956 

9-999954 
.999952 
.999950 
.999948 
-999946 

9.999944 
.999942 
.999940 
.999938 
.999936 

9-999934 



Sin. 



.02 
.03 



.02 

.03 
.02 
.02 

.03 
.02 



.03 
.02 
.03 
.03 
.02 

.03 
.03 
.02 

-03 
.03 

.03 
-03 
-03 
.03 
.03 
.03 
.03 
.03 
.03 
.03 



D. 1" 



6.463726 
.764756 
.940847 
7.065786 
7.162696 
.241878 
.308825 
.366817 
.417970 

7.463727 
.505120 
.542909 
.577672 
.609857 

7.639820 
.667849 
.694179 
.719003 
.742484 

7-764761 
.785951 
.806155 
.825460 
.843944 

7.861674 
.878708 
.895099 
.910894 
.926134 

7-940858 
.955100 



.982253 

.995219 
8.007809 
.020044 
.031945 
.043527 
.054809 

8.065806 
.076531 
.086997 
.097217 
.107203 

8.116963 
.126510 
.135851 
.144996 
.153952 

8.162727 
.171328 
.179763 
.188036 
.196156 

8.204126 

.211953 
219641 
.227195 
.234621 
8.241921 



Cot. 



5017.17 
2934.85 
2082.32 
1615.17 
1319.70 
1115-78 
966.53 
852.55 
762.62 

689.88 
629.82 
579-38 
536.42 
499.38 
467.15 
438.83 
413.73 
391.35 
371.28 

353-17 
336.73 
321.75 
308.07 
295.50 
283.90 
273-18 
263.25 
254.00 
245.40 

237-37 
229.82 
222.73 
216.10 
209.83 
203.92 
198.35 
193.03 
188.03 
183.28 

178.75 
174.43 
170.33 
166.43 
162.67 
159.12 
155-68 
152.42 

149.27 
146.25 

143.35 
140.58 
137.88 
135.33 
132.83 
130.45 
128.13 
125.90 
123.77 
121.67 



D. I". 



3.536274 
.235244 
.059153 
2.934214 
2.837304 
.758122 
.691175 
.633183 
.582030 

2.536273 
.494880 

.457091 
.422328 

•390143 
2.360180 

.332151 
.305821 
.280997 
.257516 

2.235239 
.214049 
.193845 
.174540 
.156056 

2.138326 
.121292 
.104901 
.089106 
.073866 

2.059142 
.044900 
.031 in 

.017747 

.004781 
1.992191 

.979956 
.968055 
.956473 
.945191 
1.934194 

.923469 
.913003 
.902783 
.892797 
1.883037 
.873490 

.864149 

.855004 
.846048 

1.837273 
.828672 
.820237 
.811964 
.803844 

1.795874 
.788047 

.780359 
.772805 

.765379 
1.758079 



Tan. 



• From Allen's **Field and Office Tables.'! Copyright, 



89^ 



LOGARITHMIC SINES 



M. 



Sin. 



o 


8.241855 


I 


.249033 


2 


.256094 


3 


.263042 


4 


.269881 


5 


8.276614 


6 


.283243 


7 


.289773 


8 


.296207 


9 


.302546 


10 


8.308794 


II 


.314954 


12 


.321027 


13 


.327016 


14 


.332924 


15 


8.338753 


16 


.344504 


17 


.350181 


18 


.355783 


19 


.361315 


20 


8.366777 


21 


.372171 


22 


.377499 


23 


.382762 


24 


.387962 


25 


8.393101 


26 


.398179 


27 


.403199 


28 


.408161 


29 


.413068 


30 


8.417919 


31 


.422717 


32 


.427462 


33 


.432156 


34 


. 436800 


35 


8.441394 


3b 


.445941 


37 


.450440 


38 


.454893 


39 


.459301 


40 


8.463665 


41 


.467985 


42 


.472263 


43 


.476498 


44 


. 480693 


45 


8.484848 


4b 


.488963 


47 


.493040 


48 


.497078 


49 


. 501080 


50 


8. 505045 


51 


• 508974 


52 


.512867 


53 


.516726 


54 


.520551 


55 


8.524343 


5b 


.528102 


57 


.531828 


58 


.535523 


59 


.539186 


60 


.8. 542819 



Cos. 



D. 1" 



119.63 
117.68 
115.80 
113.98 
112.22 
110.48 
108. 83 
107. 23 
105. 65 
104. 13 
102. 67 
101.22 
99.82 
98.47 
97.15 
95.85 
94.62 

93.37 
92.20 
91.03 

89.90 
88.80 
87.72 
86.67 
85.65 
84.63 
83.67 
82.70 
81.78 
80.85 

79.97 
79.08 
78.23 
77.40 
76.57 
75.78 
74.98 
74.22 

73.47 
72.73 
72.00 
71.30 
70.58 
69.92 
69.25 
68.58 
67.95 
67.30 
66.70 
66.08 

65.48 
64.88 
64.32 
63.75 
63.20 
62.65 
62, 10 
61.58 
61.05 

60.55 
D. I". 



Cos. 



999934 
999932 
999929 
999927 

999925 
099922 
999920 
999918 
999915 
999913 
999910 
999907 
999905 
999902 

999899 
999897 



999891 
999888 
999885 



999879 
999876 
999873 



999861 
999858 
999854 
999851 



999844 
999841 



999834 
999831 
999827 
999824 
999820 

999816 
999813 
999809 
999805 
999801 
999797 
999794 
999790 
999786 
999782 

999778 
999774 
999769 
999765 
999761 
999757 
999753 
999748 
999744 
999740 

999735 
Sin. 



D. i" 



.03 
.05 
.03 
.03 
.05 
.03 
.03 
.05 
.03 
.05 

.05 
.03 
.05 
.05 
.03 
.05 
.05 
.05 
.05 
.05 

.05 
.05 
.05 
.05 
.05 
.05 
.05 
.05 
.07 
.05 

.05 
.07 
.05 
.05 
.07 
.05 
.07 
.05 
.07 
.07 

.05 
.07 
.07 

.07 
.07 
.05 
.07 
.07 
.07 
.07 

.07 

.08 
.07 
.07 
.07 
.07 
.08 
.07 
.07 
.08 

D. I''. 



Tan. 



;.24i92i 
.249102 
.256165 
.263115 
. 269956 
1.276691 
.283323 
.289856 
. 296292 
.302634 

1. 308884 
.315046 
.321122 
.327114 
.333025 
1. 338856 
.344610 
.350289 
. 355895 
. 361430 

1.366895 
.372292 
.377622 



^. 393234 
.398315 
.403338 
. 408304 

.413213 
^.418068 
. 422869 
.427618 

.432315 
. 436962 
1. 441560 
.446110 
.450613 
.455070 
.459481 
5.463849 
.468172 
.472454 
.476693 
. 480892 
5.485050 
.489170 
.493250 
.497293 
.501298 

J. 505267 
. 509200 
.513098 
.516961 
. 520790 
5.524586 

.528349 
.532080 

.535779 
. 539447 
!. 543084 

Cot. 



D. I" 



119.68 
117.72 
115.83 
114.02 
112.25 
110.53 
108. 88 
107. 27 
105. 70 
104. 17 

102. 70 
101.27 
99.87 
98.52 
97.18 
95.90 
94.65 

93.43 
92.25 
91.08 

89.95 
88.83 
87.78 
86.72 
85.70 
84.68 
83.72 

82.77 
81.82 
80.92 

80.02 
79.15 
78.28 

77.45 
76.63 
75.83 
75.05 
74.28 
73.52 
72.80 

72.05 
71.37 
70.65 
69.98 
69.30 
68.67 
68.00 
67.38 
66.75 
66.15 

65.55 
64.97 
64.38 
63.82 
63.27 
62.72 
62.18 
61.65 
61.13 
60.62 

D. I'^ 



91; 



COSINES, TANGENTS, AND COTANGENTS 177^ 



Sin. 



13 
14 
15 
16 

17 
18 

19 



J. 542819 
.546422 
.549995 
.553539 
.557054 
5.560540 

.563999 
.567431 
.570836 
.574214 

^.577566 
.580892 
.584193 
.587469 
.590721 
5.593948 
.597152 
.600332 
.603489 
.606623 

i. 609734 
.612823 
.615891 
.618937 
.621962 
1.624965 
.627948 
.630911 
.633854 
.636776 

1.639680 
.642563 
.645428 
.648274 
.651102 

1.65391 1 
. 656702 

.659475 
.662230 
.664968 

1.667689 
.670393 
. 673080 

.675751 
.678405 
1. 681043 
.683665 
.686272 



.691438 
8.693998 

.696543 
.699073 
.701589 
.704090 

8.706577 
.709049 
.711507 
.713952 
.716383 

8. 718800 



P. 1" 



60.05 
59.55 
59.07 
58.58 
58.10 

57.65 
57.20 

56.75 
56.30 

55.87 

55-43 
55.02 
54.60 
54.20 
53.78 
53.40 
53.00 
52.62 
52.23 
51.85 

51.48 
51.13 
50.77 
50.42 
50.05 
49.72 
49.38 
49.05 
48.70 
48.40 

48.05 
47.75 
47.43 
47.13 
46.82 
46.52 
46.22 
45.92 
45.63 
45.35 

45.07 
44.78 
44.52 
44.23 
43.97 
43.70 
43.45 
43.18 
42.92 
42.67 

42.42 
42.17 

41.93 
41.68 

41.45 
41.20 
40.97 
40.75 
40. 52 
40.28 

D. I". 



Cos. 



D. i'\ 



9.999735 
.999731 
.999726 
.999722 
.999717 

9-999713 
.999708 

.999704 
.999699 

.999694 

9.999689 

.999685 



.999675 

.999670 

9.999665 

.999660 

.999655 
.999650 
.999645 

9.999640 
.999635 
.999629 
.999624 
.999619 

9.999614 
.999608 
.999603 
.999597 

' .999592 

9.999586 
.999581 
.999575 
.999570 
.999564 

9.999558 
.999553 
.999547 
.999541 
.999535 

9.999529 
.999524 
.999518 
.999512 
. 999506 

9.999500 
.999493 
.999487 
.999481 
.999475 

9.999469 
.999463 
.999456 
.999450 
.999443 

9.999437 
.999431 
.999424 
.999418 
.999411 

9.999404 

■Sin. 



D. I". 



Tan. 



8.543084 
.546691 
.550268 
.553817 
.557336 

8.560828 
.564291 
.567727 
.571137 
.574520 

8.577877 
.581208 

.584514 
.587795 
.591051 
8.594283 
.597492 
.600677 
.603839 
.606978 

8.610094 
.613189 
.616262 
.619313 
.622343 

8.625352 
. 628340 
.631308 
.634256 
.637184 

8. 640093 
. 642982 

.645853 
. 648704 

.651537 
8.654352 
.657149 
.659928 
. 662689 
.665433 

8.668160 
. 670870 

.673563 
.676239 
. 678900 
8.681544 
.684172 
.686784 
.689381 
.691963 

8.694529 
.697081 
. 699617 
.702139 
. 704646 

8. 707140 
. 709618 
. 712083 

.714534 

.716972 

8. 719396 

Cot. 



D. I'' 



60.12 

59.62 
59.15 
58.65 
58.20 
57.72 
57.27 
56.83 
56.38 
55.95 

55.52 
55.10 
54.68 
54.27 
53.87 
53.48 
53.08 
52.70 
52.32 
51.93 

51.58 
51.22 
50.85 
50.50 
50.15 
49.80 

49-47 
49.13 
48.80 
48.48 

48.15 
47.85 
47.52 
47.22 
46.92 
46.62 
46.32 
46.02 
45.73 
45.45 

45.17 
44.88 
44.60 

44.35 
44.07 
43.80 
43.53 
43.28 
43.03 
42.77 

42.53 
42.27 
42.03 
41.78 
41.57 
41.30 
41.08 
40.85 
40.63 
40.40 

D. I". 



Cot. 



1. 456916 

.453309 

.449732 

.446183 

.442664 
I. 439172 

.435709 

.432273 

.428863 

.425480 

I. 422123 

.418792 

.415486 

.412205 

.408949 
1.405717 

.402508 

.399323 
.396161 
. 393022 

1.389906 
.386811 
.383738 
.380687 

.377657 

1.374648 

.371660 

.368692 

. 365744 
.362816 

1.359907 

.357018 

.354147 

.351296 

. 348463 
I. 345648 

.342851 

.340072 

.337311 

.334567 
I. 331840 20 

. 329130 ig 

.326437 

.323761 

.321100 
I. 318456 

.315828 

.313216 

.310619 

.308037 

I. 305471 
. 302919 
.300383 
. 297861 

.295354 
1.292860 

. 290382 

.287917 

.285466 

. 283028 
1.280604 

Tan. 



87' 



LOGARITHMIC SINES 



176° 



Sin. 



10 
II 
12 
13 
14 
15 
16 

17 
18 

19 



22 

23 
24 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 

57 
58 
59 
60 



93' 



;. 718800 
.721204 
.723595 
.725972 
.728337 
;. 730688 
.733027 
.735354 
.737667 

.739969 

5. 742259 
.744536 
. 746802 

.749055 
.751297 
^.753528 
.755747 
.757955 
.760151 

. 762337 

^.764511 
. 766675 
.768828 
. 770970 
.773101 
^. 775223 
. 777333 
.779434 
.781524 

.783605 

3.785675 
.787736 
.789787 
.791828 

. 793859 
3.795881 

.797894 
.799897 
.801892 
.803876 

8.805852 
.807819 
.809777 
.811726 
.813667 

8.815599 
.817522 
.819436 
.821343 
. 823240 

8.825130 
.827011 



D. I". 



.830749 
.832607 

8.834456 
.836297 
.838130 
.839956 
.841774 

8.843585 

Cos. 



40.07 

39.85 
39.62 
39-42 
39.18 
38.98 
38.78 
38.55 
38.37 
38.17 

37.95 
37.77 
37.55 
37.37 
37.18 
36.98 
36.80 
36.60 

36.43 
36.23 

36.07 

35.88 
35.70 
35.52 
35.37 
35.17 
35.02 
34.83 
34.68 
34.50 

34.35 
34.18 
34.02 
33.85 
33.70 
33.55 
33.38 
33.25 
33.07 
32.93 
32.78 
32.63 
32.48 

32.35 
32.20 
32.05 
31.90 
31.78 
31.62 
31.50 

31.35 
31.22 
31.08 

30.97 
30.82 
30.68 
30.55 
30.43 
30.30 
30.18 

D. I". 



Cos. 



9.999404 



999391 
999384 
999378 
999371 
999364 
999357 
999350 
999343 

999336 
999329 
999322 
999315 
999308 
999301 
999294 
999287 
999279 
999272 

999265 
999257 
999250 
999242 
999235 
999227 
999220 
999212 
999205 
999197 

999189 
999181 
999174 
999166 
999158 
999150 
999142 

999134 
999126 
9991 18 

9991 10 
999102 
999094 
999086 
999077 
999069 
999061 

999053 
999044 

999036 
999027 
999019 
999010 
999002 
998993 



998976 
998967 



998950 
998941 

Sin. 



.13 
. 12 

.13 
.12 

.13 
.12 

•13 
.12 

.13 
.13 

.13 
.12 

.13 
.13 
.13 
.13 
.13 
.13 
.13 
.13 

.13 
• 13 
.13 
.15 
.13 
.13 
•13 
.15 
•13 
•15 

.13 
.15 
.13 
.15 
•15 
.13 
.15 
.15 
.13 
.15 



Tan. 



8. 719396 
.721806 
. 724204 
. 726588 
. 728959 

8.731317 
. 733663 
• 735996 
.738317 
. 740626 

8. 742922 
. 745207 
. 747479 
. 749740 
. 751989 

8. 754227 

. 756453 
. 758668 
. 760872 
.763065 

8. 765246 
.767417 
.769578 
.771727 
.773866 

8.775995 
.778114 
. 780222 
. 782320 
. 784408 

8. 786486 
.788554 
. 790613 
. 792662 
. 794701 

8. 796731 
.798752 
. 800763 
. 802765 
.804758 

8. 806742 
.808717 
.810683 
.812641 

.814589 

8.816529 

.818461 



D. I''. 



Cot. 



.822298 
. 824205 

8.826103 

.827992 



.831748 

. .833613 

8.835471 

.837321 

.839163 



. 842825 
8. 844644 

Cot. 



40.17 
39-97 
39-73 
39.52 
39.30 
39.10 
38.88 
38.68 
38.48 
38.27 
38.08 
37-87 
37.68 
37.48 
37.30 
37.10 
36.92 
36.73 
36.55 
36.35 
36.18 
36.02 
35.82 
35.65 
35.48 
35.32 
35.13 
34.97 
34.80 
34.63 

34.47 
34.32 
34.15 
33.98 
33.83 
33.68 
33.52 
33.37 
33.22 

33.07 

32.92 
32.77 
32.63 
32.47 
32.33 
32.20 
32.05 
31.90 
31.78 
31.63 

31.48 
31.37 
31.23 
31.08 

30.97 
30.83 
30.70 
30.58 
30.45 
30.32 

D. 1''. 



1.280604 
.278194 
.275796 
. 273412 
.271041 

1.268683 
.266337 
. 264004 
.261683 
.259374 

1.257078 

. 254793 
.252521 
. 250260 
.248011 
1.245773 
.243547 
.241332 
.239128 

.236935 

1.234754 
. 232583 
. 230422 
.228273 
.226134 

1.224005 
.221886 
.219778 
.217680 
.215592 

1.213514 
.211446 
. 209387 
. 207338 
. 205299 

1.203269 
.201248 
. 199237 
. 197235 
. 195242 

I. 193258 
. 191283 
.189317 
. 187359 
.185411 

I. 183471 
. 181539 
. 179616 
. 177702 
• 175795 

I. 173897 
. 172008 
. 170126 
. 168252 
. 166387 

I. 164529 
. 162679 
. 160837 
. 159002 
.157175 

I. 155356 

Tan. 



86° 



COSINES, TANGENTS, AND COTANGENTS 175^ 



M. 



I 
2 

3 
4 
5 
6 

I 

9 
10 
II 
12 
13 
14 
15 
16 
17 
18 

19 



22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

48 
49 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



5.843585 
.845387 
.847183 
.848971 

.850751 
>. 852525 
.854291 
.856049 
.857801 
.859546 

;. 861283 
. 863014 
.864738 

.866455 
.868165 



.871565 
.873255 
.874938 
.876615 

8.878285 

.879949 
.881607 
.883258 
. 884903 

8. 886542 



. 889801 
.891421 
.893035 

8. 894643 
. 896246 
.897842 
.899432 
,901017 

8.902596 
,904169 
.905736 
.907297 
.908853 

8. 910404 
.911949 
.913488 
.915022 
• 916550 

8. 918073 

.919591 
,921103 
.922610 
,924112 

8.925609 
,927100 
.928587 
. 930068 
.931544 

8.933015 
.934481 
.935942 
.937398 
.938850 

8,940296 

Cos. 



D. i'\ 



30.03 

29.93 
29.80 
29.67 
29.57 
29.43 
29.30 
29.20 
29.08 
28.95 

28.85 

28.73 
28.62 
28.50 
28.38 
28.28 
28.17 
28.05 
27.95 
27.83 

27.73 
27.63 
27.52 
27.42 
27.32 
27.20 
27. 12 
27.00 
26,90 
26.80 

26.72 
26.60 
26.50 
26.42 
26.32 
26.22 
26. 12 
26.02 
25.93 
25.85 

25.75 
25.65 
25.57 
25.47 
25.38 
25.30 
25.20 
25.12 
25.03 
24.95 
24.85 
24.78 
24.68 
24.60 
24.52 
24.43 
24.35 
24.27 
24.20 
24.10 

D. I''. 



Cos. 



998941 



998923 
998914 
998905 



998869 



998851 
998841 



998823 
998813 



998795 
998785 
998776 
998766 

998757 
998747 
998738 
998728 
998718 



D. i'\ 



998679 



998659 
998649 

998639 
998629 
998619 
998609 

998599 
998589 
998578 



998558 



998537 
998527 
998516 
998506 
998495 
998485 
998474 



998453 
998442 
998431 
998421 
998410 
998399 



998377 
998366 

998355 
998344 

Sin. 



.15 
.15 
.15 
.15 
.15 
.15 
.15 
.15 
.15 
.15 

.17 
.15 

• 15 
.17 
.15 
.15 
.17 
.15 
.17 
.15 

.17 
.15 
.17 
.17 

.17 
.15 
.17 
.17 
.17 
.17 

.17 
.17 
.17 
.17 
.17 
.17 
.17 
.18 

• 17 
.17 

.17 

.18 

.17 
.18 

.17 
.18 

.17 

.18 

.17 
.18 

.18 
.18 

.17 
.18 
.18 
.18 
.18 
,18 
.18 
.18 



D. i'\ 



Tan. 



. 84645 ■ 
.848260 
.850057 
.851846 
5.853628 
.855403 
.857171 
.858932 
,860686 

1.862433 
.864173 
. 865906 
.867632 
. 869351 
1.871064 
.872770 
.874469 
.876162 
.877849 
i. 879529 
.881202 



.884530 



.891112 
.892742 
.894366 

5.895984 
.897596 
. 899203 
. 900803 
. 902398 
i. 903987 
.905570 
.907147 
.908719 
. 910285 

I.911846 
.913401 

.914951 
.916495 
. 918034 
1. 919568 
,921096 
.922619 
.924136 
.925649 

i. 927156 



.930155 
,931647 

.933134 
^.934616 
.936093 
.937565 
.939032 
.940494 
5. 941952 

Cot. 



D. I' 



30.18 
30.08 

29.95 
29.82 
29.70 
29.58 
29.47 

29.35 
29.23 
29.12 

29.00 

28.88 
28.77 
28.65 
28.55 
28.43 
28.32 
28.22 
28.12 
28.00 

27.88 
27.78 
27.68 
27.58 
27.47 
27.38 
27.27 
27.17 
27.07 
26.97 

26.87 
26.78 
26.67 
26.58 
26.48 
26.38 
26.28 
26. 20 
26.10 
26.02 

25.92 
25.83 
25.73 
25.65 
25.57 
25.47 
25.38 
25.28 
25.22 
25.12 

25.03 
24.95 
24.87 
24.78 
24.70 
24.62 
24.53 
24.45 
24.37 
24.30 

D. I''. 



Cot. 



I. 155356 
. 153545 
.151740 

. 149943 

. 148154 

I. 146372 

. 144597 
. 142829 
, 14 I 068 
.139314 

I. 137567 
. 135827 
. 134094 
. 132368 
. 130649 

1. 128936 
, 127230 
. 125531 
.123838 
.122151 

I. 120471 
.118798 

.117131 
.115470 

.113815 
I. 112167 
, I 10524 
. 108888 
, 107258 
. 105634 

I. 104016 
. 102404 
, 100797 
.099197 
.097602 

1. 096013 
.094430 
.092853 
.091281 
.089715 

I. 088154 
.086599 
,085049 
.083505 
.081966 

1.080432 
, 078904 
.077381 
.075864 
.074351 

1.072844 
.071342 
.069845 
.068353 
.066866 

1.065384 
.063907 
.062435 
.060968 
. 059506 

1. 058048 

Tan. 



8s« 



LOGARITHMIC SINES 



174" 



M.; Sin. I D. i'\ 



Cos. 



2 
3 
4 
5 
6 
7 
8 

9 
10 
II 
12 
13 
14 
15 
16 

18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

47 
48 

49 
I 50 
51 
52 
53 
54 
55 
56 

57 
58 
59 
60 



95^ 



8. 940296 
.941738 
.943174 
. 944606 

.946034 
8. 947456 
.948874 
.950287 
.951696 
.953100 

8. 954499 
.955894 
.957284 
.958670 
.960052 

8.961429 
.962801 
.964170 
.965534 
.966893 

8. 968249 
.969600 

.970947 
.972289 
.973628 
8. 974962 
. 976293 
.977619 

.978941 
.980259 

8.981573 
. 982883 
.984189 

.985491 
. 986789 



.989374 
.990660 

.991943 
.993222 

8. 994497 
.995768 
.997036 
.998299 
.999560 

9.000816 
. 002069 
.003318 
.004563 
.005805 

9. 007044 
.008278 
.009510 
.010737 
.011962 

9.013182 
.014400 
.015613 
,016824 
.018031 

9.019235 

Cos. 



24.03 
23.93 
23.87 
23.80 
23.70 
23.63 
23.55 
23.48 
23.40 
23.32 

23.25 
23.17 
23.10 
23.03 
22.95 
22.87 
22.82 
22.73 
22.65 
22.60 

22.52 
22.45 
22.37 
22.32 
22.23 
22.18 
22, 10 
22.03 
21.97 
21.90 

21.83 
21.77 
21.70 
21.63 
21.57 
21.52 
21.43 
21.38 
'21.32 
21.25 

21,18 
21.13 
21.05 
21.02 
20.93 
20.88 
20.82 
20.75 
20.70 
20.65 

20.57 

20.53 
20.45 
20.42 
20.33 
20.30 
20.22 
20.18 
20. 12 
20.07 

D. I''. 



D. i". Tan. 



D. i". 



Cot. 



9. 998344 

.998333 
998322 
99831 I 
998300 
998289 
998277 
998266 

998255 
998243 

998232 
998220 
998209 
998197 
998186 
998174 
998163 
998151 
998139 
998128 

9981 16 
998104 
998092 



998056 

998044 
998032 
99S020 



997996 

997984 
997972 

997959 
997947 
997935 
997922 
997910 
997897 
997885 
997872 
997860 
997847 
997835 
997822 

997809 
997797 
997784 
997771 
997758 

997745 
997732 
997719 
997706 

997693 
997680 

997667 
997654 
997641 
997628 
997614 

Sin. 



.18 
.18 
.18 
.18 
.18 
.20 
.18 
.18 
.20 
.18 

.20 

.18 
.20 
.18 
.20 
.18 
.20 
.20 
.18 
.20 



.20 
.20 
.20 
.20 
.20 
.20 
.20 
.20 

.20 
.20 
.22 
.20 
.20 
.22 
.20 



•22 
.22 
.20 
.22 
.22 
.22 
.22 

.22 
.22 
.22 
.22 
.22 
.22 
.22 
.22 
.22 
.23 

D. i'\ 



8. 941952 
.943404 
.944852 
.946295 

. 947734 
8. 949168 

.950597 
.952021 

.953441 
.954856 

8.956267 
.957674 
.959075 
.960473 
.961866 

8.963255 
. 964639 
.966019 

.967394 
.968766 

8.970133 
.971496 

.972855 
.974209 
. 975560 
8. 976906 
.978248 
.979586 
. 98092 I 
.982251 

8.983577 
.984899 
.986217 
.987532 



8.990149 
.991451 
.992750 
.994045 
.995337 

8. 996624 
.997908 
. 999188 

9. 000465 
.001738 

9. 003007 
. 004272 

.005534 
. 006792 
.008047 

9. 009298 
.010546 
.011790 
.013031 
.014268 

9.015502 
.016732 

.017959 

.019183 

. 020403 

9.021620 



24.20 
24.13 
24.05 
23.98 
23.90 
23.82 

23.73 
23.67 
23.58 
23.52 

23. 45 
23.35 
23.30 
23.22 

23.15 
23.07 
23.00 
22.92 
22.87 
22.78 

22.72 
22.65 
22.57 
22.52 
22.43 
22.37 
22.30 
22.25 
22.17 
22.10 

22.03 

21.97 
21.92 
21.83 
21.78 
21.70 
21.65 
21.58 
21.53 
21.45 
21.40 

21.33 
21.28 
21.22 
21.15 
21.08 
21.03 
20.97 
20.92 
20.85 
20.80 
20.73 
20.68 
20.62 

20.57 
20.50 
20.45 
20.40 
20.33 
20.28 



Cot. 



D. i'\ 



1.058048 
,056596 
.055148 
.053705 
. 052266 

1.050832 
.049403 
.047979 
.046559 
.045144 

1.043733 
.042326 
.040925 
.039527 
.038134 

1.036745 
.035361 
.033981 
. 032606 
.031234 

1.029867 
. 028504 

.027145 
.025791 
.024440 

1.023094 
.021752 
.020414 
.019079 
.017749 

I. 016423 
.015101 
.013783 
.012468 
.011158 

I. 009851 
.008549 
, 007250 
.005955 
. 004663 

1.003376 
.002092 
.000812 

o. 999535 
. 998262 

o. 996993 
.995728 
.994466 
.993208 
.991953 

o. 990702 

.989454 
.988210 
.986969 
.985732 
o. 984498 

.983268 

.982041 
. 980817 
.979597 

o. 978380 



Tan. 



M. 



84° 



COSINES, TANGENTS, AND COTANGENTS 173** 



M. Sin. D. i'', 



9.019235 
.020435 
.021632 
. 022825 
.024016 

9. 025203 
.026386 
.027567 
.028744 
.029918 

9.031089 
.032257 
.033421 
.034582 

.035741 
9. 036896 
. 038048 
.039197 
.040342 
.041485 

9. 042625 
.043762 
.044895 
. 046026 
.047154 

9.048279 
. 049400 
.050519 
.051635 
.052749 

9-053859 
.054966 
.056071 

.057172 
.058271 

9.059367 
.060460 
.061551 
. 062639 
.063724 

9. 064806 
.065885 
.066962 
.068036 
.069107 

9. 070176 
.071242 
. 072306 
.073366 
.074424 

9.075480 
.076533 
.077583 
.078631 
. 079676 

9.080719 
.081759 
. 082797 
.083832 



Cos. 



D. i'^ 



9. 085894 
Cos. 



20,00 
19.95 
19.88 

19.85 
19.78 
19.72 
19.68 
19.62 
19-57 
19.52 

19.47 
19.40 

19-35 
19.32 

19-25 
19.20 

19-15 
19.08 

19-05 
19.00 

18.95 

18.88 
18.85 
18.80 

18.75 
18.68 
18.65 
18.60 
18.57 
18.50 

18.45 
18.42 

18.35 
18.32 
18.27 
18.22 
18.18 
18.13 
18.08 
18.03 

17-98 
17.95 
17.90 

17.85 
17.82 
17.77 

17-73 
17.67 
17.63 
17.60 

17.55 
17-50 
17-47 
17.42 
17-38 
17-33 
17.30 

17.25 
17.20 
17.17 

D. I''. 



9. 997614 
.997601 
.997588 
.997574 
.997561 

9-997547 
.997534 
.997520 
.997507 
.997493 

9. 997480 
.997466 
.997452 
.997439 
.997425 

9.997411 

.997397 
.997383 
.997369 
.997355 

9-997341 
.997327 
.997313 
.997299 

.997285 
9- 997271 
.997257 
.997242 
.997228 
.997214 

9- 997199 
.997185 
.997170 
.997156 
.997141 

9.997127 
.997112 
.997098 
.997083 
.997068 

9.997053 
.997039 

. 997024 
.997009 
.996994 
9-996979 
.996964 
.996949 

.996934 
.996919 

9-996904 



.996874 
.996858 
.996843 

9.996828 
.996812 
.996797 
.996782 
.996766 

9-996751 

Sin, * 



.23 
.22 

.23 
.22 

.23 
.22 

.23 
.22 

.23 
.23 
.22 

.23 
.23 
.23 
.23 
.23 
.23 
.23 

.23 
.23 
.23 
•23 
.23 
.23 
.25 
.23 
.23 
.25 

.23 
.25 
.23 
^25 

.23 
.25 
.23 
.25 
.25 
.25 

.23 
.25 
.25 
.25 
.25 
.25 
.25 
.25 
.25 
.25 

.25 
.25 
.27 

.25 
.25 

.27 

.25 
.25 
.27 
.25 

D. r". 



Tan. D. i" 



9.021620 
. 022834 
. 024044 
.025251 
.026455 

9.027655 
.028852 
, 030046 
.031237 
.032425 

9. 033609 
.034791 

.035969 
.037144 
.038316 

9.039485 
. 040651 
.041813 

.042973 
.044130 

9.045284 
•046434 
.047582 
.048727 
. 049869 

9.051008 
.052144 

.053277 
.054407 

.055535 
9-056659 
.057781 
.058900 
.060016 
.061130 
9. 062240 
.063348 
.064453 
.065556 
.066655 

9.067752 



.069938 
.071027 
,072113 
9.073197 
.074278 
.075356 
.076432 
.077505 

9-078576 
.079644 
.080710 
.081773 
.082833 

9.083891 
.084947 
.086000 
. 087050 



9.089144 
Cot. 



20.23 
20.17 
20.12 
20,07 
20.00 
19.95 
19-90 
19-85 
19.80 

19-73 
19.70 
19.63 
19-58 
19.53 
19.48 
19.43 
19.37 
19.33 
19.28 

19-23 

19.17 
19-13 
19.08 
19-03 
18.98 

18.93 
18.88 
18.83 
18.80 
18.73 
18.70 
18.65 
18.60 

18.57 
18.50 

18.47 
18.42 
18.38 
18.32 
18.28 

18.23 
18.20 
18.15 
18.10 
18.07 
18.02 
17.97 

17.93 

17.88 

17.85 
17.80 
17-77 
17-72 
17.67 
17.63 
17.60 
17.55 
. 17.50 
17.47 
17.43 

D. i'\ 



Cot. 



0.978380 
.977166 
.975956 
.974749 
•973545 

0-972345 
.971148 
.969954 
.968763 
.967575 

0.966391 
.965209 
.964031 
.962856 
.961684 

0.960515 
.959349 
.958187 
.957027 
.955870 

0.954716 
.953566 
.952418 
.951273 

.950131 
o. 948992 
.947856 
.946723 
.945593 
.944465 

0.943341 
.942219 
.941100 
.939984 
.938870 

0.937760 
.936652 
.935547 
.934444 
.933345 

0.932248 

.931154 
. 930062 

.928973 
.927887 
o. 926803 
.925722 
.924644 
.923568 
.922495 

0.921424 
. 920356 
. 919290 
.918227 

.917167 

0.9I6I09 

.915053 

,914000 

.912950 

.911902 

o. 910856 

Tan. 



83" 



LOGARITHMIC SINES 



172^ 



M. 



7 
8 

9 

10 
II 
12 
13 
14 
15 
16 

17 
18 

19 
so 
21 
22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

48 
49 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9.085894 
.086922 
.087947 
. 088970 
. 089990 

9.091008 
. 092024 

.093037 
.094047 
.095056 

9.096062 
.097065 
. 098066 
.099065 
. 100062 

9. 101056 
. 102048 
. 103037 
. 104025 
. 105010 



9. 105992 
. 106973 
.107951 
. 108927 
. 109901 

9. I 10873 
.111842 
.112809 
.113774 
.114737 

9. I 15698 
.116656 
.117613 
.118567 
.119519 

9. 120469 
.121417 
. 122362 
. 123306 
. 124248 

9. 125187 
.126125 
.127060 
. 127993 
. 128925 

9. 129854 
. 130781 
. 131706 
. 132630 
.133551 

9. 134470 
.135387 
. 136303 
.137216 
. 138128 

9. 139037 
. 139944 
. 140850 

. 141754 

. 142655 

9. 143555 

Cos. 



D. I" 



17.13 
17.08 

17.05 
17.00 
16.97 

16.93 
16.88 
16.83 
16.82 
16.77 

16.72 
16.68 
16.65 
16.62 
16.57 
16.53 
16.48 

16.47 
16.42 

16.37 

16.35 
16.30 
16.27 
16.23 
16.20 
16.15 
16. 12 
16.08 
16.05 
16.02 

15.97 
15.95 
15-90 
15.87 
15.83 
15.80 
15.75 
15.73 
15.70 
15.65 

15.63 
15.58 
15.55 
15.53 
15.48 
15.45 
15.42 
15.40 
15.35 
15.32 

15.28 
15.27 
15.22 
15.20 

15.15 
15.12 
15.10 
15.07 
15.02 
15.00 

D. 1". 



Cos. 



D. I" 



9.996751 

996735 
996720 

996704 



996673 
996657 
996641 
996625 
996610 

996594 
996578 
996562 
996546 
996530 
996514 



996482 
996465 
996449 

996433 
996417 
996400 

996384 
996368 

996351 
996335 
996318 
996302 
996285 

996269 
996252 

996235 
996219 
996202 
996185 
996168 
996151 
996134 
9961 17 

996100 
996083 
996066 
996049 
996032 
996015 
995998 
995980 
995963 
995946 

995928 
99591 I 
995894 
995876 
995859 
995841 

995823 
995806 
995788 
995771 
995753 

Sin. 



.27 

.25 
.27 

.27 
.25 
.27 
.27 
.27 
.25 
.27 

.27 
.27 
.27 
.27 
.27 
.27 
.27 
.28 
.27 
.27 

.27 
.28 
.27 
• 27 

.28 

.27 
.28 
.27 
.28 
.27 
.28 
.28 
.27 
.28 
.28 
.28 
.28 
.28 
.28 
.28 

.28 
.28 
.28 
.28 
.28 
.28 
.30 
.28 
.28 
.30 
.28 
.28 
.30 
.28 
.30 
.30 
.28 
.30 
.28 
.30 



D.I" 



Tan. 



9.089144 
.090187 
.091228 
. 092266 
. 093302 

9- 094336 
.095367 
.096395 
. 097422 
.098446 

9. 099468 
. 100487 
. 101504 
.102519 
. 103532 

9. 104542 
. 105550 
. 106556 

. 107559 
. 108560 

9. 109559 
.110556 
.111551 
.112543 
.113533 

9. 1 1452 1 
.115507 
.116491 
.117472 
.118452 

9-119429 
. 120404 

.121377 
. 122348 

.123317 
9. 124284 

. 125249 
.126211 
.127172 
.128130 

9. 129087 
. 13004 I 
. 130994 
. 131944 
. 132893 

9. 133839 
. 134784 
. 135726 
. 136667 
. 137605 

9- 138542 
. 139476 
. 140409 
. 141340 
. 142269 

9. 143196 
.144121 
. 145044 
. 145966 
. 146885 

9. 147803 

Cot. 



D. I". 



17.38 
17.35 
17.30 
17.27 
17.23 
17.18 

17.13 
17. 12 
17.07 
17.03 

16.98 

16.95 
16.92 
16.88 
16.83 
16.80 
16.77 
16.72 
16.68 
16.65 

16.62 
16.58 
16.53 
16.50 

16.47 
16.43 
16.40 
16.35 
16.33 
16.28 

16.25 
16.22 
16.18 
16.15 
16. 12 
16.08 
16.03 
16.02 
15.97 
15.95 

15.90 
15.88 
15.83 
15.82 
15.77 
15.75 
15.70 
15.68 
15.63 
15.62 

15.57 
15.55 
15.52 
15.48 
15.45 
15.42 
15.38 
15.37 
15.32 
15.30 

D. i'\ 



Cot. 



o. 910856 
.909813 
.908772 

.907734 

.906698 

o. 905664 

.904633 
.903605 
.902578 
.901554 
0.900532 
.899513 



0.895458 
.894450 
.893444 
.892441 
. 891440 

o. 890441 

.889444 
. 888449 

.887457 

.886467 
0.885479 
.884493 
.883509 
. 882528 
. 881548 

o. 880571 

. 879596 
.878623 
.877652 
.876683 
0.875716 
.874751 
.873789 

. 872828 
.871870 

0.870913 
.869959 

. 869006 

.868056 

.867107 

o. 866161 

.865216 
.864274 
.863333 
.862395 

o. 861458 
.860524 

.859591 
.858660 

.857731 

o. 856804 

.855879 
.854956 
.854034 
.853115 
0.852197 

Tan. 



'97 



82" 



COSINES, TANGENTS, AND COTANGENTS 171° 



Sin. 



143555 
144453 
145349 
146243 
147136 
148026 
148915 
149802 
150686 
151569 

152451 
153330 
154208 
155083 
155957 
156830 
157700 
158569 
159435 
160301 

161 164 
162025 
162885 

163743 
164600 

165454 
166307 
167159 
168008 



169702 

170547 
171389 
172230 
173070 
173908 
174744 
175578 
176411 
177242 

178072 
178900 
179726 
I 8055 I 

181374 
182196 
183016 

183834 
184651 
185466 

186280 
187092 

187903 
188712 
189519 
190325 
191 130 

191933 
192734 

193534 
194332 

Cos. 



D. I''. 



4.97 
4.93 
:4.9o 
4.88 
4.83 
4.82 
4.78 
4.73 
4.72 
4.70 

4.65 
4.63 
4.58 
4.57 
4.55 
4.50 
4.48 
4.43 
4.43 
:4.38 

4.35 
4.33 
4.30 
4.28 
4.23 
4.22 
4.20 
4.15 
4.13 
4.10 

4.08 
4.03 
4.02 
4.00 
3-97 
3-93 
3.90 
3.88 
3.85 
3.83 
3.80 
3.77 
3.75 
3.72 
3-70 
3.67 
3.63 
3.62 
3.58 
3.57 

3.53 
3.52 
3.48 
3.45 
3.43 
3.42 
3.38 
3.35 
3.33 
3.30 



D. 1" 



Cos. 



9- 995753 
.995735 
.995717 
.995699 
. 995681 

9. 995664 
.995646 
.995628 
. 995610 
.995591 

9-995573 
.995555 
.995537 
.995519 
.995501 

9. 995482 
.995464 
.995446 
.995427 
.995409 

9- 995390 
.995372 
.995353 
.995334 
. 995316 

9-995297 
.995278 
.995260 

.995241 
.995222 

9-995203 
.995184 
.995165 
.995146 
.995127 

9.995108 
.995089 
.995070 
.995051 
.995032 

9-995013 
.994993 
.994974 
.994955 
.994935 

9- 994916 
.994896 
.994877 
.994857 
.994838 

9.994818 
.994798 
.994779 
.994759 
.994739 

9- 994720 
.994700 
. 994680 
.994660 
.994640 

9. 994620 

Sin. 



D. I' 



.30 

.30 
.30 
.30 
.28 
.30 
.30 
.30 
.32 
.30 

.30 
.30 
.30 
.30 
.32 
.30 
.30 
.32 
.30 
.32 

.30 
.32 
.32 
.30 
.32 
.32 
.30 
.32 
.32 
.32 

.32 
.32 
.32 
.32 
.32 
.32 
.32 
.32 
.32 
.32 

.33 
.32 
.32 
.33 
.32 
.33 
.32 
.33 
.32 
.33 

.33 
.32 
.33 
.33 
.32 
.33 
.33 
.33 
.33 
.33 

D. I". 



Tan. 



147803 
148718 
149632 
150544 
151454 
152363 
153269 

154174 
155077 
155978 

156877 
157775 
158671 
159565 
160457 
161347 
162236 
163123 
164008 
164892 

165774 
166654 
167532 
168409 
169284 
170157 
171029 
171899 
172767 
173634 
174499 
175362 
176224 
177084 
177942 
178799 

179655 
180508 
181360 
182211 

183059 
183907 
184752 

185597 
186439 
187280 
188120 



189794 
190629 

191462 
192294 
193124 

193953 
194780 
195606 
196430 
197253 
198074 
198894 
199713 

Cot. 



D. I' 



5.25 
5-23 
5-20 
5-17 
5-15 
5.10 
15.08 
5-05 
5.02 
4.98 

4.97 
4.93 
4.90 
4.87 
4.83 
4.82 
4.78 
4.75 
4.73 
4.70 
4.67 
4-63 
4.62 
4.58 
4.55 
4.53 
4-50 
4.47 
4.45 
4.42 

4.38 
4.37 
4.33 
4.30 
4.28 
4-27 
4.22 
4.20 
4.18 
4.13 

4.13 

4.08 
4.08 
4.03 
4.02 
4.00 
3.97 
3-93 
3-92 
3.88 

3.87 
3-83 
3.82 
3-78 
3-77 
3-73 
3.72 
3.68 
3.67 
3.65 



D. I". 



Cot. 



0.852197 
. 851282 
.850368 
.849456 
.848546 

0.847637 
.846731 
.845826 

.844923 
.844022 

0.843123 
.842225 
.841329 
.840435 
.839543 

0.838653 

.837764 
.836877 
.835992 
.835108 

o. 834226 
.833346 
.832468 

.831591 

.830716 

o. 829843 

.828971 
.828101 
.827233 
.826366 

0.825501 
.824638 
.823776 

.822916 

.822058 

0.821201 

.820345 
. 819492 
.818640 

.817789 

0.816941 
.816093 

.815248 
.814403 
.813561 

o. 812720 
.811880 
.811042 
.810206 

.809371 
0.808538 

. 807706 
.806876 
.806047 
. 805220 

0.804394 
.803570 
.802747 

. 801926 

.801106 

o. 800287 

Tan. 



8i<= 



LOGARITHMIC SINES 



170" 



M. 



Sin. 



D. V' 



12 
13 
14 
15 
16 

17 
18 

19 
20 
21 

22 
23 
24 
25 
26 

^Z 
28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

47 
48 

49 



9. 194332 
. 195129 
.195925 
.196719 
.197511 

9. 198302 
. 19909 I 

. 199879 
.200666 
. 201451 

9. 202234 
.203017 
.203797 
.204577 
.205354 

9. 206131 
.206906 
. 207679 
.208452 
. 209222 

9. 209992 
.210760 
.211526 
.212291 

.213055 
9.213818 

.214579 
.215338 
.216097 
.216854 

9.217609 
.218363 
.219116 
.219868 
.220618 
9.221367 
.222115 
.222861 
. 223606 
.224349 
9. 225092 
.225833 
.226573 
.227311 
. 228048 
9. 228784 
.229518 
. 230252 
.230984 
.231715 



50 9.232444 

51 .233172 
.233899 
.234625 
.235349 

9. 236073 
.236795 
.237515 
.238235 
.238953 

9.239670 

Cos. 



Cos. 



13.28 
13.27 

13.23 
13.20 
13.18 
13.15 
13.13 
13.12 
13.08 
13.05 

13.05 
13.00 
13.00 
12.95 
12.95 
12.92 
12.88 
12.88 
12.83 
12.83 

12.80 
12.77 
12.75 
12.73 
12.72 
12.68 
12.65 
12.65 
12.62 
12.58 

12.57 
12.55 
12.53 
12.50 
12.48 
12.47 
12.43 
12.42 
12.38 
12.38 

12.35 
12.33 
12.30 
12.28 
12.27 
12.23 
12.23 
12.20 
12.18 
12.15 

12.13 
12.12 
12.10 
12.07 
12.07 
12.03 
12.00 
12.00 
11.97 
11.95 

D. I". 



D. I''. 



9. 994620 
, 994600 
.994580 
.994560 
.994540 

9.994519 
.994499 
.994479 
.994459 
.994438 

9.994418 
.994398 
.994377 
.994357 
.994336 

9.994316 
.994295 
.994274 
.994254 
.994233 

9.994212 
.994191 
.994171 
.994150 
.994129 
9.994108 
.994087 
. 994066 
. 994045 
.994024 

9. 994003 
.993982 
.993960 
.993939 
.993918 

9- 993897 
.993875 
.993854 
.993832 
.993811 

9.993789 
.993768 
.993746 
.993725 
. 993703 

9.993681 
.993660 
.993638 
.993616 

.993594 

9-993572 
.993550 
.993528 
.993506 
.993484 

9. 993462 
.993440 
.993418 
.993396 
.993374 

9.993351 



Tan. 



.33 
.33 
.33 
.33 
.35 
.33 
.33 
.33 
.35 
.33 

.33 
.35 
.33 
.35 
.33 
.35 
.35 
.33 
.35 
.35 

.35 
.33 
.35 
.35 
.35 
.35 
.35 
.35 
.35 
.35 

.35 
.37 
.35 
.35 
.35 
.37 
.35 
.37 
.35 
.37 

.35 
.37 
.35 
.37 
.37 
.35 
.37 
.37 
.37 
.37 

.37 
.37 
.37 
.37 
.37 
.37 
.37 
.37 
.37 
.38 



D. i" 



9. 199713 
. 200529 
.201345 
.202159 
.202971 

9.203782 
.204592 
. 205400 
. 206207 
.207013 

9.207817 
.208619 
. 209420 
,210220 
.211018 

9.211815 
.212611 
.213405 
.214198 
.214989 

9.215780 
.216568 
.217356 
.218142 
.218926 

9. 219710 
. 220492 
.221272 
.222052 
. 222830 

9. 223607 
. 224382 
.225156 
. 225929 
. 226700 

9.227471 
.228239 
. 229007 
.229773 
.230539 

9.231302 

. 232065 
. 232826 
.233586 
.234345 
9.235103 
.235859 
.236614 
.237368 
. 238120 

9.238872 
. 239622 

.240371 

.241118 

.241865 

9. 242610 

.243354 
.244097 

.244839 

.245579 

9. 246319 



Sin. 



D. i'^ 



Cot. 



13.60 
13.60 
13.57 
13-53 
13.52 
13.50 
13.47 
13.45 
13.43 
13.40 

13.37 
13.35 
13.33 
13.30 
13.28 
13.27 
13.23 
13.22 
13.18 
13.18 

13.13 
13.13 
13.10 
13.07 
13.07 
13.03 
13.00 
13.00 
12.97 
12.95 

12.92 
12.90 
12.88 
12.85 
12.85 
12.80 
12.80 
12.77 
12.77 
12.72 

12.72 
12.68 
12.67 
12.65 
12.63 
12.60 
12.58 
12.57 
12.53 
12.53 

12.50 
12.48 
12.45 
12.45 
12.42 
12.40 
12.38 
12.37 
12.33 
12.33 



Cot. 



D. r' 



o. 800287 

.799471 
.7Q8655 

.797841 
.797029 
0.796218 
.795408 
. 794600 

.793793 
.792987 

0.792183 
.791381 
.790580 
. 789780 
. 788982 

0.788185 
.787389 
.786595 
.785802 
.785011 

o. 784220 

.783432 
.782644 

.781858 

.781074 
o. 780290 

.779508 
.778728 
.777948 
.777170 

0.776393 
.775618 

.774844 
.774071 
.773300 
0.772529 
.771761 
.770993 
.770227 
. 769461 

o. 768698 

.767935 
.767174 
.766414 
.765655 
0.764897 
.764141 
.763386 

. 762632 
. 761880 

0.76II28 

.760378 
.759629 



60 

li 

57 
56 
55 
54 
53 
52 
51 

50 

48 
47 
46 

45 
44 
43 
42 
41 
40 
39 
38 
37 
36 
35 
34 
33 
32 
31 
30 
29 
28 
27 
26 

25 
24 

23 



.758135 
0.757390 
.756646 
.755903 
.755161 
.754421 
o. 753681 



18 

17 
16 

15 
14 
13 
12 



Tan. 



99° 



|M.i 
"80° 



COSINES, TANGENTS, AND COTANGENTS 169^ 



Sin. 



9. 239670 
. 240386 
.241101 
.241814 
. 242526 

9- 243237 
.243947 
.244656 

.245363 
.246069 

9.246775 
.247478 
.248181 
.248883 

.249583 
9. 250282 
. 250980 
.251677 
.252373 
.253067 

9.253761 
.254453 
.255144 
.255834 
.256523 

9. 2572 I I 
.257898 
.258583 
. 259268 

.259951 
9.260633 
.261314 
,261994 
. 262673 
.263351 
9. 264027 
.264703 

.265377 
,266051 
. 266723 

9- 267395 
.268065 
.268734 
. 269402 
.270069 

9.270735 
.271400 
,272064 
,272726 
.273388 

9.274049 
.274708 

.275367 
. 276025 
. 276681 

9.277337 
.277991 
.278645 

.279297 

.279948 

9.280599 

Cos. 



D. I". 



11.93 
11.92 
11.88 
11.87 
11.85 
11.83 
11.82 
11.78 
11.77 
11.77 

11.72 
11.72 
11.70 
11.67 
11.65 
11.63 
11.62 
11.60 
11.57 
11.57 

11.53 
11.52 
11.50 
11.48 
11.47 
11.45 
11.42 
11.42 
11.38 
11.37 

11.35 
11.33 
11.32 
11.30 
11.27 
11.27 
11.23 
11.23 
11.20 
11.20 

11.17 
11.15 
11.13 
II. 12 
II. 10 
11.08 
11.07 
11.03 
11.03 
11.02 

10.98 
10.98 
10.97 

10.93 
10.93 
10.90 
10.90 
10.87 
10.85 
10.85. 

D. l'\ 



Cos, 



9.993351 
.993329 
.993307 
.993284 
.993262 

9.993240 
.993217 
.993195 
.993172 
.993149 

9.993127 
.993104 
,993081 

.993059 
.993036 
9.993013 
.992990 
.992967 
.992944 
.992921^ 

9.992898 

.992875 
.992852 
. 992829 
.992806 
9.992783 
.992759 
,992736 

.992713 
. 992690 

9.992666 

.992643 
,992619 

.992596 
.992572 

9.992549 
.992525 
.992501 
.992478 
.992454 

9.992430 
.992406 
,992382 
.992359 
.992335 

9.992311 
.992287- 
.992263 

.992239 
.992214 

9.992190 
.992166 
.992142 
.992118 

.992093 
9. 992069 

.992044 
. 992020 
.991996 
.991971 
9.991947 

Sin. 



D. 1" 



.37 
.37 
.38 
.37 
•37 
.38 
.37 

•3? 
.38 

.37 

.38 

.38 

.37 

•3? 

•3? 
.38 

.38 

.38 

.38 

.38 

•3? 
.38 
.38 
.38 
.38 
,40 
.38 
.38 
.38 
,40 

.38 
.40 
.38 
.40 
.38 
.40 
.40 
.38 
.40 
.40 

.40 
.40 
.38 
,40 
,40 
.40 
,40 
,40 
.42 
,40 

.40 
,40 
,40 
.42 
,40 
,42 
.40 
.40 
.42 
.40 

D. I''. 



Tan. 



9.246319 
.247057 
.247794 
.248530 
. 249264 

9.249998 
.250730 
.251461 
,252191 
, 252920 

9.253648 
.254374 
.255100 
.255824 

.256547 
9. 257269 
.257990 
.258710 
.259429 
. 260146 

9. 260863 
.261578 
. 262292 
. 263005 
.263717 

9. 264428 
.265138 
.265847 
.266555 
, 267261 

9. 267967 
,268671 

.269375 
. 270077 
,270779 
9.271479 
,272178 
,272876 

.273573 
, 274269 

9.274964 
.275658 
.276351 
.277043 

.277734 

9.278424 

.279113 

. 279801 



,281174 

9.281858 
,282542 
.283225 
.283907 
.284588 

9.285268 
.285947 
. 286624 
.287301 
.287977 

9. 288652 

Cot. 



D. I" 



2.30 

2.28 

2,. 77 

2.23 

2.23 

2.20 

2.18 

2.17 

15 

13 

2.10 

12,10 

2.07 

2.05 

2.03 

2.02 

2.00 

98 

95 

95 

92 

90 

88 

?7 
85 
83 
82 
80 
77 
77 

73 
73 
70 

65 
63 
62 
60 

58 

57 
55 
53 
52 
50 
48 
47 
45 
43 
40 

40 

38 
37 
35 
33 
32 
28 
28 
27 
25 



D. I" 



Cot. 



0.753681 

.752943 
, 752206 
.751470 
.750736 
o. 750002 
,749270 

.748539 
,747809 
, 747080 

0.746352 
.745626 
.744900 
,744176 

.743453 
0.742731 
, 742010 
,741290 
.740571 
.739854 

0.739137 
.738422 
.737708 
.736995 
.736283 

0.735572 
.734862 
.734153 
.733445 
.732739 

0.732033 
.731329 
.730625 

.729923 
,729221 

0.728521 
,727822 
,727124 
,726427 
.725731 

o. 725036 

.724342 
.723649 
.722957 

.722266 

0.721576 
, 720887 
, 720199 
.719512 
.718826 

o. 718 142 

.717458 
.716775 
.716093 

.715412 

0.714732 

.714053 

.713376 

.712699 
. 712023 

0.711348 

Tan. 



79= 



ir 



LOGARITHMIC SINES 



i68 



M. 



Sin. 



2 
3 
4 
5 
6 

7 
8 

9 
lo 
n 

IC 

13 
14 
15 
i6 

17 
i8 

19 

20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 



9. 280599 
.281248 
.281897 
.282544 
.283190 

9.283836 
. 284480 
.285124 
.285766 
.286408 

9. 287048 



D. I" 



.2! 
.288964 
.289600 
9. 290236 
. 290870 
.291504 
.292137 
. 292768 

9- 293399 
. 294029 
. 294658 
. 295286 
.295913 

9. 296539 
.297164 
.297788 
.298412 
.299034 

9. 299655 
.300276 
. 300895 

.301514 
.302132 
9.302748 
.303364 
.303979 
.304593 
.305207 

9-305819 
.306430 
.307041 
. 307650 
. 308259 

9.308867 

.309474 
.310080 
.310685 
.311289 

9-311893 
.312495 
.313097 
.313698 
.314297 
9-314897 
315495 
316092 
316689 
317284 



60 9-317879 
Cos. 

XOX^ 



10.82 
10.82 
10.78 
10.77 
10.77 
10.73 
10.73 

10.70 
10.70 
10.67 

10.67 
10.63 
10.63 
10.60 
10.60 

10.57 
10.57 
10.55 
10.52 
10.52 

10.50 
10.48 

10.47 
10.45 
10.43 

10.42 
10.40 
10.40 

10.37 
10.35 

10.35 
10.32 
10.32 
10.30 
10.27 
10.27 
10.25 
10.23 
10.23 
10.20 

10.18 
10.18 
10.15 
10.15 
10.13 

10.12 
10.10 

10.08 
10.07 
10.07 

10.03 
10.03 

10.02 

9.98 

10.00 
9-97 
9.95 
9.95 
9-92 
9.92 

D. 1". 



Cos. 



D.I'' 



9.991947 
.991922 
.991897 

.991873 
. 991848 
9.991823 
.991799 
.991774 
.991749 
.991724 

9. 991699 
.991674 
.991649 
.991624 
.991599 

9.991574 
.991549 
.991524 
.991498 

.991473 

9. 991448 
.991422 
.991397 
.991372 
. 991346 

9.991321 

.991295 
.991270 
.991244 
.991218 

9.991193 
.991167 
.991141 
.991115 
.991090 

9.991064 
.991038 
.991012 
. 990986 
.990960 

9. 990934 
. 990908 



.990855 
. 990829 

9. 990803 
.990777 
.990750 
.990724 
.990697 

9.990671 

.990645 
.990618 

.990591 
.990565 
9-990538 
.990511 
.990485 
.990458 
.990431 
I 9- 990404 

Sin. 



.42 
.42 
.40 
.42 
.42 
.40 
.42 
.42 
.42 
.42 

.42 
.42 
.42 
.42 
.42 
.42 
.42 
-43 
.42 
.42 

.43 
.42 
.42 
.43 
.42 
-43 
.42 

.43 
-43 
.42 

.43 
-43 
-43 
.42 
.43 
• 43 
.43 
.43 
.43 
-43 

-43 
.43 
.45 
.43 
.43 
.43 
.45 
.43 
.45 
.43 

.43 
.45 
.45 
.43 
.45 
.45 
.43 
.45 
.45 
.45 

D. I", 



Tan. 



9. 288652 
. 289326 



.290671 
.291342 
9.292013 
. 292682 
. 293350 
.294017 
. 294684 

9- 295349 
. 296013 
. 296677 

. 297339 
.298001 
9. 298662 
■ . 299322 
. 299980 
. 300638 
.301295 

9.301951 
. 302607 
.303261 
.303914 
. 304567 

9.305218 
.305869 

. 306519 
.307168 
.307816 

9. 308463 
.309109 
.309754 
.310399 
.311042 

9.311685 
.312327 
.312968 
.313608 
.314247 

9.314885 
.315523 
.316159 
.316795 
• 317430 

9.318064 
.318697 
. 319330 
.319961 
.320592 

9. 321222 
.321851 
.322479 
.323106 

- 323733 
9.324358 
.324983 
. 325607 
.326231 
.326853 
9. 327475 

Cot. 



D. i'\ 



Cot. 



11.23 
11.22 
11.20 
11.18 
11.18 
11.15 
11.13 
II. 12 
II. 12 
11.08 

11.07 
11.07 
11.03 
11.03 
11.02 
11.00 

10.97 
10.97 

10.95 
10.93 

10.93 
10.90 
10.88 
10.88 
10.85 
10.85 
10.83 
10.82 
10.80 
10.78 

10.77 
10.75 
10.75 
10.72 
10.72 
10.70 
10.68 
10.67 
10.65 
10.63 

10.63 
10.60 
10.60 
10.58 
10.57 
10.55 
10.55 
10.52 
10.52 
10.50 

10.48 
10.47 
10.45 
10.45 
10.42 
10.42 
10.40 
10.40 

10.37 
10.37 

D. i'\ 



0.711348 
.710674 
.710001 

. 709329 
. 708658 
0.707987 
.707318 
. 706650 
.705983 
.705316 

o. 704651 
.703987 
.703323 
. 702661 

. 701999 

o. 701338 

. 700678 

. 700020 

.699362 
.698705 

o. 698049 

.697393 
.696739 
.696086 

.695433 

o. 69^782 

.694131 
.693481 
.692832 
.692184 

0.691537 

.690891 
. 690246 
.689601 
.688958 
0.688315 
.687673 

. 687032 
.686392 

.685753 

0.685115 
.684477 
.683841 
.683205 
.682570 

o. 681936 

.681303 

. 680670 
. 680039 
. 679408 

0.678778 
.678149 

.677521 

. 676894 

. 676267 

0.675642 

.675017 

.674393 
.673769 

.673147 
0.672525 

Tan. 



78° 



12^ COSINES, TANGENTS, AND COTANGENTS 167* 



M. Sin. D. \". Cos. D. V. Tan. D. \" . Cot. 






9.317879 


I 


.318473 


2 


.319066 


3 


.319658 


4 


. 320249 


5 


9. 320840 


6 


.321430 


7 


. 322019 


8 


.322607 


9 


.323194 


10 


9.323780 


II 


.324366 


12 


.324950 


13 


.325534 


14 


.326117 


15 


9. 326700 


16 


.327281 


17 


.327862 


18 




19 


.329021 


20 


9.329599 


21 


.330176 


22 


.330753 


23 


.331329 


24 


.331903 


25 


9.332478 


26 


• 333051 


^Z 


.333624 


28 


.334195 


29 


.334767 


30 


9. 335337 


31 


.335906 


32 


.336475 


33 


.337043 


34 


.337610 


11 


9.338176 


. 338742 


37 


.339307 


3« 


.339871 


39 


.340434 


40 


9.340996 


41 


.341558 


42 


.342119 


43 


.342679 


44 


.343239 


45 


9- 343797 


4b 


.344355 


47 


.344912 


48 


.345469 


49 


.346024 


50 


9.346579 


51 


.347134 


52 


.347687 


53 


.348240 


54 


.348792 


55 


9.349343 


5b 


.349893 


5Z 


.350443 


5» 


.350992 


59 


.351540 


bo 


9. 352088 



Cos. 



9.90 

9.88 
9.87 
9.85 
9.85 
9.83 
9.82 
9.80 
9.78 
9-77 

9.77 
9.73 
9.73 
9.72 
9.72 
9.68 
9.68 
9.67 
9-65 
9.63 
9.62 
9.62 
9.60 
9.57 
9.58 
9-55 
9.55 
9-52 
9-53 
9.50 

9.48 
9.48 
9.47 
9-45 
9.43 
9.43 
9.42 
9.40 
9.38 
9.37 

9.37 
9.35 
9.33 
9.33 
9.30 
9-30 
9.28 
9.28 
9.25 
9.25 

9.25 
9.22 
9.22 
9.20 
9.18 



9.13 



D. i". 



990404 

990378 

990351 
990324 
990297 
990270 

990243 
990215 
990188 
990161 

990134 
990107 

990079 
990052 
990025 

989997 
989970 
989942 
989915 



989777 
989749 
989721 
989693 
989665 
989637 
989610 

989582 
989553 
989525 
989497 

989469 
989441 
989413 
989385 
989356 
989328 

989300 
989271 
989243 
989214 



989157 
989128 
989100 
989071 



989014 



988927 
988898 
988869 
988840 



988753 
988724 

Sin. 



D. \'> 



9- 327475 
. 328095 
.328715 
.329334 
.329953 

9- 330570 
.331187 
.331803 
.332418 
.333033 

9.333646 
.334259 
.334871 
. 335482 
. 336093 

9. 336702 

.337311 
.337919 
.338527 
.339133 

9. 339739 
. 340344 
.340948 
.341552 
.342155 

9.342757 
.343358 
. 343958 
.344558 
.345157 

9-345755 
. 346353 
. 346949 
.347545 
. 348141 

9.348735 
. 349329 
.349922 
.350514 
.351106 

9.351697 
. 352287 
.352876 
.353465 
. 354053 

9. 354640 
.355227 
.355813 
.356398 
.356982 

9.357566 
.358149 
.358731 
.359313 
.359893 

9. 360474 

. 361053 
.361632 
.362210 
.362787 
9- 363364 

Cot. 



10.33 
10.33 
10.32 
10.32 
10.28 
10.28 
10.27 
10.25 
10.25 
10.22 

10.22 
10.20 
10.18 
10.18 
10.15 
10.15 
10.13 
10.13 
10. 10 
10. 10 

10.08 
10.07 
10.07 
10.05 
10.03 
10.02 
10.00 
10.00 
9.98 
9.97 

9-97 
9-93 
9.93 
9.93 
9.90 
9.90 
9.88 
9.87 
9.87 
9.85 

9.83 
9.82 
9.82 
9.80 
9.78 
9.78 
9.77 
9-75 
9.73 
9.73 
9.72 
9.70 
9.70 
9.67 
9.68 
9.65 
9-65 
9.63 
9.62 
9.62 

D. \". 



o. 672525 

.671905 
.671285 
, 670666 
. 670047 
o. 669430 

.668813 
.668197 
.667582 

.666967 

0.666354 
.665741 
.665129 
.664518 
.663907 

o. 663298 

.662689 
.662081 
.661473 
.660867 

0.660261 
.659656 
. 659052 
.658448 

.657845 
0.657243 

. 656642 
. 656042 

.655442 
.654843 

0.654245 
.653647 
.653051 
.652455 
.651859 

0.651265 
.650671 
. 650078 
. 649486 
.648894 

0.648303 
.647713 
.647124 
.646535 
.645947 

0.645360 

.644773 

.644187 
. 643602 
.643018 

0.642434 
.641851 
.641269 
.640687 
.640107 

0.639526 
.638947 
.638368 
.637790 
.637213 

o. 636636 

Tan. 



102" 



It 



13" 



LOGARITHMIC SINES 



i66" 



M. 



13 
14 
15 
16 
17 
18 

19 
20 
21 
22 
23 
24 
25 
26 
27 
28 

29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 

49 

50 
51 
52 
53 
54 
55 
56 

fs 



Sin. 



9. 352088 
.352635 
.353181 
.353726 
.354271 

9-354815 
.355358 
.355901 
.356443 
.356984 

9. 357524 
.358064 
.358603 
.359141 
.359678 

9.360215 
. 360752 
.361287 
.361822 
.362356 

9.362889 
.363422 
. 363954 
.364485 
.365016 

9- 365546 
. 366075 
. 366604 
.367131 
.367659 

9.368185 
.368711 
. 369236 
.369761 
.370285 

9. 370808 
.371330 
.371852 
.372373 
.372894 

9.373414 
.373933 
.374452 
.374970 
.375487 

9. 376003 
.376519 
.377035 
.377549 
.378063 

9.378577 
.379089 
.379601 
.380113 
. 380624 

9.381134 
.381643 
.382152 
.382661 
.383168 

9.383675 

Cos. 



D. 1". 



Cos. 



D. i" 



988695 



988607 



988519 
988489 
988460 



988371 
988342 



988252 
988223 
988193 
988163 

988133 
988103 
988073 
988043 
988013 
987983 

987953 
987922 
987892 
987862 

987832 



987771 
987740 
987710 
987679 
987649 
987618 
987588 
987557 
987526 
987496 
987465 
987434 
987403 
987372 

987341 
987310 
987279 
987248 

987217 
987186 

987155 
987124 
987092 
987061 
987030 



986967 
986936 
986904 

Sin. 



.48 
.48 
.50 
.48 
.48 
.50 
.48 
.50 
.48 
.50 

.48 
.50 
.48 

• 50 
.50 
.50 
.48 
.50 
.50 

• 50 

.50 
.50 
.50 
.50 
.50 
.50 
.52 
.50 
.50 
.50 

.52 
.50 
.52 
.50 
.52 
.50 
.52 
.50 
.52 
.52 

.50 

.52 
.52 
.52 
.52 
.52 
.52 
.52 
.52 
.52 

.52 
.52 
.52 
.53 
.52 
.52 
.53 
.52 
.52 
.53 



Tan. 



9. 363364 
. 363940 
.364515 
. 365090 
. 365664 

9. 366237 
.366810 
.367382 
• 367953 
.368524 

9. 369094 
. 369663 
.370232 
.370799 
.371367 

9.371933 
.372499 
.373064 
.373629 
.374193 

9.374756 
.375319 
.375881 
.376442 
.377003 

9.377563 
.378122 
.378681 
.379239 
.379797 

9.380354 
.380910 
.381466 
. 382020 

.382575 
9.383129 
.383682 
.384234 
.384786 
.385337 
9.385888 
.386438 
.386987 
.387536 



9.388631 
.389178 
.389724 
. 390270 
.390815 

9.391360 
.391903 
.392447 
.392989 
.393531 

9.394073 
.394614 
.395154 
.395694 
.396233 

9.396771 

Cot. 



D. 1''. 



9.60 
9.58 
9.58 
9-57 
9.55 
9.55 
9.53 
9.52 
9-52 
9.50 

9-48 
9-48 
9-45 
9-47 
9.43 
9.43 
9.42 
9.42 
9.40 
9.38 

9.38 
9.37 
9.35 
9.35 
9.33 
9.32 
9.32 
9.30 
9.30 
9.28 

9.27 
9.27 
9.23 
9.25 
9.23 
9.22 
9.20 
9.20 
9.18 
9.18 



9.17 
9.15 
9.15 
9.13 
9.12 
9.12 
9.10 
9. 10 
9.08 
9.08 

9.05 
9.07 

9.03 
9.03 
9.03 
9.02 
9.00 
9.00 
8.98 
8.97 

D. 1''. 



Cot. 



0.636636 
. 636060 

.635485 
.634910 
.634336 
0.633763 
.633190 
.632618 
.632047 
.631476 

0.630906 

.630337 
.629768 
.629201 
.628633 
o. 628067 
.627501 
. 626936 
.626371 
. 625807 

o. 625244 

.624681 
.624119 

.623558 

. 622997 
0.622437 
.621878 
.621319 
.620761 
. 620203 

0.619646 
.619090 

.618534 
.617980 
.617425 

0.6 1687 I 
.616318 
.615766 
.615214 
.614663 

0.614112 
.613562 
.613013 
.612464 
.611916 

0.611369 
. 610822 
.610276 
.609730 
.609185 

0.608640 
.608097 

.607553 
,607011 
. 606469 

0.605927 
.605386 
. 604846 
. 604306 
.603767 

o. 603229 

Tan. 



103° 



76° 



14' 



COSINES, TANGENTS, AND COTANGENTS 165° 



M. 



22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 

48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 

60 



Sin. 



9.383675 
.384182 
.384687 
.385192 
.385697 

9.386201 
.386704 
.387207 

.387709 
.388210 

9.388711 
.389211 

.389711 
. 3902 10 
. 390708 
9.391206 
.391703 
.392199 
.392695 
.393191 

9. 393685 
.394179 
.394673 
.395166 
.395658 

9.396150 
.396641 
.397132 
.397621 
.398111 

9.398600 
.399088 

.399575 
.400062 
.400549 
9.401035 
.401520 
. 402005 
.402489 
. 402972 

9.403455 
.403938 
. 404420 
. 404901 
.405382 

9. 405862 
.406341 
. 406820 
.407299 
.407777 

9.408254 
.408731 
. 409207 
. 409682 
.410157 

9.410632 
.411106 

.411579 

.412052 

.412524 

9.412996 

Cos. 



D. 1" 



Cos. 



D. 1" 



9. 986904 
.986873 



986778 
986746 
986714 
986683 
986651 
986619 

986587 

986555 
986523 
986491 

986459 
986427 

986395 
986363 
986331 
986299 

986266 
986234 
986202 
986169 
986137 
986104 
986072 
986039 
986007 
985974 
985942 
985909 
985876 
985843 
98581 I 
985778 
985745 
985712 
985679 



985613 

985580 
985547 
985514 
985480 

985447 
985414 
985381 
985347 
985314 



985247 

985213 
985180 
985146 

9851 13 
985079 

985045 
98501 I 
984978 
984944 

Sin. 



D. i'' 



.52 
.53 
.53 
.52 
.53 
.53 
.52 
.53 
•53 
.53 

•53 
.53 
.53 
.53 
•53 
•53 
.53 
.53 
.53 
.55 

.53 
.53 
.55 
.53 
•55 
•53 
.55 
.53 
.55 
.53 

.55 
" .55 
.55 
.53 
.55 
.55 
.55 
.55 
•55 
•55 

.55 
.55 
.55 
.57 
.55 
.55 
.55 
.57 
.55 
.57 

.55 
.57 
.55 
.57 
.55 
.57 
.57 
•57 
.55 
.57 

D. i". 



Tan. 



9. 396771 
.397309 
.397846 
. 398383 
. 398919 

9.399455 
.399990 
.400524 
.401058 
.401591 

9.402124 
. 402656 
.403187 
.403718 

.404249 
9.404778 
.405308 
.405836 
.406364 
. 406892 

9.407419 
.407945 
.408471 
. 408996 
.409521 

9.410045 
.410569 
.411092 
.411615 
.412137 

9.412658 
.413179 
.413699 
.414219 
.414738 

9.415257 
•415775 
.416293 
.416810 
.417326 

9.417842 
•418358 
.418873 
.419387 
.419901 

9.420415 
.420927 
.421440 
.421952 
.422463 

9.422974 
.423484 
.423993 
.424503 
.425011 

9.425519 
. 426027 

.426534 

.427041 

•427547 

9.428052 

Cot. 



D. 1' 



Cot. 



D. I' 



o. 603229 
. 602691 
.602154 
.601617 
.601081 

0.600545 
.600010 
.599476 
.598942 
.598409 

0.597876 
.597344 
.596813 
.596282 

. 595751 
o. 595222 

.594692 
.594164 
.593636 
.593108 

o. 592581 

.592055 
.591529 
.591004 

.590479 

0.589955 

.589431 

. 588908 

.588385 
.587863 

0.587342 
.586821 
.586301 

.585781 
.585262 
0.584743 
.584225 
.583707 
.583190 
.582674 

0.582158 
.581642 
.581127 
.580613 
.580099 

0.579585 
.579073 
.578560 
.578048 
.577537 

o. 577026 

.576516 
.576007 
.575497 
.574989 
0.574481 

.573973 
.573466 
.572959 
.572453 
0.571948 

Tan. 



104° 



75° 



15" 



LOGARITHMIC SINES 



164° 



M. 



o 

I 
2 
3 
4 
5 
6 

7 
8 

9 

10 
n 
12 
13 
14 
15 
16 

17 
18 

19 

20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 

58 
59 
60 



Sin. 



9.412996 
.413467 
.413938 
. 414408 
.414878 

9-415347 
.415815 
.416283 

.416751 
.417217 

9.417684 
.418150 
.418615 
.419079 

.419544 
9. 420007 
. 420470 
.420933 
.421395 
.421857 

9.422318 
.422778 
.423238 
.423697 
.424156 

9.424615 
.425073 
.425530 
.425987 
.426443 

9. 426899 

.427354 
.427809 
.428263 
.428717 
9.429170 
.429623 
.430075 
.430527 
.430978 

9.431429 
.431879 
.432329 
.432778 
. 433226 

9.433675 
.434122 

.434569 
.435016 
.435462 

9.435908 
.436353 
.436798 
.437242 
.437686 

9. 438129 
.438572 
. 439014 
. 439456 
.439897 

9. 440338 

Cos. 



D. I' 



7.85 
7.85 
7.83 
7.83 
7.82 
7.80 
7.80 
7.80 
7.77 
7.78 

7.77 
7.75 
7.73 
7.75 
7.72 
7.72 
7.72 
7.70 
7.70 
7.68 

7.67 
7.67 
7.65 
7-65 
7.65 
7.63 
7.62 
7.62 
7.60 
7.60 

7.58 
7.58 
7.57 
7-57 
7.55 
7-55 
7-53 
7.53 
7.52 
7.52 

7.50 
7-50 
7.48 
7.47 
7.48 
7.45 
7.45 
7.45 
7.43 
7.43 

7.42 
7.42 
7.40 
7.40 
7.38 
7.38 
7.37 
7.37 
7.35 
7.35 

D. i''. 



Cos. 



984910 
984876 
984842 



984774 
984740 
984706 
984672 
984638 

984603 
984569 
984535 
984500 
984466 
984432 
984397 
984363 
984328 

984294 
984259 
984224 
934190 

984155 
984120 



984050 
984015 



983946 

98391 I 
983875 
983840 
983805 
983770 
983735 
983700 
983664 
983629 
983594 
983558 
983523 
983487 
983452 
983416 
983381 
983345 
983309 
983273 
983238 

983202 
983166 
983130 
983094 
983058 
983022 



982950 
982914 
982878 



D. I'' 



Sin. 



57 
57 
57 
57 
57 
57 
57 
57 
57 
58 

57 
57 
58 
57 
57 
58 
57 
58 
57 
58 

58 
57 
58 
58 
58 
58 
58 
57 
58 
58 
60 
58 
58 
58 
58 
58 
60 
58 
58 
60 

58 
60 
58 
60 
58 
60 
60 
60 
58 
60 

60 
60 
60 
60 
60 
60 
60 
60 
60 
60 



D. 1" 



Tan. 



9.428052 
.428558 
. 429062 
.429566 
.430070 

9. 430573 
.431075 
.431577 
.432079 
.432580 

9.433080 
.433580 
. 434080 
.434579 
.435078 

9- 435576 
.436073 
.436570 
.437067 
.437563 

9.438059 
.438554 
.439048 
.439543 
.440036 

9. 440529 
.441022 
.441514 
. 442006 
.442497 

9. 442988 

.443479 
.443968 
.444458 
. 444947 
9- 445435 
.445923 
.446411 



D. 1" 



.447384 
9.447870 
.448356 
.448841 
.449326 
. 449810 
9.450294 
.450777 
.451260 

.451743 
.452225 

9.452706 
.453187 
.453668 
.454148 
.454628 

9.455107 
.455586 
. 456064 
.456542 
.457019 

9.457496 

Cot. 



8.43 
8.40 
8.40 
8.40 
8.38 
8.37 
8.37 
8.37 
8.35 
8.33 

8.33 
8.33 
8.32 
8.32 
8.30 
8.28 
8.28 
8.28 
8.27 
8.27 

8.25 
8.23 
8.25 
8.22 
8.22 
8.22 
8.20 
8.20 
8.18 
8.18 

8.18 
8.15 
8.17 
8.15 
8.13 
8.13 
8.13 
8.12 
8.10 
8.10 

8.10 
8.08 
8.08 
8.07 
8.07 
8,05 
8.05 
8.05 
8.03 
8.02 

8.02 
8.02 
8.00 
8.00 
7.98 
7.98 
7-97 
7.97 
7.95 
7-95 



D. I". 



Cot. 



0.571948 
.571442 
.570938 
.570434 
.569930 

0.569427 
.568925 
.568423 
.567921 
.567420 

o. 566920 
. 566420 
.565920 
.565421 
.564922 

0.564424 
.563927 
.563430 
.562933 
.562437 

0.56I94I 
.561446 
.560952 
.560457 
.559964 

0.559471 
.558978 
.558486 
.557994 
.557503 

0.557012 
.556521 
.556032 
.555542 
.555053 

o. 554565 

.554077 
.553589 
.553102 
.552616 

0.552130 
.551644 
.551159 
.550674 
.550190 

0.549706 
.549223 
.548740 
.548257 
.547775 

0.547294 
.546813 
.546332 
.545852 
.545372 

0.544893 
.544414 
.543936 
.543458 
.542981 

0.542504 

Tan. 



los^ 



74^ 



i6^ 



COSINES, TANGENTS, AND COTANGENTS 163*' 



M, 



12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 

47 
48 
49 

50 
51 
52 
53 
54 

5? 
56 

58 
59 
60 



Sin. 



9. 440338 
.440778 
.441218 
.441658 
. 442096 

9.442535 
.442973 
.443410 
.443847 
«. 444284 

9.444720 
.445155 
.445590 
.446025 

.446459 

9. 446893 

.447326 

.447759 
.448191 
.448623 

9.449054 
.449485 
.449915 
.450345 
.450775 

9. 451204 
.451632 
.452060 
.452488 
.452915 

9.453342 
.453768 
.454194 
.454619 
. 455044 

9- 455469 
. 455893 
.456316 

.456739 
.457162 

9. 457584 
. 458006 

.458427 



.459268 
9. 459688 
. 460108 
.460527 
.460946 
,461364 

9. 461782 
.462199 
. 462616 
.463032 
.463448 

9.463864 
.464279 

.464694 

. 465108 

.465522 

9.465935 

Cos. 



D. I" 



7.33 
7.33 
7.33 
7.30 
7.32 
7.30 
7.28 
7.28 
7.28 
7.27 

7.25 
7.25 
7.25 
7.23 
7.23 
7.22 
7.22 
7.20 
7.20 
7.18 

7.18 
7.17 
7.17 
7.17 
7.15 
7.13 
7.13 
7-13 
7.12 
7.12 

7. 10 
7. 10 

7.08 
7.08 
7.08 
7.07 
7-05 
7.05 
7.05 
7-03 

7.03 
7.02 
7.02 
7.00 
7.00 
7.00 
6.98 
6.98 
6.97 
6.97 

6.95 
6.95 
6.93 
6.93 
6.93 
6.92 
6.92 
6.90 
6.90 
6.88 



D. i". 



Cos. 



9. 982842 
982805 
982769 

982733 
982696 
982660 
982624 
982587 

982551 
982514 

982477 
982441 
982404 
982367 
'^2331 



982257 
982220 
982183 
982146 

982109 
982072 
982035 
981998 
98 1 961 
981924 



981812 
981774 

981737 
981700 
981662 
981625 
981587 
981549 
981512 
981474 
981436 
981399 

981361 
981323 
981285 
981247 
981209 
981171 

981133 
981095 
981057 
981019 



980827 
980789 
980750 
980712 
980673 
980635 
980596 

Sin. 



D. i' 



.62 
.60 
.60 
.62 
.60 
.60 
.62 
,.60 
.62 
.62 

.60 
.62 
.62 
.60 
.62 
.62 
.62 
.62 
.62 
.62 

.62 
.62 
.62 
.62 
.62 

.62 
.62 
.63 
.62 

.62 

.63 
.62 

.63 
.62 

.63 
.62 

.63 

.63 
.63 
.63 
.63 
.63 
.63 
.63 
.63 

.65 
.63 
.63 
.65 
.63 
.65 
.63 
.65 
.63 
.65 

D. 1". 



Tan. 



9- 457496 
.457973 
.458449 
.458925 
. 459400 

9.459875 
.460349 
.460823 
.461297 
.461770 

9. 462242 
.462715 
.463186 
.463658 
.464128 

9- 464599 
. 465069 

.465539 
. 466008 
.466477 

9.466945 
.467413 
. 467880 

.468347 
. 468814 
9. 469280 
.469746 
.470211 
. 470676 
.471141 

9.471605 
. 472069 
.472532 
.472995 
.473457 

9.473919 
.474381 
.474842 
.475303 
.475763 

9. 476223 
.476683 
.477142 
.477601 
.478059 

9.478517 
.478975 
.479432 
.479889 
.480345 

9. 480801 

.481257 
.481712 
.482167 
.482621 
9- 483075 
.483529 
.483982 

. 484435 



9- 485339 
Cot. 



7.95 
7.93 
7.93 
7.92 
7.92 
7.90 
7.90 
7.90 
7.88 
7.87 
7.88 
7.85 
7.87 
7.83 
7.85 
7.83 
7.83 
7.82 
7.82 
7.80 

7.80 

7.78 
7.78 
7.78 
7.77 
7.77 
7-75 
7.75 
7.75 
7.73 

7.73 
7.72 
7.72 
7.70 
7.70 
7.70 
7.68 
7.68 
7.67 
7.67 

7.67 
7.65 
7.65 
7.63 
7.63 
7.63 
7.62 
7.62 
7.60 
7.60 

7.60 

7.58 
7.58 
7.57 
7.57 
7-57 
7.55 
7.55 
7-53 
7-53 

D. I''. 



Cot. 



o. 542504 
.542027 
.541551 
.541075 
. 540600 

0.540125 
.539651 
.539177 
.538703 
.538230 

0.537758 
.537285 
.536814 
.536342 
.535872 

o. 535401 

.534931 
. 534461 
. 533992 
.533523 

0.533055 
.532587 

.532120 

.531653 
.531186 

o. 530720 

.530254 
.529789 
.529324 
.528859 

0.528395 
.527931 
.527468 
. 527005 
. 526543 

o. 526081 

.525619 
.525158 
.524697 
.524237 

0.523777 
.523317 
.522858 

.522399 
.521941 

o. 521483 
.521025 

.520568 

.520111 

.519655 

0.5I9I99 

.518743 
. 518288 

.517833 

.517379 

0.516925 

.516471 

.516018 

.515565 
.515113 

o. 514661 
Tan. 



106° 



73= 



17^ 



LOGARITHMIC SINES 



id2° 



M. 



22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 

58 
59 
60 



Sin. 



9.465935 
.466348 
. 466761 
.467173 
.467585 

9.467996 
. 468407 
.468817 
.469227 
.469637 

9.470046 

.470455 
.470863 
.47T271 
.47^679 
9. 472086 
.47^402 
.47''898 
.473304 
.473710 

9.474115 
.4745^9 
.474923 
.475327 
.475730 

9-476^33 
.476536 
.476938 
.477340 
.477741 

9.478142 
.478542 
. 478042 
.47^342 
.479*741 

9.480140 
.480539 
.480937 
.481334 
.481731 

9.482128 
.482525 
.482921 
.483316 
.483712 

9.484107 
. 484501 
.484895 
.485289 
.485682 

9.486075 
.486467 
.486860 
.487251 

.487643 

9.488034 

.488424 



D. I'' 



. 489204 

.489593 

9.489982 

Cos. 



6.88 
6.88 
6.87 
6.87 
6.85 
6.85 
6.83 
6.83 
6.83 
6.82 

6.82 
6.80 
6.80 
6.80 
6.78 
6.77 
6.77 

6.77 
6.77 

6.75 

6.73 
6.73 
6.73 
6.72 
6.72 
6.72 
6.70 
6.70 
6.68 
6.68 

6.67 
6.67 
6.67 
6.65 
6.65 
6.65 
6.63 
6.62 
6.62 
6.62 

6.62 
6.60 
6.58 
6.60 
6.58 
6.57 
6.57 
6.57 
6.55 
6.55 

6.53 

6.52 
6.53 
6.52 
6.50 
6.50 
6.50 
6.48 
6.48 

D. I''. 



Cos. 



9. 980596 
.980558 
.980519 
.980480 
. 980442 

9.980403 
.980364 
.980325 
.980286 
.980247 

9.980208 
.980169 
.980130 
.980091 
.980052 

9.980012 
. 9799*^3 
.979934 
.979895 
.979855 

9.979816 
.979776 
.979737 
.979697 
.979658 

9. 979618 
.979579 
.979539 
.979499 
.979459 

9.979420 
.979380 
.979340 
.979300 
. 979260 

9. 979220 
.979180 
.979140 
.979100 
.979059 

9.979019 
.978979 
.978939 



D. I", 



.978858 
9.978817 
.978777 
.978737 
. 978696 

.978655 
9.978615 
.978574 
.978533 
.978493 
.978452 
9. 97841 I 
.978370 
.978329 



.978247 
9. 978206 

Sin. 



.63 

'P 
.63 

.65 

'P 
.65 

.65 

.65 

.65 

'P 
.65 

.65 

.67 

'P 

'P 
.65 

.67 

.65 

'P 

'P 
.65 

.67 

'P 

•P 
.67 

.67 

.65 

.67 
.67 
.67 
.67 
.67 
.67 
.67 
.67 
.68 
.67 

.67 
.67 
.68 
.67 
.68 
.67 
.67 
.68 
.68 
.67 

,68 
.68 
.67 
.68 
.68 
.68 
.68 
.68 
.68 
.68 

D. 1", 



Tan. 



9.485339 
.485791 
. 486242 
.486693 
• .487143 
9.487593 
.488043 



.489390 
9.489838 



D. i'^ 



.490733 
.491180 
.491627 
9.492073 
.492519 
.492965 
.493410 

.493854 

9.494299 
.494743 
.495186 
.495630 
.496073 

9. 49*5515 
.496957 
.497399 
.497841 
.498282 

9.498722 
.499163 
.499603 
.500042 
.500481 

9. 500920 

.501359 
.501797 
.502235 
.502672 

9. 503109 
. 503546 
. 503982 
.504418 

. 504854 
9. 505289 

.505724 
.506159 
.506593 
.507027 

9.507460 

.507893 
.508326 

.508759 
.509191 

9. 509622 
.510054 
.510485 
. 510916 
.511346 

9.511776 

Cot. 



7.53 
7.52 
7.52 



7 

7 

7 

7 

7 . 

7.48 

7.47 

7.47 
7.45 
7.45 
7.45 
7.43 
7.43 
7-43 
7.42 
7.40 
7.42 

7.40 
7.38 
7.40 
7-38 
7.37 
7.37 
7.37 
7.37 
7-35 
7.33 

7.35 
7.33 
7-32 
7.32 
7.32 
7-32 
7-30 
7.30 
7.28 
7.28 

7.28 
7.27 
7.27 
7.27 
7.25 
7.25 
7.25 
7.23 
7.23 
7.22 

7.22 
7.22 
7.22 
7.20 
7.18 
7.20 
7.18 
7.18 
7.17 
7.17 

D. 1". 



Cot. 



o. 514661 
.514209 
.513758 
.513307 
.512857 

0.512407 
.511957 
.511508 
.511059 
.510610 

o. 510162 

.509714 
.509267 
.508820 

.508373 
0.507927 
.507481 
.507035 
.506590 
.506146 

0.505701 

.505257 
.504814 
.504370 
.503927 
0.503485 
.503043 

.502601 

.502159 
.501718 

o. 501278 
.500837 
.500397 
.499958 
.499519 

o. 499080 
.498641 
.498203 
.497765 
.497328 

0.496891 

.496454 

.496018 

.495582 
.495146 

0.49471 I 
.494276 
.493841 
.493407 
.492973 

0.492540 

.492107 

.491674 
.491241 

. 490809 

0.490378 
.489946 
.489515 

,489084 

.488654 

o. 488224 
Tan. 



107^ 



72^ 



COSINES, TANGENTS, AND COTANGENTS igjO 



Sin. 



19 



9.489982 
.490371 
.490759 
.491147 

.491535 
9.491922 
.492308 
.492695 
.493081 
.493466 

9-493851 
.494236 
.494621 
.495005 
.495388 

9- 495772 
.496154 
.496537 
.496919 
.497301 

9.497682 



.498444 
.498825 
. 499204 
?. 499584 
.499963 
. 500342 
.500721 
.501099 

?. 501476 
.501854 
.502231 
.502607 
.502984 

?. 503360 
.503735 
.504110 

.504485 
. 504860 

?. 505234 
. 505608 

.505981 
.506354 
.506727 
). 507099 
.507471 
.507843 
.508214 

.508585 
). 508956 
.509326 
.509696 
. 510065 

.510434 
). 510803 
.511172 
.511540 
.511907 
.512275 
>. 512642 

Cos. 



D. I". 



6.48 
6.47 
6.47 
6.47 
6.45 
6.43 
6.45 
6.43 
6.42 
6.42 

6.42 
6.42 
6.40 
6.38 
6.40 
6.37 
6.38 
6.37 
6.37 
6.35 

6.37 
6.33 
6.35 
6.32 

6.33 
6.32 
6.32 
6.32 
6.30 
6.28 

6.30 
6.28 
6.27 
6.28 
6.27 
6.25 
6.25 
6.25 
6.25 
6.23 

6.23 
6.22 
6.22 
6.22 
6.20 
6.20 
6.20 
6.18 
6.18 
6.18 

6.17 
6.17 
6.15 

6.15 
6.15 
6.13 
6.12 

6.13 

6.12 



D. 1' 



Cos. 



9. 978206 
.978165 
.978124 
.978083 
. 978042 

9.978001 

.977959 
.977918 

.977877 
.977835 

9.977794 
.977752 
.977711 
.977669 
. 977628 

9. 977586 
.977544 
.977503 
.977461 

.977419 

9-977377 
.977335 
.977293 
.977251 
.977209 

9. 977167 
.977125 
.977083 
.977041 
.976999 

9.976957 
.976914 
.976872 
.976830 
.976787 

9-976745 
. 976702 
. 976660 
.976617 
.976574 

9.976532 
.976489 
.976446 

.976404 

.976361 

9.976318 

.976275 
.976232 
. 976189 
, 976146 

9.976103 
.976060 
.976017 
.975974 
.975930 

9-975887 
.975844 
.975800 

.975757 

.975714 

9-975670 

Sin. 



D. 1" 



.68 
.68 
.68 
.68 
.68 
.70 



.70 
.68 

.70 
.68 
.70 
.68 
.70 
.70 
.68 
.70 
.70 
.70 

.70 
.70 
.70 
.70 
.70 
.70 
.70 
.70 
.70 
.70 

.72 
.70 
.70 
.72 
.70 
.72 
.70 
.72 
.72 
.70 

.72 
.72 
.70 
.72 
.72 
• 72 
.72 
.72 
.72 
.72 

.72 
.72 
.72 
.73 
.72 
.72 
.73 
.72 
.72 
.73 

D. 1''. 



Tan. 



9.511776 
.512206 
.512635 
.513064 
.513493 

9-513921 
.514349 
.514777 
.515204 
.515631 

9-516057 
.516484 
.516910 
.517335 
.517761 

9.518186 
.518610 
.519034 
.519458 
.519882 

9. 520305 
.520728 
.521151 
.521573 
. 521995 

9.522417 
.522838 

.523259 
. 523680 
. 524100 

9.524520 
.524940 
.525359 
.525778 
.526197 

9.526615 

.527033 
.527451 
.527868 
.528285 

9.528702 
.529119 
.529535 
.529951 
.530366 

9-530781 
.531196 
.531611 
.532025 
.532439 

9- 532853 
.533266 

.533679 
.534092 
.534504 

9- 534916 
.535328 
.535739 
.536150 
. 536561 

9. 536972 

Cot. 



D. i'' 



7.17 
7.15 
7.15 
7-15 
7-13 
7-13 
7.13 
7.12 
7.12 
7.10 

7.12 
7. 10 
7.08 
7.10 
7.08 
7-07 
7-07 
7.07 

7.07 
7.05 

7-05 
7-05 
7.03 
7-03 
7.03 
7.02 
7.02 
7.02 
7.00 
7.00 

7.00 
6.98 
6.98 
6.98 
6.97 
6.97 
6.97 
6.95 
6.95 
6.95 

6.95 
6.93 
6.93 
6.92 
6.92 
6.92 
6,92 
6.90 
6.90 
6.90 

6.88 
6.88 
6.88 
6.87 
6.87 
6.87 
6.85 
6.85 
6.85 
6.85 

D. 1''. 



Cot. 



o. 488224 

.487794 
.487365 

. 486936 
.486507 

o. 486079 

.485651 
.485223 
.484796 
.484369 

0.483943 
.483516 
.483090 
.482665 
.482239 

0.48I8I4 
.481390 
.480966 
.480542 
.480118 

0.479695 
.479272 
.478849 
.478427 
.478005 

0.477583 
.477162 
.476741 
.476320 
.475900 

0.475480 
.475060 
.474641 

. 474222 

.473803 
0.473385 
.472967 
.472549 
.472132 

.471715 

0.471298 
.470881 
.470465 
.470049 
.469634 

0.469219 

.468804 
.468389 

.467975 
.467561 

0.467147 

.466734 
.466321 
.465908 
.465496 

o. 465084 
. 464672 
.464261 

.463850 
.463439 

o. 463028 
Tan. 



lio8° 



7X' 



19^ 



LOGARITHMIC SINES 



160*^ 



M. 



z 
2 
3 
4 
5 
6 

I 

9 

10 

IX 
13 
13 

M 
15 
16 

17 
18 

19 

20 

2X 
22 
23 
24 
25 
26 

^l 
28 

29 

30 
31 
32 

33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 
46 
47 
48 
49 

50 
51 
52 
53 
54 
55 
56 

58 
59 
60 



Sin. 



9.512642 
.513009 
.513375 
.513741 
.514107 

9-514472 
.514837 
.515202 
.515566 
.515930 

9. 516294 
.516657 
.517020 
.517382 
.517745 

9.518107 
.518468 
.518829 
.519190 
.519551 

9.519911 
.520271 
.520631 
.520990 
.521349 

9.521707 
. 522066 
.522424 
.522781 
.523138 

9.523495 
.523852 
.524208 

.524564 
.524920 

9.525275 
.525630 
.525984 
.526339 
.526693 

9. 527046 
. 527400 

.527753 
.528105 

.528458 

9.528810 

.529161 

.529513 
.529864 
.530215 

9.530565 
.530915 
.531265 
.531614 
.531963 

9-532312 
. 532661 
.533009 
.533357 
.533704 

9-534052 

Cos. 



D. I". 



6.12 
6.10 
6.10 
6.10 
6.08 
6.08 
6.08 
6.07 
6.07 
6.07 

6.05 
6.05 
6.03 
6.05 
6.03 
6.02 
6.02 
6.02 
6.02 
6.00 

6.00 
6.00 
5.98 
5.98 
5.97 
5.98 
5.97 
5.95 
5.95 
5.95 

5.95 
5.93 
5.93 
5.93 
5.92 
5.92 
5.90 
5.92 
5.90 
5.88 

5-90 
5.88 
5.87 
5.88 
5.87 
5.85 
5.87 
5.85 
5-85 
5.83 

5.83 
5-83 
5.82 
5.82 
5.82 
5.82 
5.80 
5.80 
5-78 
5.80 



Cos. 



9-975670 
.975627 
.975583 
.975539 
.975496 

9-975452 
.975408 
.975365 
.975321 
.975277 

9.975233 

.975189 

.975145 
.975101 
.975057 
9.975013 
.974969 
.974925 
. 974880 
.974836 

9.974792 
.974748 
.974703 
.974659 
•974614 

9.974570 
.974525 
.974481 
.974436 
.974391 

9.974347 
.974302 

.974257 

.974212 

.974167 

9.974122 

.974077 
.974032 

.973987 
.973942 

9-973897 
.973852 
.973807 
.973761 
.973716 

9.973671 
.973625 
.973580 
.973535 
.973489 

9-973444 
.973398 
.973352 
.973307 
.973261 

9-973215 
.973169 
.973124 
.973078 
.973032 

9.972986 

Sin. 



D. 1'' 



.72 
.73 
.73 
.72 
.73 
.73 
.72 
.73 
.73 
.73 

.73 
.73 
.73 
.73 
.73 
.73 
.73 
.75 
.73 
.73 

.73 
.75 
.73 
.75 
.73 
.75 
.73 
.75 
.75 
.73 

.75 
.75 
.75 
.75 
.75 
.75 
.75 
.75 
.75 
.75 

.75 
.75 
.77 
.75 
.75 
.77 
.75 
.75 
.77 
.75 

.77 
.77 
.75 
.77 
.77 
.77 
.75 
.77 
.77 
.77 



Tan. 



9- 536972 
.537382 
.537792 
.538202 
.538611 

9. 539020 
.539429 
.539837 
.540245 
.540653 

9- 541061 
.541468 

.541875 
.542281 
.542688 
9-543094 
.543499 
.543905 
.544310 
.544715 

9-545119 

.545524 
.545928 
.546331 
.546735 
9.547138 
.547540 
.547943 
.548345 
.548747 

9-549149 
.549550 
.549951 
.550352 
.550752 

9- 551 153 
.551552 
.551952 
.552351 
.552750 

9.553149 
.553548 
.553946 
.554344 
.554741 

9-555139 
.555536 
.555933 
.556329 
.556725 

9.557121 
.557517 
.557913 
.558308 
.558703 

9- 559097 
.559491 
.559885 
.560279 
.560673 

9. 561066 

Cot. 



D. 1'' 



6.83 
6.83 
6.83 
6.82 
6.82 
6.82 
6.80 
6.80 
6.80 
6.80 

6.78 
6.78 
6.77 
6.78 
6.77 

6.75 
6.77 

6.75 
6.75 
6.73 

6.75 
6.73 
6.72 

6.73 
6.72 
6.70 
6.72 
6.70 
6.70 
6.70 

6.68 
6.68 
6.68 
6.67 
6.68 
6.65 
6.67 
6.65 
6.65 
6.65 

6.65 
6.63 
6.63 
6.62 
6.63 
6.62 
6.62 
6.60 
6.60 
6.60 

6.60 
6.60 

6.58 
6.58 

6.57 

6.57 
6.57 
6.55 

D. I". 



Cot. 



o. 463028 
.462618 
. 462208 
.461798 
.461389 

o. 460980 

.460571 

.460163 

.459755 
.459347 

0.458939 

.458532 
.458125 

.457719 
.457312 

0.456906 
.456501 
.456095 
.455690 
.455285 

0.454881 
.454476 
.454072 
.453669 
.453265 

0.452862 

.452460 

.452057 
.451655 
.451253 
0.450851 
.450450 
.450049 
.449648 
.449248 

o. 448847 

.448448 

. 448048 

.447649 
.447250 

0.446851 
.446452 
.446054 
.445656 
.445259 

0,444861 

.444464 
.444067 

.443671 

.443275 

0.442879 

.442483 

,442087 
.441692 

.441297 
0.440903 
.440509 
.440115 
.439721 
.439327 
0-438934 

Tan. 



109° 



70° 



20** COSINES, 



TANGENTS, AND COTANGENTS 159*" 



Sin. 



9. 534052 
.534399 
. 534745 
.535092 
.535438 

9-535783 
.536129 
.536474 
.536818 
.537163 

9-537507 
.537851 
.538194 
.538538 
.538880 

9- 539223 
.539565 
.539907 
.540249 

.540590 

9- 540931 
.541272 
.541613 
.541953 
.542293 

9. 542632 

.542971 
.543310 
.543649 
.543987 

9. 544325 
.544663 
.545000 
.545338 
•545674 

9-546011 
. 546347 
.546683 

.547019 
.547354 

9.547689 
. 548024 
.548359 
.548693 
.549027 

9- 549360 
.549693 
. 550026 

.550359 
.550692 

9. 551024 
.551356 
.551687 
.552018 

.552349 
9. 552680 
.553010 
.553341 
. 553670 
.554000 
9. 554329 

Cos. 



D. i". 



5-78 
5-77 
5.78 
5-77 
5.75 
5-77 
5-75 
5.73 
5-75 
5.73 

5.73 
5-72 
5-73 
5-. 70 
5-72 
5.70 
5-70 
5-70 
5.68 
5.68 

5.68 
5.68 
5.67 
5-67 
5-65 
5.65 
5.65 
5-65 
5.63 
5.63 

5-63 
5-62 
5.63 
5.60 
5.62 
5-60 
5.60 
5-60 
5-58 
5-58 

5.58 
5-58 
5-57 
5-57 
5-55 
5-55 
5-55 
5.55 
5-55 
5.53 

5.53 
5-52 
5-52 
5-52 
5.52 
5.50 
5-52 
5-48 
5.50 
5.48 

D. I''. 



Cos. 



9.972986 
.972940 
.972894 
. 972848 
. 972802 

9-972755 
.972709 
. 972663 
.972617 
.972570 

9- 972524 
.972478 
.972431 
.972385 
.972338 

9.972291 

.972245 
.972198 

.972151 
.972105 

9.972058 
.972011 
.971964 

.971917 
.971870 
9.971823 
.971776 
.971729 
.971682 
.971635 

9.971588 
.971540 
.971493 
.971446 
.971398 

9.971351 
.971303 
.971256 
.971208 
.971161 

9.971113 
. 971066 
.971018 
.970970 
. 970922 

9.970874 
. 970827 

.970779 
.970731 
.970683 

9.970635 
.970586 
.970538 
.970490 
.970442 

9-970394 
.970345 
.970297 
.970249 
. 970200 

9. 970152 

Sin. 



D. I" 



77 
77 
77 
77 
78 
77 
77 
77 
78 
77 

77 
78 
77 
78 
78 
77 
78 
78 

77 
78 

78 
78 
78 
78 
78 

7? 
78 

78 

7^ 
78 

.^ 

7? 
78 
80 
78 
80 
78 
80 
78 
80 

78 
80 
80 
80 
80 
78 
80 
80 
80 
80 

82 
80 
80 
80 
80 
82 
80 
80 
82 
80 



D. 1". 



Tan. 



9.561066 
. 561459 
.561851 
.562244 
. 562636 

9. 563028 
.563419 
.563811 
. 564202 
.564593 

9. 564983 
. 565373 
.565763 
. 566153 
. 566542 

9- 566932 
. 567320 
. 567709 



.568486 

9-568873 
. 569261 
.569648 
.570035 
.570422 

9.570809 
.571195 
.571581 
.571967 
.572352 

9- 572738 
.573123 
.573507 
.573892 
.574276 

9.574660 
.575044 
.575427 
.575810 
.576193 

9.576576 
. 576959 
. 577341 
. 577723 
.578104 

9.578486 
.578867 
.579248 
.579629 
.580009 



9^ „ , 

.580769 
.581149 
.581528 
.581907 

9. 582286 
.582665 
.583044 
.583422 
.583800 

9- 584177 

Cot. 



D. i'' 



6.55 
6.53 
6.55 
6.53 
6.53 
6.52 
6.53 
6.52 
6.52 
6.59 
6.50 
6.50 
6.50 
6.48 
6.50 
6.47 
6.48 
6.48 
6.47 
6.45 
6.47 
6.45 
6.45 
6.45 
6.45 
6.43 
6.43 
6.43 
6.42 

6.43 
6.42 
6.40 
6.42 
6.40 
6.40 
6.40 
6.38 
6.38 
6.38 
6.38 

6.38 
6.37 
6.37 
6.35 
6.37 
6.35 
6.35 
6.35 
6.33 
6.33 

6.33 
6.33 
6.32 
6.32 
6.32 
6.32 
6.32 
6.30 
6.30 
6.28 



D. 1" 



Cot. 



0.438934 
.438541 
.438149 
.437756 
.437364 

0.436972 
.436581 
. 436189 
.435798 
.435407 

0.435017 
.434627 
.434237 
.433847 
.433458 

0.433068 
. 432680 
.432291 
.431902 
.431514 

0.431127 
.430739 
.430352 
.429965 
.429578 

o. 429191 
. 428805 
. 428419 
.428033 
. 427648 

o. 427262 
.426877 

.426493 

.426108 

.425724 

0.425340 

.424956 

.424573 

.424190 
.423807 

0.423424 
.423041 
.422659 
.422277 

.421896 

0.42I5I4 

.421133 
.420752 
.420371 
.419991 

0.419611 

.419231 
.418851 
.418472 
. 418093 
C.4I77I4 
.417335 
,416956 
.416578 

.416200 

0.415823 

Tan, 



tiio^ 



69^ 



21" 



LOGARITHMIC SINES 



IS8« 



M. 



Sin. 



22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 

57 
58 

60 



9. 554329 
.554658 
.554987 
.555315 
. 555643 

9-555971 
.556299 
.556626 

.556953 
.557280 

9. 557606 
.557932 
.558258 
.558583 
.558909 

9.559234 
.559558 
.559883 
. 560207 

.560531 
9-560855 
.561178 
.561501 
.561824 
.562146 
9.562468 
.562790 
.563112 
.563433 
.563755 



D. I' 



Cos. 



D. 1" 



564075 

564396 

564716 

565036 

565356 

565676 

.565995 

.566314 

.566632 

.566951 
9. 567269 

.567587 
.567904 
.568222 

.568539 
9.568856 
.569172 
.569488 
. 569804 
.570120 

9-570435 
.570751 
.571066 
.571380 

.571695 
9.572009 

.572323 
.572636 
.572950 
.573263 
9-573575 



Cos. 



5.48 
5.48 
5.47 
5.47 
5.47 
5.47 
5.45 
5-45 
5.45 
5-43 

5.43 
5-43 
5-42 
5.43 
5-42 
5.40 
5-42 
5.40 
5-40 
5-40 

5.38 
5.38 
5-38 
5-37 
5.37 
5.37 
5.37 
5.35 
5.37 
5-33 

5-35 
5-33 
5.33 
5.33 
5-33 
5.32 
5.32 
5.30 
5.32 
5-30 

5-30 
5.28 
5.30 
5.28 
5.28 
5.27 
5.27 
5.27 
5.27 
5-25 

5.27 
5-25 
5.23 
5.25 
5.23 
5-23 

5-22 
5-23 
5-22 
5.20 



D. I' 



9-970152 
.970103 
.970055 
. 970006 

•969957 
9.969909 
. 969860 
.969811 
.969762 
.969714 

9- 969665 
.969616 
.969567 
.969518 
.969469 

9.969420 
.969370 
.969321 
.969272 
.969223 

9.969173 
.969124 

.969075 
.969025 
. 968976 
9. 968926 
. 968877 
.968827 

.968777 
.968728 

9.968678 
.968628 
.968578 
.968528 

.968479 
9.968429 

.968379 
.968329 
.968278 
.968228 

9.968178 
.968128 
.968078 
.968027 
.967977 

9.967927 
.967876 
.967826 
.967775 
.967725 

9.967674 
. 967624 

.967573 
.967522 
.967471 

9.967421 
.967370 
.967319 
.967268 
.967217 

9.967166 



Sin. 



.82 
.80 
.82 
.82 
.80 
.82 
.82 
.82 
.80 
.82 

.82 

.82 
.82 
.82 
.82 
.83 
.82 
.82 
.82 
.83 

.82 
.82 
.83 
.82 

.83 
.82 
.83 
.83 
.82 

.83 

.83 
.83 
.83 
.82 
-83 
.83 
.83 
.85 
.83 
-83 

.83 
.83 

•?5 
.83 
.83 
.85 
.83 
.85 
.83 
.85 

.83 
.85 
.85 
.85 
.83 

'P 

.85 
-85 



D. I' 



Tan. 



9-584177 
.584555 
.584932 
.585309 
.585686 

9. 586062 

.586439 
.586815 

.587190 
.587566 

9.587941 
.588316 



D. I' 



Cot. 



. 589066 
. 589440 
9-589814 
.590188 
.590562 
.590935 
.591308 

9.591681 
.592054 
.592426 
.592799 
.593171 

9-593542 
.593914 
.594285 
.594656 
.595027 

9-595398 
.595768 
.596138 
.596508 
.596878 

9-597247 
.597616 
.597985 
.598354 
.598722 

9.599091 
.599459 
.599827 
.600194 
. 600562 

9. 600929 
.601296 
.601663 
.602029 
.602395 

9.602761 
.603127 
.603493 
.603858 
.604223 

9. 604588 
.604953 
.605317 
.605682 
. 606046 

9. 606410 

Cot. 



6.30 
6.28 
6.28 
6.28 
6.27 
6.28 
6.27 
6.25 
6.27 
6.25 

6.25 
6.25 
6.25 
6.23 
6.23 
6.23 
6.23 
6.22 
6.22 
6. 22 

6.22 
6. 20 
6.22 
6.20 

6.18 
6.20 
6.18 
6.18 
6.18 
6.18 

6.17 

6.17 
6.15 

6.15 

6.13 
6.15 

6.13 
6.13 
6.12 
6.13 
6.12 
6.12 
6. 12 
6.10 
6. 10 
6. 10 

6. 10 
6.10 
6.08 
6.08 
6.08 
6.08 
6.07 
6.08 
6.07 
6.07 

D. I". 



0.415823 

.415445 
.415068 
.414691 

.414314 
0.413938 
.413561 
.413185 
.412810 

.412434 

0.412059 

.411684 

.411309 

.410934 
.410560 
0.410186 
.409812 
.409438 
.409065 
. 408692 

0.408319 
.407946 

.407574 
.407201 
. 406829 

o. 406458 
.406086 
.405715 
.405344 
.404973 

o. 404602 
.404232 
.403862 
.403492 
.403122 

0.402753 
.402384 
.402015 

.401646 
.401278 

o. 400909 
.400541 
.400173 
. 399806 
.399438 

0.399071 
.398704 
.398337 
.397971 
.397605 

0.397239 
.396873 
.396507 
.396142 
.395777 

0-395412 
.395047 
.394683 
.394318 
.393954 

o- 393590 
Tan. 



III^ 



68*^ 



122® COSINES, TANGENTS, AND COTANGENTS ^57° 



M. Sin. D. i". Cos. D. i". I • Tan. D. i". Cot. 



9.573575 

.573888 
.574200 
.574512 
.574824 
9.575136 
.575447 
.575758 
. 576069 

.576379 
9.576689 
.576999 
.577309 
.577618 
.577927 
9.578236 
.578545 
.578853 
.579162 

.579470 

9.579777 
.580085 
.580392 
.580699 
.581005 

9.581312 
.581618 
.581924 
. 582229 
.582535 

9.582840 
.583145 
. 583449 
.583754 
.584058 

9. 584361 
.584665 
.584968 
.585272 
.585574 

9.585877 
.586179 



.586783 

.587085 

9.587386 

.587688 

.587989 
.588289 

.588590 

9.588890 

.589190 

.589489 

.589789 

.590088 

9.590387 

.590686 

.590984 

.591282 

.591580 

9.591878 

Cos. 



5.22 
5.20 
5.20 
5- 20 
5- 20 
5.18 
5.18 
5.18 
5.17 
5.17 

5-17 
5.17 
5.15 
5.15 
5.15 
5-15 
5.13 
5.15 
5.13 
5.12 

5.13 
5.12 
5.12 
5.10 
5.12 
5.10 
5.10 
5.08 
5.10 
5.08 

5.08 
5.07 
5.08 
5.07 
5.05 
5-07 
5.05 
5.07 
5.03 
5.05 

5-03 
5.05 
5-02 
5.03 

5-02 

5-03 
5.02 
5.00 
5.02 
5.00 

5- 00 
4.98 
5.00 
4.98 
4.98 
4.98 
4.97 
4.97 
4.97 
4.97 

D. I". 



9.967166 
.967115 
. 967064 
.967013 
.966961 

9.966910 
.966859 



.966756 
.966705 

9.966653 
. 966602 
.966550 
.966499 
.966447 

9.966395 
.966344 
. 966292 
.966240 
.966188 

9.966136 
. 966085 
.966033 
.965981 
.965929 

9.965876 
.965824 
.965772 
.965720 
.965668 

9.965615 
.965563 
.965511 
.965458 
.965406 

9.965353 
.965301 
.965248 
.965195 
.965143 

9.965090 
.965037 



.964931 

.964879 

9. 964826 

.964773 
,964720 
. 964666 
.964613 
9.964560 
.964507 
.964454 
.964400 

.964347 
9.964294 
,964240 
.964187 
.964133 
. 964080 
9. 964026 

Sin. 



87 



87 



92 



90 
88 
88 
90 
88 
90 
88 
90 

D. I". 



9. 606410 
.606773 
.607137 
.607500 
.607863 

9. 608225 



. 608950 
.609312 
.609674 

9.610036 
.610397 
.610759 
.611120 
.611480 

9.611841 
,612201 
.612561 
.612921 
.613281 

9.613641 
.614000 

.614359 
.614718 
,615077 
9.615435 
.615793 
.616151 
.616509 
.616867 

9.617224 

.617582 

.617939 
.618295 
.618652 
9.619008 
.619364 
.619720 
,620076 
.620432 

9.620787 
,621142 
,621497 
,621852 
,622207 

9. 622561 
.622915 
,623269 
.623623 
.623976 

9.624330 
,624683 
.625036 
.625388 
.625741 

9.626093 
.626445 
.626797 
.627149 
,627501 

9,627852 

Cot. 



6.05 
6.07 
6.05 
6.05 
6.03 
6.05 
6.03 
6.03 
6.03 
6.03 

6.02 
6.03 
6.02 
6.00 
6.02 
6.00 
6.00 
6.00 
6.00 
6.00 

5.98 
5.98 
5.98 
5.98 
5.97 
5.97 
5-97 
5.97 
5.97 
5.95 

5-97 
5-95 
5.93 
5.95 
5.93 
5.93 
5.93 
5.93 
5.93 
5-92 

5.92 
5.92 
5.92 
5-92 
5.90 
5.90 
5-90 
5.90 
5-88 
5-90 
5.88 
5.88 
5.87 
5.88 
5.87 
5.87 
5.87 
5.87 
5.87 
5.85 

D. I", 



0.393590 
.393227 
.392863 
. 392500 
.392137 

0.391775 
.391412 
,391050 
,390688 
.390326 

0.389964 
,389603 

.389241 
,388880 
.388520 
0.388159 
.387799 
.387439 
.387079 
.386719 

0.386359 
,386000 

.385641 
.385282 

.384923 

0.384565 

.384207 

.383849 
.383491 
.383133 

0.382776 
.382418 
.382061 
.381705 
.381348 

o. 380992 
.380636 
. 380280 
.379924 
.379568 

o. 379213 

.378858 
.378503 
.378148 
.377793 
0.377439 
.377085 
.376731 
.376377 
.376024 

0.375670 
.375317 
.374964 
.374612 
.374259 

0.373907 
.373555 
.373203 
•372851 

.372499 
0.372148 

Tan. 



112'^ 



67^ 



23 



LOGARITHMIC SINES 



156" 



M. 



2 

3 
4 
5 
6 

7 
8 

9 
10 
II 

12 
13 
14 
15 
16 
17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 

30 
31 
32 
33 

34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9. 591878 
.592176 

.592473 
.592770 
.593067 

9- 593363 
.593659 
.593955 
.594251 
.594547 

9.594842 
.595137 
.595432 
.595727 
.596021 

9-596315 
.596609 

.596903 
.597196 
.597490 

9-597783 
.59S075 
.598368 
. 598660 
.598952 

9-599244 
.599536 
.599827 
.600118 
, 600409 

9. 600700 
. 600990 
.601280 
.601570 
.601860 

9.602150 
.602439 
.602728 
.603017 
.603305 

9.603594 



.604170 

.604457 
.604745 
9.605032 
.605319 
. 605606 
. 605892 
. 606179 

9.606465 
.606751 
. 607036 
. 607322 
. 607607 

9. 607892 
.608177 
.608461 
.608745 
,609029 

9.609313 

Cos. 



D. I". 



4.97 
4.95 
4.95 
4.95 
4.93 
4.93 
4.93 
4.93 
4.93 
4.92 

4.92 
4.92 
4.92 
4.90 
4.90 
4.90 
4.90 
4.88 
4.90 
4.88 

4.87 
4.88 
4.87 
4.87 
4.87 
4.87 
4.85 
4.85 
4.85 
4.85 

4.83 
4.83 
4.83 
4.83 
4.83 
4.82 
4.82 
4.82 
4.80 
4.82 

4.80 
4.80 
4.78 
4.80 
4.78 
4.78 
4.78 
4.77 
4.78 
4.77 

4.77 
4.75 
4.77 
4.75 
4.75 



D. I". 



Cos. 



D. 1" 



9. 964026 
963972 
963919 
963865 
9638 II 
963757 
963704 
963650 
963596 
963542 

963488 
963434 
963379 
963325 
963271 
963217 
963163 
963108 
963054 
962999 

962945 
962890 
962836 
962781 
962727 
962672 
962617 
962562 
962508 
962453 
962398 

962343 
962288 
962233 
962178 
962123 
962067 
962012 
961957 
961902 

961846 
961791 

961735 
961680 
961624 
961569 

961513 
961458 
961402 
961346 

961290 
961235 
961 179 
961 123 
961067 
961011 

960955 
960899 



9607J 
960730 

Sin. 



.90 
.88 
.90 
.90 
.90 
.88 
.90 
.90 
.90 
.90 

.90 
.92 
.90 
.90 
.90 
.90 
-92 
.90 
•92 
.90 

.92 
.90 
.92 
.90 
.92 
.92 
.92 
.90 
.92 
.92 

.92 
.92 
.92 
.92 
.92 

-93 
.92 
.92 
.92 
.93 
.92 

.93 
.92 

.93 
.92 

.93 
.92 

.93 
.93 
.93 
.92 
.93 
.93 
.93 
.93 
.93 
.93 
.93 
.95 
-93 

D. i''. 



Tan. 



9. 627852 
. 628203 
.628554 
. 628905 
. 629255 

9. 629606 
.629956 
.630306 
.630656 
.631005 

9-631355 
.631704 
.632053 
.632402 
.632750 

9.633099 
.633447 
.633795 
.634143 
.634490 

9-634838 
.635185 
.635532 
.635879 
. 636226 

9.636572 
.636919 
.637265 
.637611 
.637956 

9. 638302 
.638647 
.638992 
.639337 
.639682 

9. 640027 
.640371 
.640716 
. 641060 
.641404 

9.641747 
.642091 
.642434 
.642777 
.643120 

9.643463 
. 643806 
.644148 
.644490 
.644832 

9.645174 
.645516 

.645857 
.646199 
.646540 

9.646881 
. 647222 
.647562 
.647903 
.648243 

9-648583 

Cot. 



D. i'\ 



5-85 
5.85 
5-85 
5-83 
5-85 
5-83 
5.83 
5.83 
5.82 
5.83 

5.82 
5.82 
5-82 
5-80 
5.82 
5.80 
5-80 
5.80 
5.78 
5-80 

5.78 
5.78 
5.78 
5.78 
5.77 
5.78 
5.77 
5-77 
5.75 
5.77 

5.75 
5.75 
5.75 
5.75 
5-75 
5.73 
5.75 
5-73 
5.73 
5.72 

5.73 
5.72 

5.72 
5.72 
5.72 
5-72 
5.70 
5-70 
5-70 
5.70 

5-70 
5-68 
5.70 
5.68 
5-68 
5-68 
5-67 
5.68 

5-67 

D. i'\ 



Cot. 



0.372148 
.371797 
.371446 
.371095 
.370745 

0.370394 
.370044 
.369694 
.369344 
.368995 

0.368645 
.368296 
.367947 
.367598 
. 367250 

0.366901 

.366553 
. 366205 

.365857 
.365510 

0.365162 

.364815 
. 364468 
.364121 
.363774 
0.363428 
.363081 

.362735 
.362389 
.362044 

0.361698 

.361353 
.361008 
.360663 
.360318 
0.359973 
.359629 
.359284 
.358940 
.358596 

0.358253 
.357909 
.357566 
.357223 
.356880 

0.356537 
.356194 
.355852 
.355510 
.355168 

0.354826 
.354484 
.354143 
.353801 
.353460 

0.353 I 19 
.352778 
.352438 
.352097 
.351757 

0.351417 

Tan. 



113° 



66° 



COSINES, TANGENTS, AND COTANGENTS 155° 



Sin. 



9.609313 
.609597 
.609880 
,610164 
.610447 

9.610729 
.611012 
.611294 
.611576 
.611858 

9. 61 2140 
.612421 
,612702 
.612983 
.613264 

9-613545 
.613825 
.614105 

.614385 
,614665 

9.614944 
.615223 
.615502 
.615781 
.616060 

9.616338 
.616616 
.616894 
.617172 
.617450 

9.617727 
.618004 
.618281 
.618558 
.618834 

9.619110 
.619386 
,619662 
.619938 
.620213 

9. 620488 
. 620763 
.621038 
.621313 
.621587 

9.621861 
.622135 
. 622409 
.622682 
. 622956 

9.623229 
. 623502 
.623774 
. 624047 
.624319 

9. 624591 
.624863 
.625135 
.625406 
.625677 

9. 625948 

Cos. 



D. I'' 



4.73 
4.72 
4.73 
4.72 
4.70 
4.72 
4.70 
4.70 
4.70 
4.70 

4.68 
4.68 
4.68 
4.68 
4.68 
4.67 
4.67 
4.67 

4.67 
4.65 

4-65 
4.65 
4.65 
4.65 
4.63 
4.63 
4-63 
4.63 
4-63 
4.62 

4.62 
4.62 
4.62 
4.60 
4.60 
4.60 
4.60 
4.60 
4.58 
4.58 

4.58 
4.58 
4.58 
4.57 
4.57 
4.57 
4.57 
4.55 
4.57 
4.55 

4.55 
4-53 
4.55 
4.53 
4.53 
4-53 
4.53 
4.52 
4.52 
4.52 

D. I". 



Cos. 



9.960730 
.960674 
.960618 
. 960561 
.960505 

9.960448 
,960392 

.960335 
, 960279 
,960222 

9.960165 
.960109 
.960052 
.959995 
.959938 



.959825 
.959768 
.959711 
.959654 

9-959596 
.959539 



.959425 
.959368 
9- 959310 
.959253 
.959195 
.959138 
.959080 

9.959023 
.958965 



.958850 
.958792 
9-958734 
.958677 
,958619 
.958561 
.958503 

9-958445 
.958387 
.958329 
.958271 
.958213 

9-958154 
,958096 
.958038, 
.957979 
.957921 

9-957863 
.957804 
.957746 
.957687 
,957628 

9-957570 
.957511 
.957452 
.957393 
.957335 

9- 957276 

Sin. 



D. I" 



97 



D. 1" 



Tan. 



.648923 
.649263 
.649602 
.649942 
9. 650281 
. 650620 

.650959 
.651297 
.651636 

9.651974 
.652312 
. 652650 
.652988 
.653326 

9.653663 
.654000 
.654337 
.654674 
.655011 

9- 655348 
,655684 
, 656020 
.656356 
, 656692 

9.657028 
.657364 
.657699 
,658034 

.658369 
9.658704 
.659039 
.659373 
, 659708 
. 660042 
9. 660376 
. 660710 
.661043 
.661377 
.661710 

9. 662043 
. 662376 
, 662709 
,663042 
.663375 

9.663707 
, 664039 
.664371 
,664703 
.665035 

9. 665366 
. 665698 
,666029 
, 666360 
, 666691 

9. 667021 
.667352 
,667682 
,668013 
.668343 

9.668673 

Cot. 



D.I" 



D. I" 



Cot, 



0.351417 
.351077 
.350737 
.350398 
.350058 

0.349719 
.349380 
.349041 
.348703 
.348364 

o. 348026 
,347688 

.347350 
.347012 
.346674 
0.346337 
.346000 

.345663 
.345326 
.344989 

0.344652 
.344316 
.343980 
.343644 
.343308 

0.342972 
.342636 
. 342301 
.341966 

.341631 
0.341296 
.340961 
.340627 
.340292 
.339958 
o. 339624 

.339290 
.338957 
.338623 
.338290 

0.337957 
.337624 
.337291 
.336958 
.336625 

o. 336293 

.335961 
.335629 
.335297 
.334965 

0.334634 
.334302 
.333971 
.333640 
.333309 

o. 332979 

.332648 
.332318 
.331987 
. 331657 

o. 331327 
Tan. 



65= 



25' 



LOGARITHMIC SINES 



154° 



M. 



o 

I 
a 
3 
4 
5 
6 

I 

9 

xo 
II 

12 

13 
14 
15 
16 

x8 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
43 
43 
44 
45 
46 
47 
48 

49 
50 
51 
53 
53 
54 



Sin. 



9.625948 
.626219 
,626490 
.626760 
. 627030 

9.627300 
.627570 
. 627840 
.628109 
.628378 

9. 628647 
.628916 
.629185 
.629453 
.629721 

9. 629989 
.630257 
.630524 
.630792 
.631059 

9.631326 

.631593 
.631859 
.632125 
.632392 
9. 632658 
. 632923 
.633189 
.633454 
.633719 

9.633984 
.634249 
.634514 
.634778 
.635042 

9.635306 
.635570 
.635834 
.636097 
.636360 

9.636623 
.636886 
.637148 
.637411 
.637673 

9.637935 
.638197 
.638458 
.638720 
.638981 

9.639242 
.639503 
.639764 
. 640024 
. 640284 

9.640544 



.641064 

.641324 

.641583 

9. 641842 

Cos. 



D. I". 



4.52 
4.52 
4.50 
4.50 
4.50 
4.50 
4.50 
4.48 
4.48 
4.48 

4.48 
4.48 
4.47 
4.47 
4.47 
4.47 
4.45 
4.47 
4-45 
4.45 

4.45 
4.43 
4.43 
4.45 
4.43 
4.42 
4.43 
4.42 
4.42 
4.42 

4.42 
4.42 
4.40 
4.40 
4.40 
4.40 
4.40 
4.38 
4.38 
4.38 

4.38 
4.37 
4.38 
4.37 
4.37 
4.37 
4.35 
4.37 
4.35 
4.35 

4.35 
4.35 
4.33 
4.33 
4-33 
4.33 
4.33 
4.33 
4.32 
4.32 

D. i'\ 



Cos. 



9.957276 
.957217 
.957158 
.957099 
.957040 

9.956981 
.956921 
.956862 
.956803 
.956744 

9.956684 
.956625 
.956566 
.956506 
.956447 

9.956387 
.956327 
.956268 
.956208 
.956148 

9.956089 
.956029 
.955969 
.955909 
.955849 

9.955789 
.955729 
.955669 
.955609 
.955548 

9.955488 
.955428 
.955368 
.955307 
.955247 

9.955186 
.955126 
.955065 
.955005 
.954944 

9.954883 
.954823 
.954762 
.954701 
.954640 

9.954579 
.954518 
.954457 
.954396 
.954335 

9.954274 
.954213 
.954152 
.954090 
.954029 

9.953968 
.953906 
.953845 
.953783 
.953722 

9.953660 

Sin. 



D. I" 



.98 
.98 



.98 
1. 00 



D. I" 



Tan. 



9.668673 
.669002 
.669332 
.669661 
.669991 

9. 670320 
. 670649 

.670977 
.671306 
.671635 

9.671963 
.672291 
.672619 
.672947 
.673274 

9.673602 
.673929 
.674257 
.674584 
.674911 

9.675237 
.675564 
.675890 
.676217 

.676543 
9.676869 
.677194 
.677520 
.677846 
.678171 

9.678496 
.678821 
. 679146 
.679471 

.679795 
9.680120 
. 680444 
.680768 
.681092 
.681416 

9.681740 
.682063 
.682387 
.682710 
.683033 

9.683356 
.683679 
.684001 
.684324 
.684646 

9.684968 
. 685290 
.685612 
.685934 
.686255 

9.686577 



.687219 

.687540 

.687861 

9.688182 

Cot. 



D.I" 



5.48 
5.50 

5.48 
5.50 
5.48 
5.48 
5.47 
5.48 
5.48 
5.47 

5.47 
5-47 
5.47 
5.45 
5.47 
5.45 
5.47 
5.45 
5.45 
5.43 

5.45 
5.43 
5-45 
5-43 
5.43 
5.42 
5.43 
5.43 
5.42 
5.42 

5-42 
5.42 
5.42 
5.40 
5-42 
5-40 
5-40 
5-40 
5.40 
5.40 

5.38 
5-40 
5.38 
5-38 
5.38 
5.38 
5.37 
5.38 
5.37 
5.37 

5.37 
5.37 
5.37 
5.35 
5.37 
5.35 
5.35 
5.35 
5.35 
5.35 

D. 1". 



Cot. 



0.331327 
.330998 
,330668 

.330339 

.330009 

o, 329680 

.329351 
,329023 
.328694 
.328365 

0.328037 
,327709 
.327381 
.327053 
. 326726 

0.326398 
.326071 
.325743 
.325416 
.325089 

0.324763 
.324436 
.324110 
.323783 
.323457 

0.323I3I 
,322806 
,322480 
.322154 
.321829 

0.321504 

.321179 
,320854 
,320529 
.320205 

o. 319880 

.319556 
.319232 
.318908 
.318584 

o. 318260 

.317937 
.317613 
,317290 
,316967 

0.316644 
.316321 
.315999 
.315676 
.315354 

0.315032 
.314710 
.314388 
,314066 
.313745 

0.313423 
.313102 
,312781 
,312460 
.312139 

0.3II8I8 

Tan. 



115^ 



COSINES, TANGENTS, AND COTANGENTS 153'' 



Sin. 






9.641842 


I 


. 642101 


3 


.642360 


3 


.642618 


4 


. 642877 


5 


9- 643135 


6 


.643393 


7 


.643650 


8 


.643908 


9 


.644165 


10 


9.644423 


II 


. 644680 


12 


.644936 


13 


.645193 


14 


. 645450 


15 


9. 645706 


16 


. 645962 


17 


.646218 


18 


.646474 


19 


.646729 


20 


9.646984 


21 


. 647240 


22 


. 647494 


23 


.647749 


24 


. 648004 


25 


9. 648258 


26 


.648512 


27 


.648766 


28 


. 649020 


29 


.649274 


30 


9.649527 


31 


. 649781 


32 


.650034 


33 


.650287 


34 


.650539 




9. 650792 


36 


.651044 


37 


.651297 


38 


.651549 


39 


.651800 


40 


9.652052 


41 


.652304 


4» 


.652555 


43 




44 


.653057 


45 


9.653308 


4b 




47 


. 653808 


48 


.654059 


49 


.654309 


50 


9.654558 


51 


.654808 


52 


.655058 


53 


.655307 


54 


.655556 




9.655805 


56 


.656054 


57 


.656302 


58 


.656551 


59 


.656799 


60 


9. 657047 



Cos. 



D. 1" 



4.32 
4.32 
4.30 
4.32 
4.30 
4.30 
4.28 
4.30 
4.28 
4.30 
4.28 
4.27 
4.28 
4.28 
4.27 
4.27 
4.27 
4.27 
4.25 
4.25 
4.27 
4.23 
4.25 
4.25 
4.23 
4.23 
4.23 
4.23 
4.23 
4.22 

4.23 
4.22 
4.22 
4.20 
4.22 
4.20 
4.22 
4.20 
4.18 
4.20 

4.20 
4.18 
4.18 
4.18 
4.18 
4.17 
4.17 
4.18 

4.17 
4.15 

4.17 
4.17 
4.15 
4.15 
4.15 
4.15 
4.13 
4.15 
4.13 
4.13 

D. i". 



Cos. 



9.953660 
.953599 
.953537 
.953475 
.953413 

9- 953352 
.953290 
.953228 
.953166 
.953104 

9.953042 
.952980 
.952918 
.952855 
.952793 

9- 952731 
.952669 
.952606 
.952544 
.952481 

9.952419 
.952356 
.952294 
.952231 
.952168 

9.952106 

.952043 
.951980 

.951917 
.951854 

9.951791 
.951728 
.951665 
.951602 
.951539 

9.951476 
.951412 

.951349 
.951286 
.951222 

9. 951 159 
.951096 
.951032 
.950968 

.950905 

9. 950841 

.950778 

.950714 
.950650 
.950586 

9.950522 
.950458 
.950394 
.950330 
.950- 6 

9. 950202 
.950138 

.950074 
.950010 

.949945 
9.949881 

Sin. 



D. I" 



1.02 
1.03 
1.03 
1.03 
1.02 
1.03 
1.03 
1.03 
1.03 
1.03 

1.03 
1.03 
1.05 
1.03 
1.03 
1.03 
1.05 
1.03 
1.05 
1.03 

1.05 
1.03 
1.05 
1.05 
1.03 
1.05 
1.05 
1.05 
1.05 
1.05 

1.05 
1.05 
1.05 
1.05 
1.05 
1.07 
1.05 
1.05 
1.07 
1.05 

1.05 
1.07 
1.07 
1.05 
1.07 
1.05 
1.07 
1.07 
1.07 
1.07 

1.07 
1.07 
1.07 
1.07 
1.07 
1.07 
1.07 
1.07 
1.08 
1.07 

D. 1". 



Tan. 



9. 688182 



.688823 
.689143 
.689463 

9.6897-83 
.690103 
. 690423 
. 690742 
.691062 

9.691381 
.691700 
.692019 
.692338 
. 692656 

9.692975 

.693293 
.693612 
.693930 
.694248 

9.694566 
.694883 
.695201 
.695518 
.695836 

9-696153 
. 696470 
. 696787 
.697103 
. 697420 

9.697736 
.698053 
.698369 
.698685 
.699001 

9. 699316 
. 699632 

.699947 
. 700263 
.700578 

9.700893 
.701208 
.701523 
.701837 
.702152 

9. 702466 
.702781 
.703095 
. 703409 
. 703722 

9. 704036 
.704350 
. 704663 
.704976 
. 705290 

9. 705603 
.705916 
. 706228 
.706541 
.706854 

9. 707166 

Cot. 



D. I". 



5.33 
5-35 
5.33 
5.33 
5.33 
5-33 
5.33 
5-32 
5-33 
5-32 

5.32 
5.32 
5.32 
5.30 
5.32 
5-30 
5-32 
5-30 
5-30 
5-30 

5.28 
5.30 
5.28 
5.30 
5.28 
5.28 
5.28 
5-27 
5.28 
5.27 
5.28 
5.27 
5-27 
5-27 
5-25 
5-27 
5-25 
5-27 
5.25 
5.25 

5.25 
5.25 
5.23 
5.25 
5.23 
5.25 
5.23 
5-23 
5.22 

5.23 
5.23 

5-22 
5-22 
5.23 
5-22 
5-22 
5.20 
5-22 
5-22 

5- 20 

D. I'^ 



Cot. 



0.3II8I8 
.311498 
.311177 
.310857 

.310537 

0.3I02I7 

.309897 
.309577 
.309258 
.308938 

0.308619 
.308300 
.307981 

. 307662 

.307344 

o. 307025 
. 306707 
.306388 

.306070 

.305752 

0.305434 
.305117 
.304799 
.304482 
. 304164 

0.303847 
.303530 
.303213 
. 302897 
.302580 

o. 302264 

.301947 
.301631 
.301315 
.300999 
o. 300684 
. 300368 
.300053 
. 299737 

.299422 

o. 299107 
. 298792 

.298477 
.298163 
. 297848 
o. 297534 
. 297219 
.296905 
. 296591 
. 296278 

o. 295964 
. 295650 

. 295337 
. 295024 
. 294710 

o. 294397 
. 294084 

. 293772 
. 293459 
. 293146 

o. 292834 
Tan. 



63' 



^r 






LOGARITHMIC SINES 




152" 


M. 
o 


Sin. 


D. 1". 


Cos. 


D. i''. 


Tan. 


D. 1". 


Cot. 




9. 657047 


4.13 
4.12 

4.13 
4.12 
4.12 
4.12 
4.12 
4.12 
4.10 
4. 10 


9. 949881 


1.08 


9. 707166 




0. 292834 


60 


I 

2 


.657295 
. 657542 


.949816 
.949752 


1.07 
1.07 
1.08 


. 707478 
. 707790 


5. 20 
5.20 
5.20 
5.20 
5.20 
5.18 
5.20 
5.18 

c ^9, 


.292522 
. 292210 


11 


3 


.657790 


.949688 


.708102 


. 291898 


57 


4 


.658037 


. 949623 


I 08 


. 708414 


. 291586 


56 




9. 658284 


9-949558 


\Z 


9. 708726 


0.291274 


55 


6 


.658531 


.949494 


.709037 


. 290963 


54 


fj 


.658778 


.949429 


I 08 


.709349 


.290651 


53 


g 


.659025 


.949364 


\.1 


. 709660 


. 290340 


52 


9 


.659271 


.949300 


.709971 


5.13 
5.18 


. 290029 


51 


lO 


9.659517 


4.10 
4.10 
4. 10 
4.10 
4.08 
4.08 
4.08 
4.08 
4.08 
4.07 


9.949235 


1.08 


9.710282 


5.18 
5.17 


0. 289718 


50 


n 


.659763 


.949170 


1*08 


. 710593 


. 289407 


11 


12 


.660009 


.949105 


1.08 


.710904 


'^^Tf 


13 


.660255 


.949040 


i!o8 


.711215 


.288785 


47 


^4 


. 660501 


.948975 


i!o8 


.711525 


.288475 


46 


15 


9. 660746 


9.948910 


i!o8 


9. 71 1836 


5.15 
5.17 
5.17 
5.17 


0. 288164 


45 


16 


. 660991 


.948845 


i!o8 


.712146 


.287854 


44 


17 


.661236 


.948780 


i!o8 


.712456 


.287544 


43 


18 


.661481 


.948715 


1,08 


.712766 


.287234 


42 


19 


.661726 


.948650 


1. 10 


.713076 


5- ^7 
5. 17 


. 286924 


41 


20 


9. 661970 


4.07 
4.08 


9.948584 


1.08 

1.08 


9.713386 




0. 286614 


40 


21 


,662214 


.948519 


.713696 


5. 17 
5.15 


. 286304 


39 


22 


.662459 


.948454 




. 714005 


. 285995 


38 


23 


. 662703 


4.07 


.948388 


i!o8 


.714314 


5- 15 


. 285686 


37 


24 


. 662946 


4.05 


.948323 




.714624 


5- 17 


.285376 


36 


25 


9.663190 


4.07 


9.948257 


1. 10 
1.08 


9.714933 


5. 15 

5.15 


0. 285067 


35 


26 


. 663433 


4- 05 


.948192 




.715242 


.284758 


34 


27 


. 663677 


4.07 


.948126 




.715551 


5. 15 


. 284449 


33 


28 


. 663920 


4- 05 


. 948060 


1. 10 
1.08 
1. 10 


.715860 


5. 15 


.284140 


32 


29 


.664163 


4-05 
4-05 


.947995 


.716168 


5.13 
5.15 


.283832 


31 


30 


9. 664406 




9. 947929 




9.716477 


5.13 


0.283523 


30 


31 


.664648 


4- 03 


.947863 




.716785 


.283215 


^g 


32 


.664891 


4-05 


. 947797 




.717093 


5- ^3 


. 282907 


28 


33 


.665133 


4-03 


.947731 


1. 10 


.717401 


5. 13 
5.13 
5.13 


. 282599 


27 


34 


.665375 


4-03 


. 947665 


1.08 


.717709 


. 282291 


26 


35 


9.665617 


4-03 


9. 947600 


9.718017 


0. 281983 


25 


36 


.665859 


4-03 


.947533 


1. 12 


.718325 


5. ^3 


.281675 


24 


37 


.666100 


4. 02 


.947467 


1. 10 


.718633 


5.13 


. 281367 


23 


38 


.666342 


4- 03 


.947401 


1. 10 


.718940 


5-^2 


. 281060 


22 


39 


.666583 


4. 02 
4.02 


.947335 


1. 10 
1. 10 


. 719248 


5- 13 
5.12 


.280752 


21 


40 


9. 666824 




9. 947269 




9- 719555 


5.12 


0. 280445 


20 


4^ 


. 667065 


4.02 


. 947203 


1. 10 


.719862 


.280138 


'2 


42 


.667305 


4. 00 


.947136 


1. 12 


. 720169 


5.12 
5.1-2 
5.12 


. 279831 


18 


43 


.667546 


4.02 


.947070 


• 


. 720476 


. 279524 


^l 


44 


.667786 


4. 00 


. 947004 


1. 10 


. 720783 


.279217 


16 




9. 668027 


4. 02 


9. 946937 


1. 12 


9. 721089 


5. 10 


0.27891 1 


15 


46 


.668267 


4.00 
3.98 


.946871 


1. 10 


. 721396 


5. 12 


. 278604 


14 


47 


.668506 


.946804 


1. 12 


.721702 


5. 10 
5.12 
5.10 
5.10 


. 278298 


13 


48 


. 668746 


4.00 


.946738 


1. 10 


.722009 


.277991 


12 


49 


.668986 


4. 00 
3.98 


.946671 


1. 12 


.722315 


.277685 


11 


50 


9. 669225 


3.98 
3.98 
3.98 
3.98 


9. 946604 




9. 722621 


5.10 
5.08 


0.277379 


10 


51 


. 669464 


.946538 




.722927 


.277073 


I 


52 


.669703 


.946471 




.723232 


. 276768 


53 


.669942 


.946404 


1. 12 


.723538 


5. 10 


. 276462 


7 


54 


.670181 


. 946337 


1. 12 


. 723844 


5.10 
5.08 
5.08 
5.10 
5.08 
5.08 


. 276156 


6 


55 


9. 670419 


IV^ 


9.946270 


1. 12 


9.724149 


0. 275851 


5 


56 


.670658 


. 946203 




. 724454 


. 275546 


4 


57 


. 670896 


3-97 


.946136 


1. 12 


.724760 


.275240 


3 


58 


.671134 


3-97 


. 946069 


1. 12 


. 725065 


.274935 


2 




.671372 


3.97 


. 946002 


1. 12 


. 725370 


.274630 


I 


60 


9. 671609 


3.95 


9. 945935 


1. 12 


9.725674 


5.07 


0.274326 







Cos. 


D. 1". 


Sin. 


D. 1". 


Cot. 


D. 1". 


Tan. 


U. 



iiT 



6a° 



COSINES, TANGENTS, AND COTANGENTS 151' 



M. 



22 
23 
24 
25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9.671609 
.671847 
.672084 
.672321 
.672558 

9.672795 
.673032 
.673268 

.673505 
.673741 

9. 673977 
.674213 
.674448 
. 674684 
.674919 

9-675155 
.675390 
.675624 

.675859 
. 676094 

9. 676328 
. 676562 
.676796 
.677030 
.677264 

9. 677498 
.677731 
.677964 
.678197 
.678430 

9.678663 
.678895 
.679128 
.679360 
.679592 

9. 679824 
. 680056 
.680288 
.680519 
.680750 

9. 680982 
.681213 
.681443 
.681674 
. 681905 

9.682135 
.682365 
.682595 
.682825 
.683055 

9.683284 
.683514 
.683743 
.683972 
. 684201 

9. 684430 
.684658 



.685115 

.685343 

9. 685571 

Cos. 



D. I" 



D. 1" 



Cos. 



9-945935 



.945800 

.945733 
. 945666 

9- 945598 
.945531 
.945464 
.945396 
.945328 

9.945261 
.945193 
.945125 
.945058 
.944990 

9. 944922 
.944854 
.944786 
.944718 
.944650 

9. 944582 
.944514 
.944446 

.944377 
.944309 
9.944241 
.944172 
.944104 
.944036 
.943967 

9.943899 
. 943830 
.943761 

.943693 

. 943624 

9- 943555 

.943486 

.943417 
.943348 
.943279 

9.943210 
.943141 
. 943072 
.943003 
.942934 

9. 942864 
.942795 
.942726 
.942656 
.942587 

9- 942517 
.942448 
.942378 
.942308 
. 942239 

9.942169 
.942099 
. 942029 

.941959 

. 941889 

9.941819 

Sin. 



D. I". 



13 



D. I" 



Tan. 



9. 725674 

. 725979 
. 726284 
.726588 
. 726892 
9.727197 
.727501 
. 727805 
. 728109 
.728412 

9. 728716 
. 729020 
.729323 
. 729626 

• 729929 
9- 730233 

.730535 
.730838 
.731141 
. 731444 

9.731746 
. 732048 
. 732351 
.732653 
. 732955 

9- 733257 

• 733558 
.733860 
.734162 
. 734463 

9. 734764 
. 735066 

. 735367 
.735668 
. 735969 
9. 736269 
. 736570 
. 736870 
.737171 
.737471 

9- 737771 
.738071 

. 738371 
.738671 
.738971 
9. 739271 
. 739570 
. 739870 
. 740169 
. 740468 

9. 740767 
.741066 

. 741365 

. 741664 

. 741962 

9. 742261 

. 742559 
.742858 
.743156 
. 743454 
9. 743752 

Cot. 



D. i''. 



5.08 
5.08 
5-07 
5.07 
5.08 
5.07 
5.07 
5.07 
5.05 
5.07 

5.07 
5.05 
5.05 
5.05 
5-07 
5.03 
5-05 
5.05 
5.05 
5.03 

5-03 
5-05 
5.03 
5-03 
5.03 
5.02 

5-03 
5.03 
5.02 
5.02 

5.03 
5.02 
5.02 
5.02 
5.00 
5.02 
5.00 
5.02 
5.00 
5.00 

5-00 
5.00 
5.00 
5.00 
5- 00 
4.98 
5.00 
4.98 
4.98 
4.98 

4.98 
4.98 
4.98 
4.97 
4.98 
4.97 
4.98 
4-97 
4-97 
4.97 

D. I''. 



Cot. 



o. 274326 
. 274021 
.273716 
.273412 
.273108 

o. 272803 

. 272499 
.272195 

.271891 

.271588 

o. 271284 
. 270980 

. 270677 
.270374 

. 270071 
o. 269767 

. 269465 
. 269162 

. 268859 
.268556 

o. 268254 

. 267952 

. 267649 

.267347 
. 267045 
o. 266743 
. 266442 
. 266140 

.265838 
.265537 

o. 265236 

. 264934 
. 264633 
. 264332 
. 264031 
o. 263731 

. 263430 
. 263130 

. 262829 
. 262529 

o. 262229 
. 261929 
. 261629 
. 261329 
. 261029 

o. 260729 
, 260430 
, 260130 

.259831 
. 259532 

0.259233 
. 258934 
.258635 
. 258336 
.258038 

0.257739 

. 257441 
.257142 
. 256844 

. 256546 
o. 256248 

Tan. 



)Xi8^ 



61^ 



29* 



LOGARITHMIC SINES 



150^ 



M. 



zo 
II 

13 
13 

M 

U 
\l 

19 
ao 
21 

23 

23 
24 

25 

26 
27 
28 
29 

30 
31 
33 

33 
34 
35 
36 
37 
38 
39 

40 
41 
42 
43 
44 
45 
46 

48 
49 
50 
51 
52 
53 
54 

56 

58 

60 



Sin. 



9-685571 
.685799 
.686027 
.686254 
. 686482 

9.6S6709 
.686936 
.6S7163 
.6S7389 
.687616 

9.687843 
.68S069 
.688295 
.688521 

.688747 

9.688972 

.689198 

1689648 
.6S9873 

9.69009S 
.690323 
.690548 
.690772 
.69099') 

9.691220 
.691444 
.69166S 
.691892 
.692115 

9.692339 
.692562 
.6927S5 
. 69300S 
.693231 

9. 693453 
. 693676 
. 693898 
. 694 1 20 
.694342 

9 694564 
.694786 
. 695007 
.695229 
.695450 

9.695671 
.695892 
.696113 
.696334 
•696554 

9.696775 
.696995 
.697215 

.697435 
.697654 
9.697874 
.698094 
.698313 
.698532 

.698751 
9.698970 

Cos. 



I). i'\ I 



Cos. 



3.80 
3.80 
3.78 
3.80 
3.78 
3.78 
3.78 
3.77 
3-78 
3-78 

3-77 
3-77 
3.77 
3.77 
3-75 
3.77 
3.75 
3-75 
3-75 
3.75 

3.75 
3-75 
3-73 
3.73 
3-73 
3.73 
3.73 
3-73 
3.72 
3-73 

3.72 
3.72 
3-72 
3-72 
3.70 
3.72 
3-70 
3-70 
3- 70 
3.70 

3.70 
3.68 
3.70 

3.68 
3.68 
3-68 
3.68 
3.68 
3.67 
3.68 

3.67 
3.67 
3.67 
3-65 
3.67 
3.67 
3.65 
3.65 
3.65 
3-65 ! 

D. I". \ 



9-941819 

.941749 
.941679 
.941609 

.941539 
9.941469 

.941398 
.941328 
.941258 
.941187 

9.941117 
.941046 
.940975 
.940905 
.940834 

9.940763 
.940693 
.940622 
.940551 
.940480 

9.940409 
.940338 
.940267 
.940196 
.940125 

9. 940054 
.939982 
.939911 
.939S40 
.939768 

9- 939697 
.939625 
.939554 
.939482 
.939410 

9-939339 
.939267 

.939195 
.939123 
.939052 

9.938980 
.938908 
.938836 
.938763 
.938691 

9.938619 
.938547 
.938475 
. 938402 
.938330 

9.938258 
.938185 
.938113 
. 938040 

. 937967 

9.937895 

.937822 

.937749 

.937676 

. 937604 

9. 937531 

Sin. 



D. 1". 



1. 17 
1. 17 
1. 17 
1.17 

1. 17 

1. 18 
1. 17 

1. 17 

1. 18 

1. 17 

1. 18 
1. 18 

1. 17 
1.18 

1. 18 

1. 17 

1. 18 
1. 18 
1.18 
1. 18 

1.18 
1.18 
1. 18 
1. 18 
1.18 
1. 20 
1.18 
1. 18 
I. 20 
1.18 

I. 20 
1.18 
1.20 
I. 20 
1.18 
1.20 
1. 20 
1.20 
1. 18 
1.20 

1.20 
1.20 
I. 22 
I. 20 
I. 20 
I. 20 
1.20 
1.22 
1.20 
1.20 

1.22 
1.20 
1.22 
1.22 
1.20 
1.22 
1.22 
1.22 
1.20 
1.22 

D. I". 



Tan. 



9. 743752 
. 744050 
. 744348 
. 744645 
. 744943 

9-745240 
. 745538 
. 745>^35 
.746132 
.746429 

9. 746726 
. 747023 
.747319 
.747616 
.747913 

9. 748209 
. 748505 
.748801 

.749097 

.749393 

9.749689 

.749985 
.750281 
. 750576 
. 750872 

9. 751 167 
.751462 
.751757 
. 752052 
.752347 

9.752642 
. 752937 
.753231 
.753526 
. 753820 

9.754115 
.754409 
.754703 
.754997 
.755291 

9.755585 
.755878 
.756172 
.756465 
. 756759 

9- 757052 
. 757345 
.757638 
.757931 
.758224 

9.758517 
.758810 
. 759102 
. 759395 
.759687 

9-759979 
. 760272 

. 760564 

. 760856 

.761148 

9. 761439 

Cot. 



I). 1' 



4-97 
4.97 
4.95 
4-97 
4.95 
4.97 
4.95 
4.95 
4-95 
4.95 

4.95 
4.93 
4.95 
4.95 
4-93 
4.93 
4-93 
4.93 
4.93 
4.93 

4-93 
4.93 
4-92 
4-93 
4.92 
4.92 
4-92 
4.92 
4.92 
4-92 

4.92 
4.90 
4.92 
4-90 
4.92 
4-90 
4-90 
4.90 
4.90 
4.90 

4.88 
4.90 
4.88 
4-90 
4.88 
4.88 
4.88 
4.88 
4.88 
4.88 

4.88 
4.87 
4.88 
4.87 
4.87 
4.88 
4-87 
4.87 
4-87 
4.85 

D. I". 



Cot. 



o. 256248 

. 255950 

.255652 

. 255355 

. 255057 
o. 254760 

.254462 
.254165 
.253868 
.253571 

o. 253274 

. 252977 
.252681 

.252384 
. 252087 

o. 251791 

.251495 
.251199 
.250903 
.250607 

0.2503 1 1 

. 250015 

.249719 
. 249424 

.249128 
o. 248833 

.248538 
. 248243- 
. 247948 
. 247653 

o. 247358 
. 247063 
. 246769 

. 246474 

. 246180 
o. 245885 

. 245591 
. 245297 
. 245003 
.244709 

o. 244415 20 
.244122 ig 
.243828 ~ 

. 243535 

.243241 

o. 242948 

. 242655 
. 242362 
. 242069 
. 241776 

o. 241483 

.241190 

, 240898 

. 240605 

. 240313 
o. 240021 

. 239728 

. 239436 

. 239144 

. 238852 

o. 238561 
Tan. 



119'' 



60^ 



;0* COSINES, TANGENTS, AND COTANGENTS 149^ 



M. Sin. D. 1". Cos. D. i". i Tan. D. i". Cot 



9. 698970 
.699189 
.699407 
. 699626 
.699844 

9.700062 
. 700280 
. 700498 
.700716 
. 700933 

9.701151 
. 701368 

.701585 
. 701802 
. 702019 
9. 702236 
. 702452 
. 702669 
.702885 
. 703 lOI 

9. 703317 
. 703533 
.703749 
.703964 
.704179 

9. 704395 
.704610 
.704825 
. 705040 
.705254 

9. 70.5469 
.705683 
.705898 
,706112 
.706326 

9- 706539 
. 706753 
.706967 
.707180 
. 707393 

9. 707606 

.707819 
, 708032 
. 708245 
.708458 
9. 708670 
. 708882 
.709094 
. 709306 
.709518 

9. 709730 
.709941 
.710153 
.710364 

.710575 
9.710786 
.710997 
.711208 
.711419 
.711629 
9-711839 

Cos. 



3.65 
3.63 

3-63 
3.63 
3.63 
3-63 
3.63 
3.62 
3.63 
3-62 
3-62 
3.62 
3-62 
3-62 
3.60 
3.62 
3- 60 
3.60 
3- 60 

3.60 
3- 60 
3.58 
3.58 
3- 60 
3.58 

3.58 
3-57 
3.58 

3.57 
3.58 
3.57 
3.57 
3-55 
3.57 
3-57 
3.55 
3.55 
3.55 

3.55 
3-55 
3.55 
3.55 
3.53 
3-53 
3.53 
3-53 
3.53 
3-53 

3-52 
3.53 
3.52 
3.52 
3.52 
3.52 
3.52 
3.52 
3.50 
3.50 

D. I". 



9-937531 
.937458 
.937385 
.937312 
.937238 

9.937165 
.937092 
.937019 
.936946 
.936872 

9.936799 

.936725 
. 936652 
.936578 
. 936505 

9.936431 
.936357 
. 936284 
.936810 
.936136 

9. 936062 
.935988 
.935914 
.935840 
.935766 

9. 935692 
.935618 
.935543 
. 935469 
.935395 

9.935320 
.935246 
.935171 
.935097 
. 935022 

9. 934948 
.934873 
.934798 
.934723 
.934649 

9.934574 
.934499 
.934424 
.934349 
.934274 

9.934199 
.934123 
.934048 
.933973 
.933898 

9.933822 
.933747 
.933671 
•933596 
.933520 

9.933445 
.933369 
.933293 
.933217 
.933141 

9. 933066 

Sin. 



1.22 
I. 22 
1.22 
1.23 
1.22 
1.22 
1.22 
1.22 
1.23 
1.22 

1.23 
1.22 
1.23 
1.22 
1.23 
1.23 
1.22 
1.23 
1.23 
1.23 

1.23 
1.23 
1.23 
1.23 
1.23 
1.23 
1.25 
1.23 
1.23 
1.25 
1.23 

1.25 
1.23 
1.25 
1.23 
1.25 
1.25 
1.25 
1.23 
1.25 

1.25 
1.25 
1.25 
1.25 
1.25 
1.27 
1.25 
1.25 
1.25 
1.27 

1.25 
1.27 
1.25 
1.27 
1.25 
1.27 
1.27 
1.27 
1.27 
1.25 

D. l'\ 



9. 761439 
.761731 
. 762023 

.762314 

. 762606 

9.762897 

.763188 

.763479 
. 763770 
. 764061 

9. 764352 
.764643 
. 764933 
.765224 
.765514 

9. 765805 
. 766095 
.766385 
. 766675 
.766965 

9.767255 
.767545 
.767834 
.768124 
. 768414 

9. 768703 
. 768992 
, 769281 

.769571 
.769S60 

9.770148 

.770437 
. 770726 

.771015 
.771303 
9.771592 
.771880 
.772168 
. 772457 
.772745 

9.773033 
.773321 
. 773608 
. 773896 
.774184 

9. 774471 
.774759 
. 775046 
• 775333 
.775621 

9.775908 
.776195 
. 776482 
. 776768 
.777055 

9. 777342 
.777628 

.777915 
.778201 



9- 778774 
Cot. 



4.87 
4.87 
4.85 
4.87 
4.85 
4.85 
4.85 
4.85 
4.85 
4.85 

4.85 
4.83 
4.85 
4.83 
4.85 
4.83 
4.83 
4.83 
4.83 
4.83 

4.83 
4.82 
4.83 
4.83 
4.82 
4.82 
4.82 
4.83 
4.82 
4.80 

4.82 
4.82 
4.82 
4.80 
4.82 
4.80 
4.80 
4.82 
4.80 
4.80 

4.80 
4.78 
4.80 
4.80 
4.78 
4.80 
4.78 
4.78 
4.80 
4.78 

4.78 
4.78 
4.77 
4.78 
4.78 
4.77 
4.78 
4.77 
4.78 
4.77 

D. I". 



o. 238561 
. 238269 

.237977 
.237686 

. 237394 

o. 237103 

.236812 

. 236521 
. 236230 
.235939 

o. 235648 

. 235357 
. 235067 
.234776 
. 234486 

o. 234195 

.233905 
.233615 

. 233325 

.233035 

0.232745 

.232455 

.232166 

. 231876 
.231586 
0.231297 
.231008 
. 230719 
. 230429 

. 230140 

o. 229852 
. 229563 

. 229274 

.228^5 

. 228697 
o. 228408 
.228120 
. 227832 
.227543 
. 227255 

0.226967 
. 226679 
. 226392 
. 226104 

. 225816 

o. 225529 

. 225241 

. 224954 

. 224667 

. 224379 

o. 224092 
. 223805 
. 223518 
. 223232 
. 222945 

o. 222658 
. 222372 
.222085 
. 221799 
.221512 

0.221226 

Tan. 



59' 



31" 



LOGARITHMIC SINES 



M. 



Sin. 



xo 
zz 

Z3 

13 

19 



22 

23 
24 

26 
27 
28 
29 

30 
31 
32 
33 

34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 
47 
48 

49 
50 
51 
53 
53 
54 
55 
56 

52 
58 

59 
60 



121^ 



9.711839 
712050 
712260 
712469 
712679 
712889 
713098 
713308 
713517 
713726 

713935 

714144 
714352 
714561 
714769 
714978 
715186 

715394 
715602 
715809 

716017 
716224 
716432 
716639 
716846 

717053 
717259 
717466 
717673 
717879 

718085 
718291 
718497 
718703 
718909 
719114 
719320 

719525 
719730 

719935 

720140 

720345 
720549 
720754 
720958 
721162 
721366 
721570 
721774 
721978 

722181 
722385 
722588 
722791 
722994 
723197 
723400 
723603 
723805 
724007 
724210 



Cos. D. I 



D. i". 



50 



Cos. 



9. 933066 
.^32990 
.932914 
.932838 
.932762 

9.932685 
. 932609 
.932533 
.932457 
.932380 

9-932304 
.932228 

.932151 
.932075 
.931998 
9-931921 
.931845 
.931768 
.931691 
.931614 

9-931537 
.931460 

.931383 
.931306 
.931229 

9.931152 
.931075 
.930998 
.930921 
.930843 

9.930766 



.930611 
.930533 
.930456 
9-930378 
. 930300 
.930223 

.930145 
.930067 

9.929989 
.929911 
.929833 
.929755 
.929677 

9.929599 
. 929521 
.929442 
.929364 
. 929286 

9. 929207 
.929129 
.929050 
. 928972 
.928893 

9-928815 
.928736 
.928657 
.928578 
.928499 

9. 928420 

Sin. 



D. 1" 



D. z" 



Tan. 



9. 778774 
. 779060 
.779346 
. 779632 
.779918 

9. 780203 



.780775 
.781060 
.781346 

9. 781631 
.781916 
.782201 
.782486 
.782771 

9. 783056 

.783341 
.783626 
.783910 
.784195 

9. 784479 
.784764 
.785048 
. 785332 
.785616 

9. 785900 
.786184 
.786468 
.786752 
. 787036 

9- 787319 
. 787603 
. 787886 
.788170 

-788453 
9.788736 
. 789019 
. 789302 
.789585 



9- 790151 
. 790434 
.790716 
. 790999 
.791281 

9- 791563 
. 791846 
.792128 
. 792410 
. 792692 

9- 792974 
.793256 
.793538 
.793819 
.794101 

9.794383 
. 794664 
. 794946 
.795227 
. 795508 

9- 795789 

Cot. 



D. i'\ 



4-77 
4.77 
4.77 
4.77 
4.75 
4-77 
4-77 
4.75 
4.77 
4.75 

4.75 
4.75 
4.75 
4.75 
4.75 
4.75 
4.75 
4.73 
4.75 
4.73 

4.75 
4-73 
4.73 
4.73 
4.73 
4.73 
4.73 
4.73 
4.73 
4.72 

4.73 
4.72 
4.73 
4.72 
4.72 
4.72 
4.72 
4.72 
4.72 
4.72 

4.72 
4.70 
4.72 
4.70 
4.70 
4.72 
4.70 
4.70 
4-70 
4.70 
4.70 
4.70 
4.68 
4.70 
4.70 
4.68 
4.70 
4.68 
4.68 
4.68 

D. I''. 



COSINES, TANGENTS, AND COTANGENTS 147° 



Sin. 



9. 724210 
. 724412 
. 724614 
.724816 
. 725017 

9. 725219 
. 725420 
. 725622 
. 725823 
. 726024 

9. 726225 
. 726426 
.726626 
. 726827 
. 727027 

9. 727228 
. 727428 
. 727628 
. 727828 
. 728027 

9. 728227 
. 728427 
. 728626 
.728825 
. 729024 

9. 729223 
. 729422 
.729621 
. 729820 
. 730018 

9. 730217 

.730415 
. 730613 
.730811 
.731009 
9.731206 
. 731404 
.731602 

.731799 
. 731996 

9- 732193 
. 732390 
.732587 
.732784 
. 732980 

9. 733177 
. 733373 
.733569 
. 733765 
. 733961 

9.734157 
. 734353 
. 734549 
. 734744 
. 734939 

9.735135 
. 735330 
. 735525 
. 735719 
. 735914 

9- 736109 

Cos. 



D. I" 



3.37 
3.37 
3.37 
3.35 
3.37 
3.35 
3.37 
3-35 
3.35 
3.35 

3-35 
3.33 
3.35 
3.33 
3.35 
3.33 
3-33 
3-33 
3.32 
3.33 

3.33 
3.32 
3.32 
3.32 
3-32 
3-32 
3-32 
3.32 
3.30 
3.32 

3.30 
3.30 
3-30 
3.30 
3.28 
3.30 
3.30 
3.28 
3.28 
3.28 

3-28 
3.28 
3.28 
3.27 
3.28 
3.27 
3.27 
3.27 
3-27 
3.27 

3.27 
3.27 
3.25 
3.25 
3-27 
3-25 
3.25 
3.23 
3.25 
3.25 

D. I''. 



Cos. 



9. 928420 
.928342 
, 928263 
.928183 
.928104 

9. 928025 
.927946 
. 927867 
.927787 
, 927708 

9.927629 

.927549 
,927470 
.927390 
,927310 
9.927231 

.927151 
,927071 
, 926991 
,926911 

9. 926831 
.926751 
.926671 
.926591 
.926511 

9. 926431 

.926351 
, 926270 
,926190 
.926110 

9. 926029 

.925949 
.925868 
.925788 

.925707 
9. 925626 

.925545 
.925465 
.925384 
.925303 

9. 925222 
.925141 
. 925060 
.924979 
.924897 

9.924816 

.924735 
.924654 
.924572 
.924491 

9.924409 
.924328 
. 924246 
. 924164 
. 924083 

9. 924001 
.923919 
.923837 
. 923755 
. 923673 

9. 923591 

Sin. 



D. I" 



1.30 
1.32 
1.33 
1.32 
1.32 
1.32 
1,32 

1-33 
1.32 

1.32 

1.33 
1.32 

1.33 
1.33 
1.32 

1.33 
1-33 
1.33 
1-33 
1-33 

1.33 
1.33 
1.33 
1.33 
1-33 
1-33 
1.35 
1-33 
1-33 
1.3s 

1.33 
1.35 
1.33 
1.35 
1.35 
1.35 
1.33 
1.35 
1.35 
1.35 

1.35 
1.35 
1.35 
1.37 
1.35 
1.35 
1.35 
1.37 
1-35 
1.37 

1.35 
1.37 
1.37 
1-35 
1.37 
1-37 
1.37 
1.37 
1.37 
1.37 

D. i'\ 



Tan. 



9. 795789 
. 796070 

.796351 
. 796632 

. 796913 
9. 797194 

. 797474 
. 797755 
. 798036 
.798316 

9. 798596 
.798877 
. 799157 
. 799437 
. 799717 

9. 799997 
. 800277 
.800557 
.800836 
.801116 

9. 801396 
.801675 
.801955 
. 802234 
. 802513 

9. 802792 
. 803072 

.803351 
. 803630 
,803909 

9.804187 
. 804466 

.804745 
. 805023 
. 805302 
9. 805580 
.805859 
.806137 
.806415 
.806693 

9. 806971 
. 807249 
.807527 
. 807805 



9. 808361 



.809193 
.809471 

9. 809748 
.810025 
.810302 
.810580 
.810857 

9-811134 
.811410 
.811687 
.811964 
.812241 

9-812517 

Cot. 



D. I". 



4.68 
4.68 
4.68 
4.68 
4.68 
4.67 
4.68 
4.68 
4.67 
4.67 

4.68 
4.67 
4.67 
4.67 
4.67 
4.67 
4.67 
4-65 
4.67 
•4.67 

4.65 
4.67 
4.65 
4.65 
4.65 
4.67 
4.65 
4.65 
4.65 
4.63 

4.65 
4.65 
4.63 
4.65 
4.63 
4.65 
4.63 
4.63 
4-63 
4.63 

4.63 
4.63 
4.63 
4.63 
4.63 
4.62 
4-63 
4.62 
4.63 
4.62 

4.62 
4.62 
4.63 
4.62 
4.62 
4.60 
4.62 
4.62 
4.62 
4.60 

D. I". 



Cot. 



0.20421 I 
. 203930 
. 203649 
. 203368 
. 203087 

o. 202806 
. 202526 
, 202245 
. 201964 
. 201684 

o. 201404 
,201123 
, 200843 

, 200563 

. 200283 
o. 200003 

. 199723 
. 199443 

, I99I64 

. 198884 

o. 198604 

.198325 
. 198045 
. 197766 

. 197487 

o. 197208 
. 196928 
. 196649 
. 196370 

. I9609I 

o. 195813 
. 195534 
. 195255 
. 194977 

. 194698 
o. 194420 

.194141 
. 193863 
. 193585 
. 193307 

o. 193029 

. I9275I 
. 192473 
. I92I95 
.191917 

o. 191639 

. I9I362 

. I 9 1084 
. 190807 

. 190529 

o. 190252 

. 189975 
. 189698 
, 189420 
. I89I43 

o. 188866 
, 188590 
. I883I3 
. 188036 
. 187759 

o. 187483 
Tan. 



57^ 



33° 



LOGARITHMIC SINES 



146" 



M. 



38 
39 
40 
41 
42 
43 
44 
45 
46 

48 
49 

50 
51 
53 
53 
54 
55 
56 

II 



Sin. 



9. 736109 
.736303 
.736498 
. 736692 
. 736886 

9.737080 
.737274 
.737467 
.737661 

.737855 

9. 738048 

.738241 

.738434 
.738627 
.738820 

9- 739013 
. 739206 

. 739398 
.739590 
.739783 

9- 739975 
. 740167 

. 740359 
. 740550 
. 740742 

9- 740934 
.741125 
.741316 
.741508 
.741699 

9.741889 
. 742080 
.742271 
. 742462 
. 742652 

9. 742842 
.743033 
.743223 
.743413 
. 743602 

9.743792 
.743982 
.744171 
. 744361 
. 744550 

9. 744739 
. 744928 
.745117 
. 745306 
.745494 

9.745683 
.745871 
. 746060 
. 746248 
. 746436 

9. 746624 
.746812 

.746999 

.747187 

.747374 

9. 747562 



Cos. D. I". 



D. I'' 



3 

3 

3 

3 

3 

3 

3 

3.23 

3.23 

3.22 

3.22 

3-22 

3.22 
3.22 
3.22 

3-22 
3.20 
3.20 
3.22 
3.20 

3-20 

3.20 
3.18 
3.20 
3.20 

3.18 

3.20 

3.18 
3.17 

3.18 
3.18 
3.18 
3.17 



3.17 
3.15 



3.13 
3.15 

3.13 
3.15 
3.13 
3.13 
3.13 
3.13 

3.12 

3.13 

3.12 

3.13 



Cos. 



9.923591 
.923509 
.923427 
.923345 
. 923263 

9.923181 
. 923098 
,923016 

.922933 
.922851 

9. 922768 



. 922603 
. 922520 
. 922438 
9. 922355 
.922272 
.922189 
.922106 
. 922023 

9. 921940 
.921857 
.921774 
.921691 
.921607 

9.921524 
.921441 
.921357 
.921274 
.921190 

9. 921 107 
.921023 

.920939 
. 920856 
.920772 
9. 920688 
. 920604 
. 920520 
. 920436 
.920352 

9. 920268 
.920184 
. 920099 
.920015 
.919931 

9.919846 
.919762 
.919677 

.919593 
.919508 

9.919424 
. 919339 
.919254 
.919169 

. 919085 
9. 919000 
.918915 
.918830 
.918745 
. 918659 
9-918574 

Sin. 



D. I" 



1.37 
1.37 
1.37 
1.37 
1.37 
1.38 
1.37 
1.38 
1.37 
1.38 

1.37 

1.38 
1.38 
1-37 
1.38 
1.38 

'•^! 

1.38 

1.38 

'•^? 
1.38 

1.40 
1.38 
1.38 
1.40 
1.38 
1.40 
1.38 
1.40 
1.40 
1.38 
1.40 
1.40 
1.40 
1.40 
1.40 
1.40 
1.40 

1.40 
1.42 
1.40 
1.40 
1.42 
1.40 
1.42 
1.40 
1.42 
1.40 

1.42 
1.42 
1.42 
1.40 
1.42 
1.42 
1.42 
1.42 

1.43 
1.42 

D. I". 



Tan. 



D. I". 



9.812517 
.812794 
. 813070 

.813347 
.813623 
9.813899 
.814176 
.814452 
.814728 
. 815004 

9. 815280 
.815555 
.815831 
.816107 
.816382 

9.816658 
.816933 
.817209 
.817484 
.817759 

9. 818035 
.818310 
.818585 
.818860 

.819135 

9. 819410 

.819684 

. 819959 
.820234 



9. 820783 
.821057 
.821332 
.821606 
. 821880 

9.822154 
. 822429 
. 822703 
. 822977 
. 823251 

9. 823524 
.823798 
. 824072 
.824345 
. 824619 

9. 824893 
.825166 
.825439 
.825713 
.825986 

9.826259 
.826532 
. 826805 
. 827078 
.827351 

9. 827624 
.827897 
.828170 
. 828442 
.828715 

9. 828987 

Cot. 



4.62 
4.60 
4.62 
4.60 
4.60 
4.62 
4.60 
4.60 
4.60 
4.60 

4.58 
4.60 
4.60 
4.58 
4.60 
4.58 
4.60 
4.58 
4.58 
4.60 

4.58 
4.58 
4.58 
4.58 
4.58 
4.57 
4.58 
4.58 
4.57 
4.58 

4.57 
4.58 
4.57 
4.57 
4.57 
4.58 
4.57 
4.57 
4.57 
4.55 

4.57 
4.57 
4.55 
4.57 
4.57 
4.55 
4.55 
4.57 
4.55 
4.55 

4-55 
4.55 
4.55 
4.55 
4.55 
4.55 
4-55 
4.53 
4.55 
4.53 

D. 1''. 



Cot. 



o. 187483 
.187206 
. 186930 
.186653 
.186377 

o. 186101 

.185824 
.185548 
. 185272 
. 184996 

o. 184720 

. 184445 

. I84I69 

.183893 

. I836I8 

o. 183342 

. 183067 
. I8279I 
. I825I6 

. 18224 I 

o. 181965 
. I8I690 

.181415 

.181140 
. 180865 
o. 180590 
.180316 
. I 8004 I 
. 179766 
.179492 

o. 179217 

. 178943 
. 178668 

.178394 

.178120 
o. 177846 

.177571 
. 177297 
. 177023 
. 176749 

o. 176476 
. 176202 

.175928 
.175655 
. I7538I 

o. I 75 107 
.174834 
. 174561 
. 174287 
. 174014 

o. 173741 
. 173468 
.173195 
. 172922 
. 172649 

o. 172376 
. I72I03 
. I7I830 
. I7I558 
. I7I285 

o. 171013 
Tan. 



"3 



56° 



COSINES, TANGENTS, AND COTANGENTS 145° 



Sin. 



9. 747562 
.747749 
.747936 
.748123 
.748310 

9. 748497 
.748683 
. 748870 
. 749056 
.749243 

9. 749429 
. 749615 
. 749801 
. 749987 
.750172 

9. 750358 
. 750543 
. 750729 

.750914 
. 751099 

9.751284 
. 751469 
. 751654 
. 751839 
. 752023 

9. 752208 
. 752392 
. 752576 
. 752760 
. 752944 

9.753128 
.753312 
.753495 
. 753679 
.753862 

9. 754046 
. 754229 
. 754412 
. 754595 
.754778 

9. 754960 
• 755143 
.755326 
.75550S 
.755690 

9. 755872 
. 756054 
. 756236 
.756418 
. 756600 

9.756782 
.756963 
.757144 
.757326 
.757507 

9.757688 
.757869 
. 758050 
. 758230 
.758411 



Cos. 



12 



10 



10 



3. 

3" 

3. 

3. 

3- 

3- 

3. 

3. 

3- 

3.10 

3.10 

3.10 

3- 10 

3^08 

3- 10 

3.08 

3.10 

3.08 

3.08 

3.08 

3.08 
3.08 
3.08 
3.07 
3.08 
3.07 
3.07 
3.07 
3.07 
3.07 

3-07 
3.05 
3.07 
3.05 
3.07 
3.05 
3.05 
3-05 
3.05 
3.03 

3.05 
3.05 
3.03 
3.03 
3.03 
3.03 
3.03 
3.03 
3.03 
3.03 

3.02 
3.02 
3.03 
3.02 
3.02 
3.02 
3.02 
3.00 
3.02 
3.00 

D. I". 



Cos. 



9.918574 
.918489 
, 918404 
.918318 
.918233 

9.918147 
. 918062 
.917976 
.917891 
.917805 

9.917719 
.917634 
.917548 
. 917462 
. 917376 

9.917290 
.917204 
.917118 
.917032 
.916946 

9. 916859 

.916773 
.916687 
.916600 
.916514 
9. 916427 
.916341 
.916254 
.916167 
.916081 

9. 915994 
.915907 
.915820 

.915733 
.915646 

9.915559 
.915472 
.915385 
.915297 
.915210 

9.915123 

.915035 
.914948 
. 914860 

.914773 
9.914685 

. 914598 
.914510 
.914422 
.914334 

9.914246 
.914158 
, 914070 
.913982 

.913894 
9. 913806 
.913718 
.913630 
.913541 
.913453 
9.913365 

Sin. 



.42 

.42 
•43 
.42 
•43 
.42 
•43 
.42 
•43 
.43 
.42 
.43 
•43 
•43 
•43 
.43 
.43 
.43 
•43 
.45 

.43 
.43 
• 45 
.43 
.45 
.43 
.45 
•45 
.43 
.45 

.45 
.45 
•45 
•^5 
.45 
.45 
.45 
.47 
.45 
.45 

.47 
•45 
.47 
.45 
.47 
.45 
.47 
.47 
.47 
.47 

.47 
.47 
.47 
.47 
.47 
.47 
.47 
.48 
.47 
.47 



D. i'\ 



Tan. 



9. 828987 
.829260 
.829532 
.829805 
.830077 

9.830349 
. 830621 
.830893 
.831165 
.831437 

9.831709 
.831981 
.832253 
.832525 
.832796 

9.833068 
.833339 
.833611 
.833882 
.834154 

9. 834425 
.834696 

.834967 
.835238 
. 835509 
9.835780 
. 836051 
.836322 

.836593 
.836864 

9- 837134 
.837405 
.837675 
.837946 
.838216 

9.838487 
.838757 
.839027 
.839297 
.839568 

9.839838 
.840108 
.840378 



D. i". 



Cot. 



. 840917 
9. 841 187 
.841457 
.841727 
.841996 
.842266 

9.842535 
.842805 

.843074 

.843343 

.843612 

9.843882 

.844151 
. 844420 
.844689 
.844958 
9.845227 

Cot. 



4.55 
4.53 
4.55 
4.53 
4.53 
4.53 
4.53 
4.53 
4.53 
4.53 

4.53 
4.53 
4.53 
4.52 
4^53 
4.52 
4.53 
4.52 
4.53 
4.52 

4.52 
4.52 
4.52 
4.52 
4.52 
4.52 
4.52 
4-52 
4^52 
4.50 

4.52 
4.50 
4.52 
4.50 
4.52 
4.50 
4.50 
4.50 
4.52 
4.50 

4.50 
4.50 
4.50 
4.48 
4.50 
4.50 
4.50 
4.48 
4.50 
4.48 

4.50 
4.48 
4.48 
4.48 
4.50 
4.48 
4.48 
4.43 
4.48 
4.48 

D. I". 



o. 171013 
. 170740 
. 170468 
. 170195 
. 169923 

o. 16965 I 

. 169379 

, I69I07 

. 168835 
.168563 

o. 168291 
. 1680 I 9 
. 167747 
. 167475 
. 167204 

o. 166932 

.166661 
. 166389 
.166118 
. 165846 

o. 165575 

. 165304 
. 165033 

. 164762 

. I6449I 

o. 164220 

. 163949 
.163678 
.163407 
.163136 

o. 162866 

. 162595 
. 162325 

. 162054 

.161784 

o. 161513 

. I6I243 
. 160973 

. 160703 
. 160432 

o. 160162 

. 159892 
. 159622 
. 159352 
.159083 

o. 158813 

. 158543 
. 158273 

. 158004 

.157734 

o. 157465 

. I57I95 
. 156926 
. 156657 
. 156388 

o. 156118 

. 155849 
.155580 
.155311 
. 155042 

o. 154773 
Tan. 



55' 



35^ 



LOGARITHMIC SINES 



144" 



M. 



Sin. 



2 
3 
4 
5 
6 

I 

9 

10 
II 
12 
13 
14 
15 
16 
17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

47 
48 

49 
50 
51 
52 
53 
54 
55 
56 

58 
59 
60 



125' 



. 758591 
.758772 
.758952 
. 759132 
.759312 
• 759492 
. 759672 
.759852 
.760031 
.760211 

. 760390 
. 760569 
. 760748 
. 760927 
.761106 
.761285 
. 761464 
.761642 
.761821 
. 761999 
.762177 
. 762356 
. 762534 
.762712 



h 763067 
. 763245 
. 763422 
. 763600 
.763777 

}■ 763954 
.764131 
. 764308 
. 764485 
. 764662 

?. 764838 
. 765015 
.765191 
. 765367 
. 765544 

). 765720 
.765896 
. 766072 
. 766247 
. 766423 

?. 766598 
. 766774 
. 766949 
.767124 
. 767300 

?. 767475 
.767649 
.767824 
.767999 
.768173 
?. 768348 
. 768522 
. 768697 
.768871 

. 769045 
). 769219 

Cos. 



D. i". 



3.02 
3.00 
3- 00 
3- 00 
3- 00 
3.00 
3- 00 
2.98 
3- 00 
2.98 

2.98 
2.98 
2.98 
2.98 
2.98 
2.98 
2.97 
2.98 
2.97 
2.97 

2.98 
2.97 
2.97 

2.95 
2.97 
2.97 

2.95 
2.97 

2.95 
2.95 

2.95 
2.95 
2.95 
2.95 
2.93 
2.95 
2.93 
2.93 
2.95 
2.93 

2.93 
2.93 
2.92 

2.93 
2.92 

2.93 
2.92 
2.92 

2.93 
2.92 

2.90 
2.92 
2.92 
2.90 
2.92 
2.90 
2.92 
2.90 
2.90 
2.90 

D. i'\ 



Cos. 



9.913365 
.913276 
.913187 
.913099 
.913010 

9.912922 
.912833 
.912744 
.912655 
.912566 

9.912477 
.912388 
.912299 
.912210 
.912121 

9.912031 
.911942 
.911853 
.911763 
.911674 

9. 91 1 584 
.911495 
.911405 
.911315 
.911226 

9. 91 I 136 
.911046 
.910956 
.910866 
.910776 

9. 910686 
.910596 
.910506 
.910415 
.910325 

9.910235 
.910144 
.910054 
.909963 
.909873 

9. 909782 
.909691 
.909601 
.909510 
.909419 

9.909328 
.909237 
.909146 

.909055 
. 908964 

9.908873 



. 908690 
.908599 
.908507 

9.908416 
.908324 
.908233 
.908141 
. 908049 

9. 907958 

Sin. 



Tan. 



D. i'\ 



9. 845227 
.845496 

.845764 
. 846033 
. 846302 
9. 846570 
.846839 
.847108 
.847376 
.847644 

9.847913 
.848181 
.848449 
.848717 



9. 849254 
. 849522 
.849790 
.850057 
.850325 

9. 850593 
. 850861 
.851129 
.851396 
.851664 

9.851931 
.852199 
. 852466 

.852733 
.853001 

9.853268 

.853535 
.853802 
. 854069 
. 854336 
9. 854603 
.854870 
.855137 
• 855404 
.855671 

9. 855938 
. 856204 
.856471 

.856737 
. 857004 

9. 857270 
.857537 
.857803 
. 858069 
.858336 

9. 858602 



.859134 
. 859400 
. 859666 

9. 859932 
.860198 
. 860464 
. 860730 
.860995 

9. 861261 

Cot. 



D. I" 



4.48 
4.47 
4.48 
4.48 
4.47 
4.48 
4.48 
4.47 
4-47 
4.48 

4.47 
4.47 
4.47 
4.48 
4.47 
4.47 
4.47 
4.45 
4.47 
4.47 

4.47 
4.47 
4.45 
4.47 
4.45 
4.47 
4-45 
4.45 
4.47 
4.45 

4.45 
4.45 
4.45 
4-45 
4.45 
4.45 
4.45 
4.45 
4.45 
4.45 

4.43 
4.45 
4.43 
4.45 
4.43 
4.45 
4.43 
4.43 
4.45 
4.43 

4.43 
4.43 
4.43 
4.43 
4.43 
4.43 
4.43 
4.43 
4.42 
4-43 

D. I". 



Cot. 



o. 154773 
. 154504 
. 154236 
. 153967 
. 153698 

o. 153430 
.153161 
. 152892 
. 152624 
. 152356 

o. 152087 

.151819 
.151551 
.151283 
.151014 

o. 150746 

. 150478 

. 150210 

. 149943 
. 149675 

o. 149407 

. 149139 
.148871 
. 148604 

. 148336 

o. 148069 
. I4780I 

. 147534 
. 147267 
. 146999 

o. 146732 

. 146465 
. 146 1 98 

. 145931 
. 145664 

o. 145397 

. 145130 
. 144863 
. 144596 
. 144329 

o. 144062 

. 143796 
. 143529 
. 143263 

. 142996 
o. 142730 

. 142463 
.142197 
.141931 

. I4I664 
o. 141398 

.141132 

. 140866 
. 140600 

. 140334 

o. 140068 

. 139802 
. 139536 
. 139270 
. 139005 
0.138739 

Tan. 



54" 



36^ 



COSINES, TANGENTS, AND COTANGENTS 143* 



M. 



■| 



Sin. 



D. i" 



Cos. 



D. : 



Tan. 



9. 769219 

• 769393 
. 769566 
. 769740 
. 769913 

9. 770087 
. 770260 

• 770433 
. 770606 
. 770779 

9- 770952 
.771125 
.771298 
.771470 
.771643 

9-771815 
.771987 
.772159 
.772331 
. 772503 

9. 772675 
.772847 
.773018 
.773190 
.773361 

9- 773533 
. 773704 
.773875 
. 774046 

• 774217 
9.774388 

•774558 
. 774729 
.774899 
. 775070 
9. 775240 
.775410 
.775580 
. 775750 
. 775920 

9.776090 
. 776259 
. 776429 
.776598 
. 776768 

9. 776937 
.777106 

.777275 

• 777444 
.777613 

9.777781 
. 777950 
.778119 
.778287 

. 778455 
9. 778624 
. 778792 
. 778960 
.779128 
. 779295 
9. 779463 

Cos. 



2.90 

2.88 
2.90 
2.88 
2.90 

2.88 
2.88 
2.88 
2.88 
2.88 

2.88 
2.88 
2.87 
2.88 
2.87 
2.87 
2.87 
2.87 
2.87 
2.87 

2.87 
2.85 
2.87 
2.85 
2.87 
2.85 
2.85 
2.85 
2.85 
2.85 

2.83 
2.85 
2.83 
2.85 
2.83 
2.83 
2.83 
2.83 
2.83 
2.83 

2.82 
2.83 
2.82 
2.83 
2.82 
2.82 
2.82 
2.82 
2.82 
2.80 

2.82 
2.82 
2.80 
2.80 
2.82 
2.80 
2.80 
2.80 
2.78 
2.80 

D. I". 



9. 907958 
.907866 
.907774 
.907682 
.907590 

9. 907498 
. 907406 
.907314 
.907222 
.907129 

9.907037 

.906945 
. 906852 
. 906760 
. 906667 

9. 906575 
. 906482 
.906389 
. 906296 
. 906204 

9. 9061 I I 
.906018 
.905925 
.905832 
.905739 

9.905645 

.905552 
.905459 
.905366 
.905272 

9.905179 
.905085 
.904992 
.904898 
. 904804 

9. 9047 1 1 
.904617 

.904523 
.904429 

.904335 
9.904241 
.904147 
.904053 
.903959 
. 903864 
9.903770 
.903676 
.903581 
.903487 
.903392 

9.903298 
.903203 
.903108 
.903014 
.902919 

9. 902824 
.902729 
.902634 

.902539 

.902444 

9.902349 

Sin. 



.53 
.53 
•53 
.53 
.53 
.53 
.53 
.53 
•55 
.53 

.53 
.55 
•53 
•55 
•53 
.55 
.55 
•55 
•53 
•55 

•55 
.55 
•55 
•55 
.57 
•55 
•55 
■55 
.57 
.55 

.57 
.55 
.57 
.57 
.55 
.57 
.57 
.57 
.57 
.57 

.57 

.57 
.57 
.58 
■57 
.57 
.58 
.57 
.58 
■57 

58 
58 
57 
58 
58 
58 
58 
58 
58 
58 



D. I' 



9.861261 
.861527 
.861792 
.862058 
.862323 

9.862589 
.862854 
.863119 
.863385 
.863650 

9.863915 
.864180 
.864445 
.864710 
.864975 

9. 865240 
.865505 
.865770 
. 866035 
. 866300 

9. 866564 



D. I' 



. 867094 
.867358 
.867623 
9. 867887 
.868152 
.868416 
.868680 



9. 869209 
.869473 
.869737 
.870001 
. 870265 

9. 870529 
. 870793 
.871057 
.871321 
.871585 

9.871849 
.872112 
.872376 
. 872640 
.872903 

9.873167 
.873430 
.873694 

•873957 
. 874220 

9.874484 
.874747 
. 875010 
.875273 
.875537 

9. 875800 
.876063 
.876326 
.876589 
.876852 

9.877114 

Cot. 



4.43 
4.42 
4^43 
4.42 
4^43 
4.42 
4.42 
4^43 
4.42 
4.42 

4.42 
4.42 
4.42 
4.42 
4.42 
4.42 
4.42 
4.42 
4.42 
4.40 
4.42 
4.42 
4.40 
4.42 
4.40 
4.42 
4.40 
4.40 
4.42 
4.40 

4.40 
4.40 
4.40 
4.40 
4.40 
4.40 
4.40 
4.40 
4.40 
4.40 

4.38 
4.40 
4.40 
4.38 
4.40 
4.38 
4.40 
4.38 
4.38 
4.40 

4.38 
4.38 
4.38 
4.40 
4.38 
4.38 
4.38 
4.38 
4.38 
4.37 

D. I". 



Cot. 



o. 138739 

. 138473 
. 138208 
. 137942 
. 137677 

0.137411 
.137146 
. 13688 I 
. 1366 I 5 
. 136350 

o. 136085 

. 135820 
. 135555 
. 135290 
. 135025 

o. 134760 

. 134495 
. 134230 
. 133965 
. 133700 

o. 133436 

.133171 

. 132906 
. 132642 
. 132377 

o. 132113 

. I3I848 

.131584 
.131320 

. I3I055 

o. 130791 

. 130527 
. 130263 
.129999 
. 129735 

o. I 2947 I 
. 129207 

.128943 

. 128679 

. I284I5 

o. 128151 

.127888 
.127624 
. 127360 
. 127097 
o. 126833 

.126570 

. 126306 

.126043 
. 125780 

o. 125516 

.125253 

.124990 

.124727 
. 124463 

o. 124200 

.123937 
. 123674 
.123411 
. 1 23 148 
o. 122886 

Tan. 



I 126^ 



53^ 



37" 



LOGARITHMIC SINES 



142" 



M. 



Sin. 



D. I". 



Cos. 



23 
24 
25 
26 
27 
28 
29 

30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

48 
49 
50 
51 
52 
53 
54 

P 



9- 779463 
.779631 
.77979S 
.779966 
.780133 

9. 780300 
.780467 
.780634 
.780801 
.780968 

9. 781 134 
.7S1301 
.781468 
.781634 
.7S1800 

9. 78 1 966 
.782132 
. 782298 
. 782464 
. 782630 

9. 782796 
.782961 
.783127 
.783292 
.7S345S 

9.783623 
.7S3788 
.783953 
.784118 
. 784282 

9. 784447 
.784612 
.7S4776 
.784941 
.785105 

9. 785269 
.785433 
.785597 
.785761 
.785925 

9.786089 
.786252 
.786416 
.786579 
.786742 

9. 786906 
. 787069 
.787232 
.787395 
.787557 

9.787720 
.787883 
.788045 



.788370 

9.788532 

. 788694 



.789018 

.789180 

9. 789342 

Cos. 



2.80 
2.78 
2.80 
2.78 
2.78 
2.78 
2.78 
2.78 
2.78 
2.77 

2.78 
2.78 
2.77 
2.77 
2.77 
2.77 
2.77 
2.77 
2.77 
2.77 

2.75 
2.77 
2.75 
2.77 
2.75 
2.75 
2.75 
2.75 
2.73 
2.75 

2.75 
2.73 
2.75 
2.73 
2.73 
2.73 
2.73 
2.73 
2.73 
2.73 
2.72 

2.73 
2.72 
2.72 

2.73 
2.72 
2.72 
2.72 
2.70 
2.72 

2.72 
2.70 
2.72 
2.70 
2.70 
2.70 
2.70 
2.70 
2.70 
2.70 

D. l'\ 



902349 
902253 
902158 
902063 
901967 
901872 
901776 
901681 

901585 
901490 

901394 
901298 
901202 
901106 
901010 
900914 
900S18 
900722 
900626 
900529 

900433 
900337 
900240 
900144 
900047 
S99951 
899854 

899757 
899660 
899564 

899467 
899370 
899273 
899176 
899078 



898787 



898592 
898494 

898397 
898299 
898202 
898104 



897908 
897810 
897712 
897614 

897516 
897418 
897320 
897222 
897123 
897025 
896926 



896729 
896631 
896532 

Sin. 



D. i". I! Tan. 



.60 

.58 
58 
,60 
58 
60 
58 
60 
58 
60 

60 
60 
60 
60 
60 
60 
60 
60 
62 
60 

60 
62 
60 
62 
60 
62 
62 
62 
60 
62 

62 
62 
62 

63 
62 
62 
62 

62 

63 

62 

63 
62 

63 
63 

63 
63 
63 

63- 
63 
63 
65 
63 
65 
63 
65 
63 
65 

D. I". 



877114 
877377 
877640 

877903 
878165 



878691 

878953 
879216 
879478 

879741 
880003 
880265 



880790 
881052 
881314 

881577 
881839 
882101 

882363 
882625 
882887 
883148 
883410 
883672 

883934 
884196 

884457 
884719 

884980 
885242 
885504 

885765 
886026 



886549 
886811 
887072 
887333 

887594 
887855 
888116 



889161 
889421 



889943 

890204 
890465 
890725 



891247 
891507 
891768 
892028 
892289 
892549 
892810 

Cot, 



D. I" 



4.38 
4.38 
4.38 
4.37 
4.38 
4.38 
4.37 
4.38 
4.37 
4.38 

4.37 
4.37 
4.38 
4.37 
4.37 
4.37 
4.38 
4-37 
4-37 
4.37 

4.37 
4.37 
4.35 
4.37 
-4.37 
4.37 
4.37 
4.35 
4.37 
4.35 

4.37 
4-37 
4.35 
4.35 
4.37 
4.35 
4.37 
4.35 
4-35 
4.35 

4.35 
4.35 
4.37 
4.35 
4.35 
4.35 
4.33 
4.35 
4.35 
4-35 

4.35 
4.33 
4.35 
4.35 
4.33 
4-35 
4.33 
4.35 
4-33 
4.35 

D. 1". 



Cot. 



Tan. 



127' 



52^ 



38^ COSINES, TANGENTS, AND COTANGENTS 141' 



M. 



Sin. 



9. 789342 
.789504 
.789665 
.789827 



9. 790149 
. 790310 
.790471 
.790632 
. 790793 

9.790954 
.791115 
.791275 
. 791436 
.791596 

9- 791757 
.791917 
. 792077 
. 792237 
• 792397 

9-792557 
.792716 
. 792876 
. 793035 
. 793195 

9. 793354 
.793514 
. 793673 
. 793832 
. 793991 

9- 794150 
. 794308 
.794467 
.794626 

.794784 
9. 794942 
. 795101 
.795259 
.795417 
.795575 

9- 795733 
. 795891 
. 796049 
.796206 
. 796364 

9. 796521 
. 796679 
.796836 
.796993 
.797150 

9. 797307 
. 797464 
.797621 
.797777 
•797934 

9.798091 
.798247 
.798403 
.798560 
.798716 

9.798872 

Cos. 



D. i'\ 



Cos. 



D. I" 



Tan. 



D. 1" 



Cot. 



2.70 

2.68 
2.70 
2.68 
2.68 
2.68 
2.68 
2.68 
2.68 
2.68 

2.68 
2.67 
2.68 
2.67 
2.68 
2.67 
2.67 
2.67 
2.67 
2.67 

2.65 
2.67 
2.65 
2.67 
2.65 
2.67 
2.65 
2.65 
2.65 
2.65 

2.63 
2.65 
2.65 
2.63 
2.63 
2.65 
2.63 
2.63 
2.63 
2.63 

2.63 
2.63 
2.62 
2.63 
2.62 
2.63 
2.62 
2.62 
2.62 
2.62 

2.62 
2.62 
2.60 
2.62 
2.62 
2.60 
2.60 
2.62 
2.60 
2.60 

D. I''. 



896532 
896433 
896335 
896236 

896137 



895939 
895840 

895741 
895641 

895542 
895443 
895343 
895244 

895145 
895045 
894945 
894846 
894746 
894646 

894546 
894446 
894346 
894246 
894146 
894046 
893946 
893846 
893745 
893645 

893544 
893444 
893343 
893243 
893142 
893041 
892940 
892839 
892739 
892638 

892536 
892435 
892334 
892233 
892132 
892030 
891929 
891827 
891726 
891624 

891523 
891421 
891319 
891217 
891115 
891013 
89091 I 
890809 
890707 
S90605 
890503 



Sin. 



D. 1" 



892810 
893070 
893331 
893591 
893851 
8941 I I 
894372 
894632 
894892 
895152 
895412 
895672 
895932 
896192 
896452 
896712 
896971 
897231 
897491 
897751 
898010 
898270 
898530 



899049 
899308 
899568 
899827 
900087 
900346 
900605 
900864 
901 124 
901383 
901642 
901901 
902160 
902420 
902679 
902938 

903197 
903456 
903714 

903973 
904232 
904491 
904750 
905008 
905267 
905526 

905785 
906043 
906302 
906560 
906819 
907077 
907336 
907594 
907853 
908111 
908369 

Cot. 



4.33 
4.35 
4.33 
4.33 
4.33 
4.35 
4.33 
4.33 
4.33 
4.33 

4.33 
4-33 
4.33 
4.33 
4-33 
4.32 
4.33 
4.33 
4.33 
4-32 

4-33 
4.33 
4-32 
4.33 
4.32 
4-33 
4.32 
4.33 
4.32 
4.32 

4.32 
4.33 
4.32 
4.32 
4.32 
4.32 
4.33 
4-32 
4.32 
4.32 



4.30 
4.32 
4.32 
4-32 

4.30 
4.32 
4.30 
4.32 
4.30 
4.32 
4- 30 
4.32 
4- 30 
4.30 

D. I". 



o. 107190 
. 106930 
.106669 
. 106409 
. 106 149 

o. 105889 

. 105628 
. 105368 

. 105108 
. 104848 

o. 104588 

. 104328 

. 104068 

. 103808 
. 103548 

o. 103288 
. 103029 
. 102769 
. 102509 
. 102249 

o. 101990 
. IOI730 
. IOI470 

.I0I2II 
.100951 

o. 100692 
. 100432 
.100173 
.099913 
.099654 

0.099395 
.099136 
.098876 
. 098617 
.098358 

o. 098099 
. 097840 
.097580 
.097321 
.097062 

0.096803 
.096544 

.096286 
. 096027 

.095768 
0.095509 
.095250 
.094992 
.094733 
.094474 
0.094215 

.093957 
.093698 
.093440 
.093181 
o. 092923 
,092664 
,092406 

.092147 

.091889 

o. 091631 

Tan. 



SI' 



39^ 



LOGARITHMIC SINES 



140" 



M. 



2 
3 
4 
5 
6 

7 
8 

9 

10 

XI 

12 
13 
14 

li 

17 
18 

19 

20 

21 
22 
23 
24 
25 
16 
27 
28 
29 

30 
31 
32 

33 
34 
35 
36 

38 
39 

40 
41 
42 
43 
44 

49 

50 
51 
52 
53 
54 
55 
56 

5J 
58 



Sin. 



9.798872 
.799028 
.799184 
.799339 
. 799495 

9.799651 
.799806 
.799962 
,800117 
.800272 

9. 800427 
.800582 
.800737 
,800892 
.801047 

9. 801201 
.801356 
.801511 
.801665 
.801819 

9.801973 
.802128 
.802282 
. 802436 
.802589 

9. 802743 
. 802897 
.803050 
.803204 
.803357 

9. 80351 I 
.803664 
.803817 
.803970 
.804123 

9. 804 276 



.804581 
.804734 
.804886 

9. 805039 
.805191 
.805343 
.805495 
.805647 

9.805799 
.805951 
.806103 
. 806254 
.806406 

9.806557 
. 806709 
. 806860 
.807011 
.807163 

9. 807314 
.807465 
.807615 
.807766 
.807917 

9. 808067 

Cos. 



D. I''. 



2.60 
2.60 
2.58 
2.60 
2.60 

2.60 

2.58 
2.58 

2.58 
2.58 

2.58 
2.57 

2.58 
2.57 
2.57 
2.57 

2.58 
2.57 
2.57 
2.55 
2.57 
2.57 
2.55 
2.57 
2.55 
2.57 

2.55 
2.55 
2.55 
2.55 
2.55 
2.53 
2.55 
2.55 
2.53 
2.55 

2.53 
2.53 
2.53 
2.53 
2.53 
2.53 
2.53 
2.52 
2.53 
2.52 

2.53 
2.52 
2.52 
2.53 
2.52 
2.52 
2.50 
2.52 
2.52 
2.50 

D. I". I 



Cos. 



9.890503 
.890400 
.890298 
.890195 
.890093 



889785 



889579 
889477 
889374 
889271 



888755 



888444 



888237 
888134 



887822 
887718 
887614 
887510 



8873c 

887198 

887093 

886989 

886885 



886676 



886466 

886362 
886257 
886152 
886047 



885837 
885732 
885627 
885522 
885416 

885311 
885205 
885100 
884994 



884783 
884677 
884572 
884466 
884360 
884254 

Sin. 



D. I' 



72 
70 
72 
70 

72 
70 
72 
72 
72 
70 

72 
72 

72 

73 

72 
72 
72 

73 

72 

73 
72 
73 
72 
73 
73 
73 
73 
73 
73 
73 

73 
73 
75 
73 
73 
75 
73 
75 
.75 
73 

.75 
.75 

.75 
.75 
.75 
.75 
.75 
.75 
.77 
.75 

.77 
.75 
.77 
.75 
.77 
.77 
.75 
.77 
77 
77 



D. I" 



Tan. 



9. 908369 



.909144 
.909402 
9. 909660 
.909918 
.910177 

.910435 
.910693 

9.910951 
.911209 
.911467 
.911725 
.9119S2 

9.912240 
.912498 
.912756 
.913014 
.913271 

9.913529 
.913787 
.914044 
.914302 
.914560 

9.914817 
.915075 
.915332 
.915590 
.915847 

9.916104 
. 916362 
.916619 
.916877 

.917134 
9.917391 
.917648 
.917906 
.918163 
.918420 

9.918677 
.918934 
.919191 
.919448 

.919705 

9.919962 

.920219 

. 920476 

.920733 
,920990 

9.921247 

.921503 
.921760 
.922017 
.922274 
9.922530 
.922787 
.923044 
.923300 

.923557 
9.923814 

Cot. 



D. I''. 



4.32 
4-30 
4.30 
4.30 
4-30 
4-30 
4.32 
4.30 
4.30 
4-30 

4.30 
4.30 
4.30 
4.28 
4-30 
4.30 
4.30 
4.30 
4.28 
4-30 

4.30 
4.28 
4.30 
4.30 
4.28 
4.30 
4.28 
4.30 
4.28 
4.28 

4.30 
4.28 
4.30 
4.28 
4.28 
4.28 
4.30 
4.28 
4.28 
4.28 

4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.28 
4.28 

4.27 
4.28 
4.28 
4.28 
4.27 
4.28 
4.28 
4.27 
4.28 
4.28 

D. i'\ 



Cot. 



0.091631 
.091372 
.091114 
. 090856 
.090598 

o. 090340 
.090082 
.089823 
.089565 
.089307 

o. 089049 

.088791 

.088533 
.088275 
.088018 

o. 087760 
. 087502 
.087244 

.086986 
. 086729 

0.086471 
.086213 

.085956 
.085698 
.085440 
0.085183 
.084925 
.084668 

.084410 

.084153 

o. 083896 

.083638 
.083381 
.083123 
. 082866 
o. 082609 

.082352 

.0S2094 

.081837 
.081580 

0.081323 

.081066 
,080809 

.080552 

. 080295 
o. 080038 

.079781 
.079524 

.079267 
.079010 

0.078753 
.078497 

.078240 

.077983 
.077726 
0.077470 
.077213 
.076956 

, 076700 

.076443 

0.076186 
Tan. 



129° 



50° 



40" 



COSINES, TANGENTS, AND COTANGENTS 139^ 



M. 



Sin. 



o 
z 
2 
3 
4 
5 
6 

I 

9 
10 
n 

12 
13 
14 
15 
16 

'2 

z8 
19 
20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

30 
31 
32 

33 
34 

36 

3Z 
38 

39 

40 

41 
42 

43 
44 
45 
46 
47 
48 

49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



130^ 



9. 808067 
808218 



808519 



809119 
809269 
809419 

809569 
809718 



810017 
810167 
810316 
810465 
810614 
810763 
810912 

811061 
811210 
811358 
81 1507 
81 1655 
81 1804 
811952 
812100 
812248 
812396 

812544 
812692 
812840 



813135 
813283 

813430 
813578 
813725 
813872 

8140T9 
814166 

814313 
814460 
814607 

814753 
814900 
815046 
815193 
815339 

815485 
815632 
815778 
815924 
816069 
816215 
8 1636 I 
816507 
816652 
816798 
816943 

Cos. 



D. I" 



2.52 

2.50 
2.52 
2.50 
2.50 
2.50 
2.50 
2.50 
2.50 
2:50 

2.48 
2.50 
2.48 
2.50 

2.48 
2.48 
2.48 
2.48 
2.48 
2.48 

2.48 

2.47 
2.48 

2.47 
2.48 
2.47 
2.47 
2.47 
2.47 
2.47 

2.47 
2.47 
2.47 
2.45 
2.47 
2.45 
2.47 
2.45 
2.45 
2.45 

2.45 
2.45 
2.45 
2.45 
2.43 
2.45 
2.43 
2.45 
2.43 
2.43 

2.45 
2.43 
2.43 
2.42 

2.43 
2.43 
2.43 
2.42 

2.43 
2.42 



Cos. 



9. 884254 



883936 
883829 
883723 
883617 
883510 
883404 
883297 



882977 
882871 



882657 
882550 

882443 
882336 
882229 

882121 
882014 
881907 
881799 
881692 
881584 
881477 
881369 
881 261 
881153 

881046 
880938 



880722 
880613 
880505 
880397 



880180 
880072 

879963 

879855 
879746 
879637 
879529 
879420 
8793 I I 
879202 
879093 



878875 
878766 
878656 

878547 
878438 



878219 
878109 

877999 
877890 
877780 



Sin. 



D. i" 



D. 1" 



Tan. 



9.923814 
. 924070 
.924327 
.924583 
. 924840 

9.925096 
.925352 
.925609 
.925865 
.926122 

9.926378 
. 926634 
. 926890 
.927147 
.927403 

9. 927659 
.927915 
.928171 
.928427 



9. 928940 
.929196 
.929452 
. 929708 
.929964 

9. 930220 
. 930475 
.930731 
.930987 
.931243 

9.931499 
.931755 
.932010 
. 932266 
. 932522 

9. 932778 
.933033 
.933289 
.933545 
.933800 

9.934056 
.934311 
.934567 
.934822 
.935078 

9- 935333 
.935589 
.935844 
.936100 

.936355 

9. 9366 I I 

. 936866 

.937121 

.937377 
.937632 

9.937887 
.938142 
.938398 
• 938653 
.938908 

9.939163 

Cot. 



D. I'', 



4.27 
4.28 
4.27 
4.28 
4.27 
4.27 
4.28 
4.27 
4.28 
4.27 
4.27 
4.27 
4.28 
4.27 
4.27 
4.27 
4.27 
4.27 
4.28 
4.27 

4.27 
4.27 
4.27 
4.27 
4.27 
4.25 
4.27 
4.27 
4.27 
4.27 
4.27 
4.25 
4.27 
4.27 
4.27 
4.25 
4.27 
4.27 
4.25 
4.27 

4.25 
4.27 
4.25 
4.27 
4.25 
4.27 
4.25 
4.27 
4.25 
4.27 

4.25 
4.25 
4.27 
4.25 
4.25 
4.25 
4.27 
4.25 
4.25 
4.25 

D. i'\ 



Cot. 



0.076186 
.075930 
.075673 
.075417 
.075160 

0.074904 
. 074648 
.074391 
.074135 
.073878 

o. 073622 
.073366 
.073110 
.072853 

.072597 

0.072341 

. 072085 

.071829 

.071573 
.071316 

o. 071060 
. 070804 

.070548 

,070292 

. 070036 

o. 0697S0 

.069525 

. 069269 
.069013 

.068757 

o. 068501 
.068245 
. 067990 

.067734 

. 067478 
o. 067222 
. 066967 
.066711 
,066455 
.066200 

0.065944 

. 065689 

.065433 
.065178 

. 064922 
o. 064667 
,064411 
,064156 
.063900 

.063645 

0.063389 
.063134 

.062879 
. 062623 
.062368 

0.0621 13 

.061858 

.061602 

.061347 

.061092 

o. 060837 

Tan. 



49" 



41'' 



LOGARITHMIC SINES 



138° 



M 



12 
13 

M 

\l 

18 
19 
20 
21 
22 
23 
24 
25 
26 

27 
28 
29 

30 
31 
32 
33 
34 

36 

38 
39 
40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
51 
52 
53 
54 

5| 
56 

57 
58 
59 
60 



Sin. 



9.816943 
.817088 
.817233 
.817379 
.817524 

9.817668 
.817813 
.817958 
.818103 
.818247 

9.818392 
.818536 
.818681 
.818825 
.818969 

9.819113 
.819257 
.819401 
.819545 
.819689 

9.819832 
.819976 
.820120 
. 820263 
. 820406 

9. 820550 
.820693 
. 820836 
. 820979 
.821122 

9. 821265 
.821407 
.821550 
.821693 
.821835 

9.821977 
.822120 
.822262 
.822404 
. 822546 

9. 822688 
. 822830 
. 822972 
.823114 
.823255 

9- 823397 
. 823539 
. 823680 
.823821 
.823963 

9. 824104 
.824245 
.824386 
.824527 
.824668 

9. 824808 
. 824949 
. 825090 
. 825230 
.825371 

9. 82551 1 

Cos. 



D. i' 



2.42 
2.42 

2.43 
2.42 
2.40 
2.42 
2.42 
2.42 
2.40 
2.42 

2.40 
2.42 
2.40 
2.40 
2.40 
2.40 
2.40 
2.40 
2.40 
2.38 
2.40 
2.40 
2.38 
2.38 
2.40 
2.38 
2.38 
2.38 
2.38 
2.38 

2.37 
2.38 
2.38 
2.37 
2.37 
2.38 
2.37 
2.37 
2.37 
2.37 

2.37 
2.37 
2.37 
2.35 
2.37 
2.37 
2.35 
2.35 
2.37 
2.35 

2.35 
2.35 
2.35 
2.35 
2.33 
2.35 
2.35 
2.33 
2.35 
2.33 

D. i'\ 



Cos. 



9. 877780 
.877670 
. 877560 
.877450 
.877340 

9. 877230 
.877120 
.877010 
.876899 
. 876789 

9. 876678 
.876568 
.876457 

.876347 
.876236 
9.876125 
.876014 
.875904 

.875793 
.875682 

9.875571 
. 875459 
.875348 
.875237 
.875126 

9.875014 
.874903 
.874791 
. 874680 
.874568 

9. 874456 

.874344 
.874232 
.874121 
. 874009 
9.873896 
.873784 
. 873672 
. 873560 
.873448 

9.873335 
.873223 
.873110 
.872998 
.872885 

9.872772 
.872659 
.872547 
.872434 
.872321 

9. 872208 
.872095 
.871981 
.871868 

.871755 
9.871641 
.871528 
.871414 
.871301 
.871187 
9. 871073 

Sin. 



D. i" 



.83 
.83 
.83 
.83 
.83 
.83 
.83 
.85 
.83 
.85 

.83 

.85 

•^^ 

.85 

.85 
.85 
.83 
.85 
.85 
.85 

.87 
.85 
.85 
.85 
.87 
.85 
.87 
.85 
.87 
.87 

.87 
.87 
.85 
.87 
.88 
.87 
.87 
.87 
.87 
.88 

.87 
.88 
.87 



87 



90 

88 
88 
90 
88 
90 
88 
90 
90 



Tan. 



9.939163 
.939418 
.939673 
. 939928 
.940183 

9. 940439 
. 940694 

.940949 
.941204 

.941459 

9.941713 
.941968 
.942223 
.942478 
.942733 

9.942988 

.943243 
.943498 
. 943752 
.944007 

9. 944262 
.944517 
.944771 
. 945026 
.945281 

9. 945535 
. 945790 
. 946045 
. 946299 
« 946554 

9. 946808 
. 947063 
.947318 
.947572 
.947827 

9.948081 
.948335 
. 948590 



D. I". 



. 949099 

9. 949353 
. 949608 
. 949862 
.950116 
.950371 

9. 950625 
• 950879 
.951133 
.951388 
. 951642 

9.951896 
.952150 
.952405 
.952659 
.952913 

9.953167 
.953421 
.953675 
. 953929 
.954183 

9. 954437 

Cot. 



4.25 
4.25 
4.25 
4.25 
4.27 
4.25 
4.25 
4.25 
4.25 
4.23 

4.25 
4.25 
4.25 
4.25 
4.25 
4.25 
4.25 
4.23 
4.25 
4.25 

4.25 
4.23 
4.25 
4.25 
4.23 
4.25 
4.25 
4.23 
4.25 
4.23 

4.25 
4.25 
4.23 
4.25 
4.23 
4.23 
4.25 
4.23 
4.25 
4.23 

4.25 
4.23 
4.23 
4.25 
4.23 
4.23 
4.23 
4.25 
4.23 
4.23 

4.23 
4.25 
4.23 
4.23 
4.23 
4.23 
4.23 
4.23 
4.23 
4.23 

D. I". I 



Cot. 



o. 060837 
. 060582 
. 060327 
. 060072 
.059817 

o. 059561 

. 059306 
.050051 
.058796 
.058541 

o. 058287 

.058032 

.057777 
.057522 
. 057267 

0.057012 

. 056757 
. 056502 
. 056248 

.055993 
0.055738 

. 055483 
. 055229 
. 054974 
.054719 

o. 054465 

. 054210 

. 053955 
. 053701 
.053446 

0.053192 
. 052937 

. 052682 
. 052428 

.052173 
0.05I9I9 
.051665 
.051410 
.051156 
. 050901 

o. 050647 

. 050392 
.050138 
.049884 
. 049629 

o. 049375 
.049121 
. 048867 
.048612 

.048358 

o. 048104 

.047850 
.047595 
.047341 

. 047087 
o. 046833 

.046579 
. 046325 
.046071 
.045817 
0.045563 



Tan. 



X3r 



M. 



48" 



42" 



COSINES, TANGENTS, AND COTANGENTS 137^^ 



M. 



12 
13 
14 
15 
16 

17 
18 

19 
20 
21 
22 
23 
24 

26 
27 
28 
29 
30 
31 
32 

33 
34 

36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 

48 
49 
50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Sin. 



9.S25511 
.825651 
.825791 
.825931 
.826071 

9. 826211 
. 826351 
.826491 
.826631 
. 826770 

9. 826910 
. 827049 
.827189 

- .827328 
. 827467 

9. 827606 
.827745 



.828162 
9. 828301 



.828578 
.828716 
.828855 
9.828993 
.829131 
. 829269 
. 829407 
.829545 

9.829683 
.829821 
.829959 
.830097 
. 830234 

9. 830372 
.830509 
. 830646 
.830784 
. 830921 

9.831058 
.831195 
.831332 
.831469 
.831606 

9.831742 
.831879 
.832015 
.832152 
.832288 

9.832425 
.832561 
.832697 
.832833 
. 832969 

9.833105 
.833241 

.833377 

•833512 

.833648 

9.833 783 

Cos. 



D. I". 



2.33 
2.33 
2.33 
2.33 
2.33 
2.33 
2.33 
2.33 
2.32 

2.33 

2.32 

2.33 
2.32 

2.32 
2.32 
2.32 
2.32 
2.32 
2.32 
2.32 

2.30 
2.32 
2.30 
2.32 
2.30 
2.30 
2.30 
2.30 
2.30 
2.30 

2.30 
2.30 
2.30 
2.28 
2.30 
2.28 
2.28 
2.30 
2.28 
2.28 

2.28 
2.28 
2.28 
2.28 
2. 27 
2.28 
2. 27 
2.28 
2.27 
2.28 

2.27 
2.27 
2.27 
2. 27 
2.27 
2.27 
2.27 
2.25 
2.27 
2.25 

D. I". 



Cos. 



871073 
870960 
870846 
870732 
870618 
870504 
870390 
870276 
870161 
870047 

869933 
869818 
869704 
869589 

869474 
869360 
869245 
869130 
869015 



868785 



868555 



868324 



868093 
867978 



867747 
867631 

867515 
867399 
867283 
867167 
867051 
866935 
866819 
866703 
866586 

866470 
866353 
866237 
866120 
866004 



865770 
865653 
865536 
865419 

865302 
865185 
865068 
864950 
864833 
864716 
864598 



864363 
864245 
864127 



Sin. 



D. 1" 



1.88 
1.90 
1.90 
1.90 
1.90 
1.90 
1.90 
1.92 
1.90 
1.90 

1.92 
1.90 
1.92 
1.92 
1.90 
1,92 
1.92 
1.92 
1.92 
1.92 

1.92 
1.92 
1.92 

1.93 
1.92 

1-93 
1.92 

1-93 
1.92 

1-93 

1-93 
1.93 
^.93 
1-93 
1.93 
1.93 
1.93 
1-93 
1.95 
1.93 

1.95 
1.93 
1.95 
1.93 
1.95 
1.95 
1.95 
1.95 
1.95 
1.95 

1-95 
1-95 
1.97 
1.95 
1.95 
1.97 
1.95 
1,97 
1.97 
1,97 

D. I". 



Tan. 



9-954437 
.954691 
.954946 
.955200 
. 955454 

9- 955708 
.955961 
.956215 
.956469 
.956723 

9-956977 
.957231 
.957485 
.957739 
.957993 

9. 958247 
.958500 

.958754 
.959008 
. 959262 

9-959516 

• 959769 
. 960023 
. 960277 
.960530 
9. 960784 
. 961038 
.961292 

. 961545 
.961799 

9. 962052 
. 962306 
. 962560 
.962813 
. 963067 

9. 963320 
.963574 



. 964081 
.964335 
9. 964588 
.964842 
.965095 
. 965349 
. 965602 

9-965855 
. 966109 
. 966362 
.966616 
.966869 

9.967123 
. 967376 
. 967629 
.967883 
.968136 

9. 968389 
.968643 
.968896 
.969149 
.969403 

9- 969656 

Cot. 



D. i' 



Cot. 



4.23 
4-25 
4-23 
4-23 
4.23 
4.22 



4-23 
4-23 
4.23 



4-23 
4.22 
4-23 
4-23 
4.22 
4.23 
4.23 
4.23 
4.22 
4.23 
4.22 

4-23 
4.23 
4.22 
4.23 
4.22 
4-23 
4.23 
4.22 
4.23 
4.22 

4-23 
4.22 
4-23 
4.22 
4.22 

4-23 
4.22 
4.23 
4.22 
4.23 
4.22 
4.22 
4.23 
4.22 
4.22 
4.23 
4.22 
4.22 
4.23 
4.22 

D. I". 



o. 045563 
.045309 
.045054 
. 044800 
.044546 

o. 044292 

.044039 
.043785 
.043531 
.043277 

o. 043023 
. 042769 

.042515 

. 042261 
. 042007 

0.041753 

. 041500 
,041246 
. 040992 

.040738 

0.040484 
.040231 
.039977 
.039723 
.039470 

0.039216 
, 038962 

.038708 
.038455 

.038201 
0.037948 
.037694 
.037440 
.037187 

.036933 
0.036680 
.036426 
.036172 
.035919 
.035665 

o. 035412 

.035158 
.034905 
.034651 
.034398 
0.034145 
.033891 
.033638 
.033384 
.033131 

0.032877 
.032624 
.032371 
.032117 
.031864 

0.03I6II 

.031357 
.031104 
.030851 
.030597 

o. 030344 
Tan. 



13a' 



47^ 



43" 



LOGARITHMIC SINES 



136' 



Sin. 



12 

13 
M 
15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 

43 
44 
45 
46 
47 
48 

49 

50 
51 
52 
53 
54 
55 
56 
57 
58 
59 
60 



9. 833783 
.833919 
.834054 
.834189 

.834325 
9. 834460 

.834595 
.834730 
.834865 

.834999 

9.835134 
. 835269 
.835403 
.835538 
.835672 

9.835807 

.835941 
.836075 
. 836209 
.836343 

9-836477 
.836611 

.836745 

.836878 

.837012 

9.837146 

.837279 
.837412 
.837546 
.837679 

9.837812 
.837945 
.838078 
.838211 
.838344 

9- 838477 
.838610 
.838742 
.838875 
.839007 

9.839140 
.839272 
.839404 
.839536 
. 839668 

9. 839800 
.839932 
. 840064 
.840196 
.840328 

9. 840459 
.840591 
. 840722 
.840854 
.840985 

9. 841116 
.841247 
.841378 
.841509 
.841640 

9. 841 771 

Cos. 



D. i". 



2.27 
2.25 
2.25 
2.27 
2.25 
2.25 
2.25 
2.25 
2.23 
2.25 

2.25 
2.23 
2.25 
2.23 
2.25 
2.23 
2.23 
2.23 
2.23 
2.23 

2.23 
2.23 
2.22 
2.23 
2.23 
2. 22 
2.22 
2.23 
2.22 
2.22 

2. 22 
2. 22 
2. 22 
2. 22 
2. 22 
2. 22 
2. 20 
2. 22 
2.20 
2. 22 

2.20 
2. 20 
2. 20 
2. 20 
2. 20 
2. 20 
2. 20 
2. 20 
2. 20 
2.18 

2. 20 
2.18 
2. 20 
2.18 
2.18 
2.18 
2.18 
2.18 
2.18 
2.18 



Cos. 



9.864127 
.864010 
.863892 
. 863774 
.863656 

9.863538 
.863419 
.863301 
.863183 
. 863064 

9. 862946 
.862827 
. 862709 
. 862590 
.862471 

9- 862353 
.862234 
.862115 
.861996 
.861877 

9.861758 
.861638 
.861519 
.861400 
.861280 

9.861161 
.861041 
.860922 
. 860802 
. 860682 

9. 860562 
. 860442 
. 860322 
. 860202 
.860082 

9. 859962 
.859842 
.859721 
.859601 
. 859480 

9. 859360 

.859239 
.859119 



.858877 
9.858756 
.858635 
.858514 
.858393 
.858272 

9.858151 
. 858029 
.857908 
.857786 
.857665 

9.857543 

.857422 

.857300 

.857178 

. .857056 

9. 856934 

Sin; 



D. 1" 



1.95 
1.97 
1.97 
1.97 
1.97 
1.98 
1.97 
1.97 
1.98 
1.97 
1.98 
1.97 
1.98 
1.98 

1.97 
1.98 
1.98 
1.98 
1.98 
1.98 

2,00 
1.98 
1.98 
2.00 
1.98 
2.00 
1.98 
2.00 
2.00 
2.00 

2.00 
2.00 
2.00 
2.00 
2.00 
2.00 
2.02 
2.00 

"2.02 
2.00 

2.02 
2.00 
2.02 
2.02 
2.02 
2.02 
2.02 
2.02 
2.02 
2.02 

2.03 
2.02 
2.03 
2.02 
2.03 
2.02 
2.03 
2.03 
2.03 
2.03 

D. i" 



Tan. 



9. 969656 

.969909 
.970162 
.970416 
. 970669 
9.970922 

.971175 
.971429 
.971682 
.971935 

9.972188 
.972441 
.972695 
.972948 
.973201 

9-973454 
.973707 
.973960 

.974213 
.974466 

9.974720 

.974973 
.975226 

.975479 
.975732 
9- 975985 
.976238 
.976491 
.976744 
.976997 

9.977250 
.977503 
.977756 
. 978009 
.978262 

9-978515 
. 978768 
.979021 
.979274 
.979527 

9.979780 
. 980033 
. 980286 
.980538 
.980791 

9.981044 
.981297 
.981550 
.981803 



9. 982309 
.982562 
.982814 
.983067 
.983320 

9.983573 



D. i" 



.984079 

.984332 

. 984584 

9.984837 

Cot. 



4.22 
4. 22 
4-23 
4.22 
4.22 
4. 22 
4.23 
4.22 
4.22 
4.22 

4.22 

4.23 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.23 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 

4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4. 22 
4.22 
4.22 

4.22 
4.22 
4.20 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 

4.22 
4.20 
4.22 
4.22 
4.22 
4.22 
4.22 
4.22 
4.20 
4.22 

D. 1". 



Cot. 



0.030344 
.030091 
.029838 
.029584 
.029331 

o. 029078 
.028825 
.028571 
.028318 
.028065 

0.027812 
.027559 
.027305 
. 027052 
. 026799 

o. 026546 
. 026293 
. 026040 

.025787 
.025534 

o. 025280 
. 025027 

.024774 
.024521 

.024268 
0.024015 
.023762 
.023509 
.023256 
.023003 

o. 022750 

.022497 

.022244 
.021991 
.021738 
0.021485 
.021232 
. 020979 
,020726 

.020473 

o. 020220 
.019967 

.019714 

,019462 
.019209 
o. 018956 
.018703 
.018450 
.018197 

.017944 

0.0 I 7691 

.017438 

.017186 
.016933 
. 016680 

0.016427 
.016174 
.015921 
.015668 
.015416 

0.015163 

Tan. 



133 



46^ 



44^ 



COSINES, TANGENTS, AND COTANGENTS 135^ 



M. 



I 
2 
3 
4 

i 

7 
8 

9 

zo 
II 
12 
13 
14 

II 

17 
x8 

19 
20 
21 

22 
23 
24 
25 
26 
27 
28 

29 
30 
31 
32 

33 
34 
35 
36 
37 
38 
39 
40 
41 
42 
43 
44 
45 
46 

48 
49 

50 
51 
52 
53 
54 
55 
56 

57 
58 
59 
60 



Sin. 



9.841771 
.841902 
.842033 
.842163 
. 842294 

9.842424 

.842555 
. 842685 
.842815 
. 842946 

9.843076 
.843206 
.843336 
.843466 

. 843595 
9.843725 
.843855 
.843984 
.844114 
.844243 

9. 844372 
. 844502 
.844631 
. 844760 



9. 845018 
.845147 
. 845276 
.845405 
.845533 

9. 845662 

.845790 
.845919 
. 846047 
.846175 
9. 846304 
. 846432 
, 846560 



.846816 

9. 846944 
.847071 
.847199 
.847327 
. 847454 

9. 847582 
.847709 
.847836 
.847964 
.848091 

9. 848218 

.848345 
. 848472 
.848599 
. 848726 
9.848852 
.848979 
.849106 
.849232 

.849359 
9.849485 

Cos. 



D. 1". 



2.18 
2.18 
2.17 
2.18 
2.17 
2.18 
2. 17 
2.17 
2.18 
2.17 

2. 17 
2.17 
2.17 
2.15 
2.17 
2.17 

2.15 
2.17 

2.15 
2.15 
2.17 
2.15 
2.15 
2.15 
2.15 
2.15 
2.15 

2.15 
2.13 
2.15 

2.13 
2.15 
2.13 
2.13 

2.15 
2.13 
2.13 
2.T3 
2.13 
2.13 
2.12 
2.13 
2.13 
2. 12 

2.13 
2.12 
2.12 

2.13 
2. 12 
2. 12 

2. 12 
2. 12 
2. 12 
2. 12 
2. 10 
2. 12 
2. 12 
2. 10 
2. 12 
2. 10 



D. I'' 



Cos. 



9-856934 
.856812 
. 856690 
.856568 
. 856446 

9.856323 
. 856201 
. 856078 
.855956 
.855833 

9.855711 
.855588 
.855465 
.855342 
.855219 

9.855096 

.854973 
.854850 
.854727 
.854603 

9. 854480 
.854356 
.854233 
.854109 
.853986 

9.853862 
.853738 
.853614 
.853490 
.853366 

9. 853242 
.853118 
.852994 



.852745 

9. 852620 

. 852496 

.852371 
.852247 
.852122 

9.851997 

.851S72 

.851747 
.851622 

.851497 
9.851372 
.851246 
.851121 
.850996 
. 850870 

9.850745 
.850619 

. 850493 



. 850242 
9.850116 
. 849990 
. 849864 
.849738 
.849611 
9. 849485 

Sin. 



D. i". 



2.03 

2.03 
2.03 
2.03 
2.05 
2.03 
2.05 
2.03 
2.05 
2.03 

2.05 
2.05 
2.05 
2.05 
2.05 
2.05 
2.05 
2.05 
2.07 
2.05 

2.07 
2.05 
2.07 
2.05 
2.07 
2.07 
2.07 
2.07 
2.07 
2.07 

2.07 
2.07 

_2. 08 
2.07 
2.08 
2.07 
2.08 
2.07 
2.08 
2.08 

2.08 
2.08 
2.08 
2.08 
2.08 
2. 10 
2.08 
2.08 
2. 10 
2.08 

2. 10 
2. 10 
2.08 
2.10 
2.10 
2. 10 
2. 10 
2. 10 
2.12 
2.10 



Tan. 



9.984837 
985090 
985343 
985596 



986101 

986354 
986607 
986860 
987112 

987365 
987618 
987871 
988123 
988376 
988629 



989134 

989387 
989640 



990145 
990398 
990651 
990903 
991156 
991409 
991662 
991914 
992167 

992420 
992672 

992925 
993178 

993431 
993683 
993936 
994189 
994441 
994694 

994947 
995199 
995452 
995705 
995957 
996210 

996463 
996715 
996968 
997221 

997473 
997726 

997979 
998231 

998484 
998737 



D. i'\ 



999242 
999495 
999747 
000000 

Cot. 



4.22 
4. 22 
4.22 
4.20 
4.22 
4.22 
4.22 
4.22 
4.20 
4.22 

4.22 
4. 22 
4.20 
4.22 
4.22 
4. 22 
4. 20 
4.22 
4. 22 
4.22 

4.20 
4.22 
4.22 
4.20 
4.22 
4.22 
4.22 
4. 20 
4.22 
4.22 

4.20 
4. 22 
4. 22 
4. 22 
4.20 
4.22 
4.22 
4. 20 
4.22 
4.22 

4.20 
4.22 
4.22 
4. 20 
4. 22 
4. 22 
4.20 
4. 22 
4.22 
4.20 

4.22 
4.22 
4. 20 
4. 22 
4.22 
4.20 
4.22 
4. 22 
4. 20 
4.22 

D. I"; 



Cot. 



0.015163 
.014910 
.014657 
. 014404 
.014152 

0.013899 
. 013646 

.013393 
.013140 
.012888 

0.012635 
.012382 
.012129 
.011877 
.011624 

0.011371 
.011118 
,010866 
.010613 
. 010360 

0.010107 
.009855 
.009602 
.009349 
.009097 

o. 008844 
.008591 
.008338 
.008086 
.007833 

o. 007580 
.007328 

.007075 

.006822 
.006569 
0.006317 
.006064 
.005811 

.005559 
.005306 

o. 005053 
.004801 
.004548 
.004295 
. 004043 

o. 003790 

.003537 
.003285 
.003032 
.002779 

o. 002527 
.002274 
,002021 
,001769 
.001516 

0.001263 
.001011 
.000758 
.000505 
.000253 

0,000000 
Tan. 



134° 



45= 



950 



GENERAL TABLES AND FORMULAE 



Table 76. Giving the Weights of Different Materials per 
Cubic Foot^ 



Material 



Weight per Cu. Ft. 



Ash timber 

Brick (pressed) 

'* (common building) 

Cement (Portland) 

(Natural 

Concrete 1:2:4 Mixture (Trap rock) 

(Gravel) 

" (Limestone) 

" (Sandstone) 

(Cinder) 

'' 1:3:6 Mixture (about 5 lbs. less) 

Earth (conmion loam, loose and dry) , 

'' (common loam, moist and rammed) . . . 

" (sand or gravel loose and dry) 

" (sand or gravel rammed) 

'^ (sand or gravel wet) 

Hemlock timber 

Hickory " 

Iron (cast) 

" (wrought) 

Maple timber 

Oak " (white) 

(black) 

Masonry (dressed granite or limestone) 

" (mortar rubble) 

(dry " ) 

Pine (white) 

" (northern yellow) 

" (southern yellow) 

Steel 

Water 



75 
50 



40 
150 
125 
to 90 
to 56 
155 
152 
150 

145 
no 

70 

100 



25 

50 
450 
480 

50 

48 

40 

165 
155 
125 

25 

34 
40 
490 
62.5 



lbs. 



Miscellaneous Weights 

I bbl. Portland cement 376 lbs. 

I '' natural '^ 235 ** 

I gal. water '* 8.345 ^' 

1 For weight of road rocks, see Tables 2sa and 2sb, page 233. 



STRENGTH OF MATERIALS 



951 



^ Table 77. Giving Moduli of Elasticity, Working Stress 
AND Ultimate Strength 



Moduli of Elasticity 



Material 



Lbs. per Sq. In. 



Concrete 

Hemlock 

Iron (cast) 

Iron (wrought) . 

Oak 

Pine (white) . . 
Pine (yellow) . . 
Steel (medium) 
Spruce 



2,000,000 

900,000 

17,500,000 

29,000,000 

1,500,000 

1,600,000 

1,600,000 

30,000,000 

1,600,000 



Working Stresses in Lbs. per Square Inch 



Material 



Tension 



Compression 



Shear 



Concrete 

Hemlock 

Iron (cast) . . . . 

" (wrought) . 
Oak.......... 

Pine (white) . . . 

" (yellow) . . 

Steel (medium) . 

Spuce 



60 

600 

3,000 

10,000 

1,200 

700 

1,200 

12,000 

800 



600 
W. G.i 600 A. G.2 150 

18,000 
8,000 
W. G. 1,200 A. G. 500 
W. G. 700 A. G. 200 
W. G. 1^00 A. G. 350 

12,000 
W G. 800 A. G. 200 



60 to 100 
W. G. 100 A. G. 600 

5,000 

8,000 
W. G. 200 A. G. 1,000 
W. G. 100 A. G. soo 
W. G. 150 A. G. 1,250 

12,000 
W. G. 100 A. G. 750 



Ultimate Strength in Lbs. per Square Inch 



Material 



Tension 



Compression 



Shear 



Concrete' 

Hemlock] 

Iron (cast) 

" (wrought) . . 

Oak 

Pine (white) .... 

" (yellow; . . . 

Steel (medium) . 

Spruce 



300 

6,000 

18,000 

50,000 

12,000 

7,000 

12,000 

60,000 

8,000 



3,000 
W. G. 6,000 A. G. 600 

90.000 

40,000 
W. G 7,000 A. G. 2-000 
W G. 5,500 A. G. 700 
W. G. 7,000 A. G. 1,400 

60,000 
W. G. 6,000 A. G. 700 



1300 
W. G. 350 A. G. 2,500 
20,000 to 30,000 
35,000 to 55,000 
W. G. 800 A. G. 4,000 
W. G 400 A. G. 2,000 
W. G. 600 A. G. 5,000 

50,000 to 70,000 
W. G. 400 A. G. 3,200 



» W. G. — With Grain. 



2 A. G. — Across Grain. 



952 



GENERAL TABLES AND FORMUL/E 



Table 78. Uniform Beams. Maximum Bending Moment 
AND Deflections (Simple Cases) 



Case I. Beam with ends free. Single concentrated load P in 
middle of span; weight of beam disregarded. 

The maximum moment occurs at 
the center of the span. 

P 4 

The maximum deflection occurs at 
the center of the span. 




Concentrated Load in Cen- 
ter of span 



D = 



Pl_ 
4SEI 



Where D 
P 
I 
E 



= the deflection in inches 
= load in pounds 
= span in inches 
= modulus of elasticity in lbs. 
per sq. inch 
/ = moment of inertia in inches* 
Mp = maximum moment in inch 
pounds. 




Case 2, Cantilever beam con- 
centrated load P; weight of beam 
disregarded. 

The maximum moment occurs at 
the support. 

M -=Pl 
P 

PP 



Cantilever Beam 



Z) = . 



3EI 



Case J. Beam with ends free. Uniformly distributed load. 
The maximum moment occurs at the center of the span. 



The maximum deflection occurs at 
the center of the span. 

3^4 EI 

In these formulae W equals the total 
uniformly distributed load. 




Uniform Load 



FT.EXURE FORMUL.^' 



953 



Case 4. Cantilever beam. Uniform load W. 
Maximum moment occurs at the 
point of support. 

2 

The maximum deflection occurs at 
the free end. 



D = 



SEI 




Case 5, Beam with fixed ends, concentrated load P in center of 
span; weight of beam disregarded. 

The maximum bending moment 
occurs at the points of support and 
at the middle of the beam. 



M ■■ 



PI 



D = . 



PP 
ig2 EI 




Case 6. Beam with fixed ends and a uniformly distributed load. 
Maximum bending moment occurs at the supports. 

12 

M =^^ 

24 



Maximum deflection 



WP 
SHEI 




Resisting Moment of a beam is expressed by the formula 



M,= 



pi 



Where M^ — moment of resistance in inch 
pounds 

P = maximum allowable fiber stress 
in lbs. per sq. inch. 

I — moment of inertia of the beam 
in inches ^ 

e = distance in inches from the neu- 
tral axis to the outer fiber 



954 GENERAL TABLES AND FORMUT..^. 

Table 79. Centers of Gravity of Ordinary Plane Figures 



ift.G. 




Squares, rectangles, parallelograms. Center of gravity is at 
the intersection of the diagonals or midway between the bases 
on a line drawn between the centers of those bases. 




Center of gravity is at the intersection of the medial lines 
a b and c d; a medial line is a line drawn from any apex to the 
middle of the opposite side The distance h (C. G.) = \ ah; that 
is, the center of gravity is on the medial line \ of the distance from 
the base to the apex. 



9— tnz" 



Trapezoid 



-^-.iCG. 



_ — .-z.^=.*h 



Graphic Method. Prolong h a to g, making a g = c d. Pro- 
long c d to h, making d h = ah. Connect g h. Bisect ah dit e. 
Bisect cd at /. Connect ef: the intersection of gh and e/ is 
the center of gravity. 

The distance/ (C.G.) = ^ X ^ f ^ f 
3 ab -{- cd 




Any Quadrilateral 

Graphic Method. Draw 
the diagonals a c and h d 
intersecting at e. 

Lay oQ a f = e c 
Lay oQ h g = e d 

Bisect eg at/j; bisect ef 
Sit i. 

The intersection of / /f and 
g i is the center of gravity 
of the figure. 



MOMENTS OF INERTIA 



955 



Circles 
Center of gravity at the center 




Semicircle 

The center of gravity lies on the radius 
perpendicular to the diameter. The distance 
c (C.G.) = radius X 0.4244 a 



Quadrant 

The center of gravity lies on the radius which 
bisects the /_ ach. The distances: {C.G.) = radius 
X 0.600? 




Sector 

The center of gravity lies on the radius bisect- 
ing the /_ach. The distance c (C. G.) = f radius X ^ 
chord a b radius^ X chord 



arc adb 



3 X area 




Segment 

The center of gravity lies on the perpen- 
dicular erected at the center of the chord ab. 



The distance c (C. G.) 



chord ab 




1 2 X area of segment 



Table 80. Moments of Inertia of Simple Sections 



/ = Moment of Inertia 
bd^ 



! = • 



12 



i. 



-b^ 



956 



GENERAL TABLES AND FORMUT.iT; 



^— 


Square 


I. it 

12 


- 


■Af 


-1 




t* — (• — i 

Triangles 


36 


Circles 


/ = 0.7854/^4 


1 




1 


12 



APPENDIX A 
TRAFFIC RULES AND REGULATIONS, STATE OF OHIO 
FOREWORD 

Inasmuch as Section 249 of the Cass Law, (G. C. 7246) directing 
the state highway commissioner to prepare and publish a set of 
traffic rules and regulations, is for the protection of hfe and limb, it 
is undoubtedly the most important section of the road laws of Ohio. 

After much thought and investigation of rules and regulations 
governing traffic conditions in a number of states, we submit the 
following in as condensed form as explicitness will permit, having 
selected, as we beheve, the better parts of such laws and regulations 
governing the traffic of other states and municipahties, and putting 
them into a code of rules and regulations that will fit, as nearly as 
may be, all conditions and localities requiring a code of regulations, 
which will at the same time govern traffic on aU the highways of 
Ohio. 

A cursory examination of these rules may lead many to the con- 
clusion that unreasonable restrictions have been imposed, but we 
believe a thoughtful study of each section will reveal an effort on 
the part of the State Highway Department to furnish the public 
with a code of traffic regulations, permitting of the greatest amount 
of freedom consistent with safety first. 

The original draft of the following regulations was submitted 
to Mr. W. A. Alsdorf, Secretary of the Ohio Good Roads Federation, 
Mr. Harry Gordon of Cincinnati, and Mr. Fred Caley of Cleveland, 
who carefully studied the entire code, section by section, and sug- 
gested many valuable and important changes. 

We now put forth the result of our efforts with the belief that if 
the prescribed rules and regulations are followed, many embarrassing 
situations and distressing accidents may be averted. 

Clinton Cowen, 
State Highway Commissioner, 

ARTICLE I — DEFINITIONS 

Sec. I — The term "vehicle" shall apply to a horse being rode 
or led, and to any conveyance except a baby carriage or street car. 

Sec. 2 — The term "street car" shall apply to any conveyance 
confined to tracks. 

Sec. 3 — The term "driver" shall apply to the rider, driver, or 
leader of a horse, a person who pushes, draws, propels, operates, or 
who is in charge of a vehicle. 

Sec. 4 — The term "road" shall apply to that part of a street 
or public highway intended for vehicles. 

9S1 



95^ APPENDIX 

Sec. 5. — The term ^^curb" shall apply to the boundary line of 
a road. 

Sec. 6 — The term "sidewalk'^ shall apply to a path or walk 
intended for pedestrians. 

Sec. 7 — The term "horse" shall apply to any draft animal or 
beast of burden. 

Sec. 8 — ^The term "motor vehicle'' shall apply to all vehicles 
propelled by power other than muscular, except a street car, traction 
engine, road roller, and police, fire or ambulance vehicles. 

ARTICLE n — RESPECTIVE RIGHTS AND DUTIES OF 
DRIVERS AND PEDESTRIANS 

Sec. I — Roads are primarily intended for vehicles, but pedestrians 
have the right to cross them in safety, and drivers shall exercise all 
possible care not to endanger them. 

Sec. 2 — Pedestrians should observe the following precautions; 

1st. Avoid interference with vehicular traffic, and to this end not 
step onto the road without first looking to see what is approaching: 

2nd. Cross the road at right angles — at regular crossings where 
such exist, — and where a traffic officer is stationed, wait for his signal. 

Sec. 3 — Pedestrians will aid in expediting traffic on side-walks 
by keeping to the right, and when stopping for any purpose by doing 
so on one side and out of the way of a crossing or driveway. 

ARTICLE m — PASSING, TURNING, STOPPING, 
STANDING AND STARTING 

Sec. I — A vehicle meeting another shall keep to the right, so as 
to leave half the road free for the coming vehicle. (6310 G. C.) 

Sec. 2 — A vehicle overtaking another shall pass to the left, the 
front vehicle giving half the road to the rear vehicle. (6310 G. C.) 

Sec. 3 — A vehicle turning into a road to the right shall turn the 
corner as near the right hand curb as practicable. 



This Way 

Sec. 4 — A vehicle turning into a road to the left shall pass around 
the point of intersection of the center lines of the two roads. 



n 



I 



This Way ''' I j I Not this Way 



TRAFFIC RULES 959 

Sec. 5 — A vehicle crossing from one side to the other of a road 
shall head in the same direction as the traffic on that side of the road. 



Thia Way Not this Way 

Sec. 6 — On heavy traffic roads, slow moving vehicles shall keep 
close to the right hand curb so as to leave the center of the road clear 
for overtaking traffic — the slower the speed the nearer the curb. 

Sec. 7 — A vehicle in passing around a circle shall keep to the right 
from entrance to exit. 

Sec. 8 — A vehicle on a road divided longitudinally by a parkway, 
walk, rope or other obstruction, shall keep to the right of such 
division. 

Sec. 9 — A vehicle shall not back to make a turn if by so doing it 
obstructs traffic, but shall go forward to a point where a turn can be 
made without backing. 

Sec. 10 — A vehicle shall not follow another too closely for safety. 

Sec. II — No vehicle shall stop in the road in such a position as 
to prevent the free passage of other vehicles in both directions at 
the same time. ^ 

Sec. 12 — A vehicle shall not pass a street car which has stopped 
to receive or discharge passengers at a less distance than ten feet, 
nor at a greater speed than six miles per hour. A vehicle shall come 
to a stop if necessary to prevent interference or injury to such 
passengers. 

Sec. 13 — No horse or vehicle shall be driven, propelled or allowed 
to stand, on any side-walk except for purposes of crossing the same 
when necessary, and then only the shortest way from the road to 
the abutting premises. 

Sec. 14 — No vehicle shall stop in such a way as to interfere with 
the passage of pedestrians at regular crossings, or within 10 feet of 
a fire plug. 

Sec. 15 — No street car shall stop or stand within the intersection 
of any road. 

ARTICLE IV — LOADS, LOADING, WIDTH OF TIRE, 
TRAILERS, ETC. 

Sec. I — No traction engine or other vehicle whose wheels have 
tires equipped with lugs, spikes, chains or other projections seriously 
destructive to the surface, shall be driven over the road. (1342 1- 
12 G. C.) 

Sec. 2 — No vehicle or load, the total width of which is greater 
than twelve feet, shall be operated or drawn over a road unless said 
greater width will leave one-half the road free for passing vehicles. 

Sec. 3 — No more than thirty-four hundred pounds including 
weight of vehicle, shall be transported over a gravel, macadam or 
stone road in a vehicle having a tire less than three inches in width. 
(7477 G. C.) 



960 APPENDIX 

Sec. 4 — For vehicles having tires three inches and over in width 
the load on any wheel per lineal inch of width of tire on any road shall 
not exceed six hundred pounds; and during such times as the road 
surface is soft, because of thawing or because of excessive rains, the 
load per lineal inch of width of tire on any wheel shall not exceed 
three hundred pounds on gravel or macadam roads. 
I Sec. 5 — Trailers used in hauhng over the road shall be so con- 
nected that the wheels of no two will follow in the same tracks. 

Sec. 6 — No vehicle carrying a load in excess of fifteen tons, 
including the weight of the vehicle, shall be moved over any 
road except under the written permission of the State Highway 
Commissioner. 

ARTICLE V — SPEEDS 

Sec. I — No motor vehicle shall operate on a road at a greater 
speed than: 

8 miles per hour in the business or closely built up portions of a 
municipaUty; 

15 miles per hour in other portions of a municipality; 

20 miles per hour outside of municipalities. (12604 G. C.) 

Sec. 2 — No vehicle shall operate on a road at a speed greater 
than is reasonable or proper or so as to endanger the property, life 
or limb of any person. (12603 G. C.) 

Sec. 3 — No motor or other power vehicle carrying a weight in 
excess of four tons including a vehicle shall be operated upon any 
road at a speed greater than 15 miles per hour; and no such vehicle 
carrying a weight in excess of eight tons including the vehicle shall 
be operated at a speed greater than 6 miles per hour when such vehicle 
is equipped with iron or steel tires, nor greater than 12 miles per 
hour when the vehicle is equipped with tires of rubber or other similar 
substance. 

Sec. 4 — No vehicle shall cross a road or make any turn at a 
dangerous speed. 

Sec. 5 — Where "Danger'' and "Go Slow" signs appear, the 
speed of any vehicles shall not exceed twelve miles per hour. 

Sec. 6 — Trucks and heavy wagons shall not be driven recklessly 
so as to endanger the public. 

Sec. 7 — No vehicle shall emerge from an alley, stable, garage 
or any private drive or entrance faster than a walk or six miles 
per hour. 

Sec. 8 — A vehicle upon approaching a cross road shall slow down 
sufficiently to prevent any danger from meeting other vehicles on 
the cross road. 

Sec. 9 — No person shall race any horse or motor vehicle on a 
road whether the running, racing or trotting be for trial or speed or 
for the purpose of passing another horse or vehicle. 

Sec. 10 — A motor vehicle, road roller or traction engine shall 
slow down when approaching a horse, if the horse appears to be 
frightened, and if the driver of the horse shall signal the driver of 
the vehicle the latter shall be brought to a stop, and if the circum- 
stances require it, the engine shall be stopped, provided such signal 



TRAFFIC RULES 961 

be given in good faith and under circumstances of necessity. Such 
vehicle shall remain stationary so long as may be reasonable to allow 
such horse to pass. (12605 G. C.) 

Sec. II — In case of injury or damage to person or property, 
due to the operation of vehicle, the operator or driver of said vehicle 
shall stop, and, upon request of the person injured or any one present, 
give his name and address and that of the owner of the vehicle. 
(12606 G. C.) 



ARTICLE VI — SIGNALS, HORNS, SIGNS AND NOISES 

Sec. I — All motor vehicles and bicycles shall be equipped with 
a suitable bell or horn for signaUing. (126 14 G. C.) 

Sec. 2 — When a vehicle is slowing up or stopping, the driver 
shall give a timely signal to those in the rear, by raising the arm or 
whip vertically (preferably) or horizontally or by some other unmis- 
takable manner. 

Sec. 3 — When about to turn either from a standstill or while in 
motion, the driver of a vehicle shall give timely signal by hand or 
whip or in some other unmistakable manner, to indicate the direction 
of the turn. This is especially important when turning to the left. 

Sec. 4 — Before a vehicle is backed, the driver shall give timely 
warning. 

Sec. 5 — Sound signals are prohibited except for necessary warn- 
ing, and must be reserved for that purpose. Signals shaU not be 
sounded by unauthorized persons on standing vehicles. 

Sec. 6 — All signs, signals and orders of a traffic officer shall be 
promptly complied with. 

Sec. 7 — Every driver of a motor vehicle shall give a timely warn- 
ing when overtaking a person or vehicle on a road or when approach- 
ing a crossing or curve where the sight of approaching vehicles may 
be obscured. 

Sec. 8 — No vehicle shall be so loaded as to cause an objectionable 
or unnecessary noise by parts of the load striking together or upon 
the vehicle. 

Sec. 9 — The use between the hours of 8 P. M. and 6 A. M. of 
the muffler cut-out or the production of any other unnecessarily 
loud noise on any vehicle, is prohibited within 100 yards of any 
residence or within such distance as might seriously disturb the in- 
habitants of such residence. 

Sec. 10 — No vehicle shall pass over any road which is closed 
against traffic to be repaired or constructed. A suitable sign or 
barricade shall be considered as sufficient evidence that such road 
is closed. (1342 1--9 G. C.) 



ARTICLE Vn — RIGHT OF WAY 

Sec. I — Every driver of a vehicle approaching the intersection 
of a road where a traffic officer is not stationed, shall grant the right 
of way at such intersection to any vehicle approaching from his right. 



962 APPENDIX 

Sec. 2 — A vehicle In front of a street car shall immediately turn 
out upon the signal of the operator of the car. 

Sec. 3 — A vehicle shall not so occupy any road as to obstruct 
traffic. 

Sec. 4 — When in the performance of duty, the following vehicles 
shall have the right of way: PoHce, Fire, Fire Patrol, Ambulance, 
U. S. Mail; also the militia. 

Sec. 5 — During blockades and stoppages a clear space shall be 
kept open between all street cars at crossings. 

Sec. 6 — Pedestrians about to get on, or just having been dis- 
charged from a street car shall have the right of way and vehicles 
shall come to a stop when necessary to give such pedestrians the right 
of way. 

ARTICLE Vm — LIGHTS 

Sec. I — Motor vehicles shall display between 30 minutes after 
sunset and 30 minutes before sunrise, two white hghts in front of 
sufficient power to be visible 200 feet away in the direction the vehicle 
is moving, and one red light visible in the opposite direction; also 
one rear white light which shall illuminate and make plainly visible 
the license number tag. Provided that motorcycles need have but 
one front light. (12614 G. C.) 

Sec. 2 — During the same period given in Sec. i, bicycles shall 
have a light of sufficient power to be seen 200 feet in the direction 
the bicycle is moving. 

Sec. 3 — Bright lights on any vehicle or street car operated within 
the limits of the right of way of any road shall be dimmed or con- 
trolled while approaching and passing another vehicle so as to pro- 
tect from the direct glare, the eyes of a driver 200 feet ahead and whose 
eyes are 5 feet abov^e the road surface. 

Sec. 4 — In order to avoid accidents and for the purpose of secur- 
ing the greatest possible safeguard to human life, all drivers of horse 
drawn vehicles are urged and requested to display a light at night 
that can be seen both in front and in the rear. 



ARTICLE IX — MISCELLANEOUS REGULATIONS 

Sec. I — The unnecessary emission of dense smoke from motors 
is forbidden. 

Sec. 2 — No horse or other domestic animal shall be allowed to 
run loose and unattended upon the road. 

Sec. 3 — No vehicle shall be used or so loaded as to permit its 
load to be scattered over the road in such a way as to be objectionable 
to traffic or detrimental to the road. In no case shall ashes, garbage 
or other vegetable matter be scattered over the road surface. 

Sec, 4 — No one shall ride on any vehicle without the consent of 
the driver. 

Sec, 5 — No road shall be blocked or obstructed by any farm 
implements or other machinery or obstructions except when the 
road is legally closed for repair or construction. (13421-11 G. C.) 



TRAFFIC RULES 963 

Sec. 6 — No person shall operate a motor vehicle while in a state 
of intoxication, (i 2626-1 G. C.) 

Sec. 7 — Any special rules or regulations for any road or portion 
of a road which are conspicuously displayed at either end of such 
road or have been made known to the driver of a vehicle by a road 
official, shall be strictly observed by all drivers of vehicles over the 
road. (7246 G. C.) 

Sec. 8 — Drivers of vehicles shall observe such care as is neces- 
sary to preserve the life of the road; — avoid following the tracks of 
a vehicle preceding them, and avoid driving in the ruts that may 
have started to form in the road surface. 

Sec. 9 — Any person operating a vehicle or moving a load, or 
who is responsible for the operating of a vehicle or the moving of a 
load over a road in violation of any of the rules and regulations apply- 
ing to such road, in addition to the fine imposed shall be responsible 
for all damage which said road may sustain as a result of such vio- 
lation. (1342 i-i 7 G. C.) 

While a good set of Traffic Rules and Regulations will be of great 
service to the public, yet in connection with any set of rules and regu- 
lations that may be in force, it will be necessary for drivers to exer- 
cise common sense and good judgment to avoid accidents and protect 
the roads. By a careful distribution of the traffic over a good road 
surface, roads may be made to last several times as long as they will 
last when all traffic concentrates in a single track. Every individual 
should remember that he helps build and maintain the roads regard- 
less of the direct taxes he pays, and hence it is to his interest that the 
roads be used in such a way as to preserve them and render the 
greatest service to the general public. 

APPENDIX 

Sec. 6290 (G. C.) ["Motor vehicle" defined.] The term 
"motor vehicle," as used in this chapter and in the penal laws, except 
where otherwise provided, shall be deemed to include all vehicles 
propelled by power other than muscular power, except road rollers, 
traction engines, police patrol wagons, police automobiles, public 
ambulances, vehicles run upon rails or tracks, fire engines, fire trucks 
. or other vehicles or apparatus belonging to any police department, 
municipal fire department, volunteer fire company or salvage com- 
pany, organized under the laws of Ohio, or used by such police depart- 
ment, volunteer fire company, or salvage company, in the discharge 
of its functions or in transporting its officers, members, employes, 
men or articles necessary and proper for the proper discharge of 
such functions, to or from a fire or in response to any alarm of fire 
or to any other alarm or call to which it may respond. (100 v. 72; 
Am. 103 V. 763; 106 V. 139). 

Sec. 6310 (G. C.) [Meeting vehicle on highway.] A person 
driving a carriage or vehicle on a public turnpike, road or highway, 
on meeting a carriage or vehicle, shall keep to the right so as to leave 
half of the road free for the coming vehicle. 



964 APPENDIX 

A person riding on horseback or on a bicycle, tricycle, or tandem 
bicycle, or driving a locomobile, automobile, or any motor vehicle 
operated by its own power, on meeting a carriage or vehicle drawn 
by horses or oxen, shall keep to the right so as to leave one-half of 
the road free for the use of the vehicle drawn by horses, mules or 
oxen. 

A person driving a carriage, vehicle, automobile, or any kind of 
vehicle, who desires to pass a vehicle going in the same direction on 
any pubhc road or highway shall give an alarm or demand to the 
person or persons driving the vehicle in front and going in the same 
direction, of such desire, and the person so driving the front vehicle 
shall immediately give the half of the road to the rear vehicle, by 
turning to the right, so that the rear vehicle can pass to the left of 
the front vehicle. 

[Definition; penalty.] The term vehicle herein shall apply 
to any vehicle propelled by its own power or drawn by horses or oxen. 
Any person or persons driving any vehicle, horse-drawn or otherwise, 
on any public road, who shall fail, in meeting or passing, to give the 
required road as herein stated, shall be subject to a fine in a court 
having jurisdiction thereof, in any sum not less than one dollar, nor 
more than ten dollars, and costs of prosecution. (R. S. Sec. 3490. 
Am. 103 V. 556). 

Sec. 7246 (G. C.) [Publication of traffic rules and regula- 
tions; special rules; enforcement.] The state highway com- 
missioner within sixty days after the taking effect of this act, shall 
prepare and publish a set of traffic rules and regulations governing 
the use of, and traffic on, all state roads. All rules and regulations 
that are to apply generally throughout the state, including those 
applicable to roads constructed of the various kinds of road material, 
shall become effective thirty days after publication. Special rules 
and regulations or orders, applying only to specified sections of 
state roads, shall become effective as soon as posted at each end, and 
at all road crossings on such specified section. For the purpose of 
carrying into effect the provisions of this section, it shall be the duty 
of the state highway commissioner, the county commissioners, the 
county highway superintendent, the township highway superinten- 
dent, township trustees, and all patrolmen or deputies employed 
on any highways within the state, to prosecute any violation of this 
section. It shall be unlawful for any person or persons, firm or cor- 
poration to enter upon, or travel over said state roads, except in 
accordance with the traffic rules and regulations promulgated by 
the state highway commissioner. 

Sec. 7477 (G. C.) [Weight of load and tire width pre- 
scribed.] No person, firm or corporation, in a county having 
macadamized, graveled or stone roads shall transport over such roads, 
in a vehicle having a tire of less than three inches in width, a burden, 
including weight of vehicle, of more than thirty-four hundred pounds. 

[Board of directors and duties; penalty.] The county com- 
missioners shall constitute a board of directors for their respective 
counties, with power to prescribe the increased gross weight in excess 
of thirty-four hundred pounds that may be carried, including weight 



TRAFFIC RULES 965 

of vehicles, in vehicles having a width of tire three inches or upwards, 
and cause such regulations to be recorded in their journal. Any 
person violating this section or any regulation duly prescribed by the 
board of county commissioners, made in pursuance thereof, shall be 
fined not less than five dollars nor more than fifty dollars. 

[Enforcement of traffic regulations..] The township trustees 
of any township and the county commissioners of any county, shall 
cause to be prosecuted all persons violating this section or any regu- 
lations prescribed by the board of county commissioners made in 
pursuance of the authority conferred in this section. The county 
commissioners within their respective counties, may appoint a suit- 
able person or persons to enforce such section and regulations. The 
person or persons so appointed shall receive for each conviction by 
them secured under this section, such portion of the fine or penalty 
as the commissioners deem just and proper. 

Sec. 7478 (G. C.) [Publication of traffic rules in coun- 
ties.] The state highway commissioner shall furnish the county 
highway superintendent with a copy of the rules and regulations pro- 
mulgated by said state highway commissioner, and applicable to his 
county. The coimty highway superintendent shall cause the rules 
and regulations so furnished to him by said highway commissioner 
to be published, at least once each week, for two successive weeks, 
in a newspaper pubHshed and of general circulation in said county, 
if there be any such paper published in said county, but if there be 
no newspaper published in said county then in a newspaper having 
general circulation in said county. When such regulations are pub- 
lished in the manner aforesaid, it shall be deemed a sufficient pub- 
lication under the provision of this act. 

Sec. 12603 (G. C.) [Operating motor vehicle unreasonably 
and improperly; penalty.] Whoever operates a motor vehicle 
or motorcycle on the pubhc roads or highways at a speed greater 
than is reasonable or proper, having regard for width, traffic, use and 
the general and usual rules of such road or highway, or so as to en- 
danger the property, fife or limb of any person, shall be fined not 
more than twenty-five dollars, and for a second offense shall be fined 
not less than twenty-five dollars nor more than fifty dollars. (99 
V. 541, 543, Sees. 14, 25. Am. 103 v. 161). 

Sec. 12604 (G. C.) [Violation of speed limit.] Whoever 
operates a motorcycle or motor vehicle at a greater speed than eight 
miles an hour in the business and closely built-up portions of a 
municipality or more than fifteen miles an hour in other portions 
thereof or more than twenty miles an hour outside of a municipaHty, 
shall be fined not more than twenty-five dollars, and for a second 
offense shall be fined not less than twenty-five dollars nor more than 
fifty dollars. (99 v. 541, 543, Sec. 15, 25). 

Sec. 12605 (G. C.) [Failure to stop motor vehicle when 
signalled.] Whoever, operating a motor vehicle, fails to slow down 
and stop it when signalled so to do upon meeting or overtaking a 
horsedrawn vehicle or person on horseback and to remain stationary 
until such vehicle or person has passed, provided such signal to stop 
is given in good faith, under circumstances of necessity, and only 



966 APPENDIX 

as often and for such length of time as required for such vehicles 
or person to pass, whether approaching from the front or rear, shall 
be fined not more than twenty-five dollars, and for a second offense 
shall be fined not less than twenty-five dollars nor more than fifty 
dollars. (99 v. 541, 543. Sees. 16, 25). 

Sec. 12606 (G. C.) [Failure to stop motor vehicle in case 
of accident.] Whoever, operating a motor vehicle on a pubhc road 
or highway, in case of an accident to a person or property thereon 
due to the operation of such motor vehicle, fails to stop upon the 
request of the person injured or a person present, give his name and 
address, and, if not the owner thereof, the name and address of such 
owner, shall be fined not more than twenty-five dollars, and for a 
second offense shall be fined not less than twenty-five dollars nor more 
than fifty dollars. (90 v. 541, 543, Sees. 16, 25). 

Sec. 12607 (G. C.) [Third or subsequent offense.] For a 
third or subsequent offense, a person convicted of a violation of any 
provision of the next four preceding sections, shall be fined not less 
than fifty dollars nor more than one hundred dollars or imprisoned 
not more than thirty days, but if such subsequent offense occurred 
within one year after any former offense, he shall be imprisoned not 
less than ten days nor more than thirty days. (99 v. 543, Sec. 25.) 

Sec. 1 2614 (G. C.) [Penalty for failing to provide motor 
vehicle with bell, brakes, and lights.] Whoever operates or 
drives a motor vehicle upon the public roads and highways without 
providing it with sufficient brakes to control it at all times and a suit- 
able and adequate bell or other device for signalling, or fails during the 
period from thirty minutes after sunset to thirty minutes before 
sunrise to display a red light on the rear thereof and three white 
lights, two on the front and one on the rear thereof, the rays of which 
rear white light shall shine upon and illuminate each and every part 
of the distinctive number borne upon such motor vehicle, the light 
of which front lamps to be visible at least two hundred feet in the 
direction in which such motor vehicle is proceeding, shall be fined 
not more than twenty-five dollars. Provided, that motor vehicles 
of the type commonly called motor cycles shall display one white 
light in front to be visible at least two hundred feet in the direction 
in which such motor vehicle is proceeding, and one rear combination 
red and white light, showing red in the direction from which such 
motor vehicle is proceeding, and such rear light to be so placed that 
it will reflect its white light upon and fully and clearly illuminate the 
distinctive license identification mark of such motor vehicle. (99 
V. 540, 543, Sees. 12, 24. Am. 103 v. 766). 

Sec. 1 2628-1 (G. C.) [Intoxicated person operating motor 
vehicle upon public highway or street, unlawful.] That it shall 
be a misdemeanor for any person to operate a motor cycle or motor 
vehicle of any kind upon any public highway or street while in a state 
of intoxication, and upon conviction he shall be subject to punish- 
ment by a fine not less than twenty-five dollars, nor more than one 
hundred dollars, or imprisonment in the county jail for not more 
than six months, or both. (99 v. 544, Sec. 32. Am. 103 v. 133). 

Sec. 1342 1-9 (G. C.) [Driving over closed highway; penalty.] 



TRAFFIC RULES 967 

Whoever drives over, upon, along or across a public highway, or 
any part thereof, which has been closed, while in the process of con- 
struction, reconstruction or repair by order of the state highway 
commissioner, county highway superintendent, county commis- 
sioners, township trustees or other official or employe having au- 
thority to close such highway, shall be fined not more than fifty 
dollars, nor less than five dollars. 

Sec. 13421-11 (G. C.) [Placing obstruction in highway; 
penalty.] Whoever imlawfully places any obstruction in, or upon 
a pubhc highway, shall be fined not more than fifty dollars, nor less 
than five dollars. 

Sec. 1342 i-i 2 (G. C.) [Driving traction engine with destruc- 
tive tires; penalty.] WTioever drives over the improved highways 
of the state, or any political subdivision thereof, a traction engine 
with tires of wheels equipped with lugs, spikes, chains or other pro- 
jections seriously destructive to such highways, or by any other 
means damages such highways, shall be fined for each offence 
not less than ten dollars nor more than two hundred dollars. 

Sec. 1342 1-14 (G. C.) [Digging, excavating, piling earth or 
building fence on highways; penalty.] Whoever digs up, removes, 
excavates or places any earth or mud upon any portion of any public 
highway or builds a fence upon the same without legal authority or 
permission so to do, shall be fined not more than two hundred dollars 
nor less than ten dollars. Each day that such person continues to 
dig up, remove or excavate any portion of the public highway shall 
constitute a separate offence. 

Sec. 1342 1-16 (G. C.) [Placing nails, tacks, glass, etc., upon 
highway ; penalty.] Whoever places upon any part of a public 
highway, lane, road, street or alley, any tacks, bottles, wire, glass, 
nails or other articles, except such substances as may be placed there 
by proper authorities for the repair or construction thereof, which 
may damage or injure any person, vehicle or animal travehng along 
or upon said pubhc highway, shall be fined not more than two hun- 
dred dollars or imprisoned not more than six months or both. 

Sec. 13421-17 (G. C.) [Violation of traffic rules; penalty.]] 
Whoever enters upon, or travels over any portion of the highways, 
within the state, in violation of the traffic rules and regulations duly 
prescribed by law, or the state highway commissioner, or the county 
highway superintendent of any county, shall be fined not more than 
one hundred dollars, nor less than five dollars, and in addition thereto, 
such person shall be liable for all damage done to such highway. 



968 APPENDIX 



State of New York 
Highway Commission 



AMENDED RULES AND REGULATIONS FOR STATE 
AND COUNTY HIGHWAYS 

Adopted by the Commissioner of Highways of the State of New York 

Sec. I. No traction engine, road engine, hauling engine, trailer, 
steam roller, automobile truck, motor or other power vehicle shall be 
operated upon or over State or County Highways of this State, the 
face of the wheels of which are fitted with flanges, ribs, clamps, 
cleats, lugs or spikes. This regulation applies to all rings or flanges 
upon guiding or steering wheels on any such vehicle. In case of 
traction engines, road engines or hauling engines which are equipped 
or provided with flanges, ribs, clamps, cleats, rings or lugs, such 
vehicles shall be permitted to pass over such highways provided that 
cleats are fastened upon all the wheels of such vehicles, not less than 
2\ inches wide and not more than i^ inches high, and so placed that 
not less than two cleats of each wheel shall touch the ground at all 
times, and the weight shall be the same on all parts of said cleats. 

The foregoing regulations relating to flanges, ribs, clamps, cleats, 
rings or lugs shall not apply to traction engines used solely for agri- 
cultural purposes, but the following requirements shall apply to such 
traction engines: 

The guide band on the front wheels shall not be less than two 
inches in width, but no flanges, ribs, clamps, cleats, rings or lugs 
shall be required upon the front wheels. The full set of cleats upon 
the rear wheels of the original design as furnished with the engines 
must be used, and no rivet heads or bolt heads shall project, and the 
use of such traction engines for agricultural purposes shall not permit 
the use for hauhng purposes, excepting the hauling of threshing and 
other agricultural equipment necessary for threshing and agricultural 
purposes. 

This provision shall in no case relieve the owner of any traction 
engines from Uability for damage to roads from defective wheels. 

The use also of ice picks or mud lugs shall be strictly prohibited 
on State and County Highways. 

Sec. 2. No traction engine, trailer, steam roller, automobile 
truck, motor or other power vehicle shall be operated upon or over 
the State or County Highways of this State, nor shall any object be 
moved over or upon any such highways upon wheels, rollers or 
otherwise, in excess of a total weight of fourteen tons, including the 
vehicle, olDJect or contrivance and load, without first obtaining the 
permission of the State Commission of Highways as hereinafter 
provided. No weight in excess of nine tons shall be carried on any 
one axle of any such vehicle. 

Sec. 3. The tire of each wheel of a traction engine, road engine, 
hauling engine, trailer, steam roller, automobile truck, motor or 
other power vehicle (except traction engines, road engines, and haul- 
ing engines) shall be smooth, and the weight of such vehicle, including 



TRAFFIC REGULATIONS 969 

load, shall not exceed 800 lbs. upon any inch in width of the tire, 
wheel, roller or other object, and any weight in excess of 800 lbs. 
upon an inch of tire is prohibited unless permission is obtained from 
the State Commission of Highways as hereinafter provided. 

Sec. 4. No motor or other power vehicle shall be operated upon 
any State or County Highway of a greater width than ninety inches, 
except traction engines which may have a width of one hundred ten 
inches. 

Sec. 5. No traction engine, road engine, hauling engine, trailer, 
steam roller, automobile truck, motor, or other power vehicle, carry- 
ing a weight in excess of four tons, including the vehicle, shall be 
operated upon any State or County Highway of this State at a speed 
greater than fifteen miles an hour; and no such vehicle carrying a 
weight in excess of six tons, including the vehicle, shall be operated 
upon any such highway at a speed greater than six miles an hour 
when such vehicle is equipped with iron or steel tires, nor greater 
than twelve miles an hour w^hen the vehicle is equipped with tires of 
hard rubber or other similar substance. 

Sec. 6. The State Commission of Highways of the State of New 
York, upon proper application in writing, may grant permission for 
the moving of heavy vehicles, loads, objects, or structures in excess 
of a total weight of fourteen tons over its State and County High- 
ways upon proper application in writing being made therefor, and 
under such restrictions as said Commission may prescribe. 

Sec. 7. The owner, driver, operator or mover of any vehicle over 
any State or County Highway shall be responsible for all damage 
which said highway may sustain as a result of a violation of any of 
the provisions of the foregoing Rules and Regulations, and the 
amount thereof may be recovered in an action of tort by the State 
Commission of Highways or by any County Superintendent of 
Highways of any county or by any Town Superintendent of High- 
ways in any town in which said violation occurs. 

Sec. 8. These amended regulations to take effect February 24, 
1914. 

"Section 24 of Chapter 25 of the Consolidated Laws, entitled 
* The Highway Law,' provides that any disobedience of any of the 
foregoing rules and regulations shall be punishable by a fine of not 
less than $10, and not more than $100, to be prosecuted by the 
Town, County or District Superintendent, and paid to the County 
Treasurer to the credit of the fund for the maintenance of such 
highways in the town where such fine is collected." 



INDEX 



Note. — The first page number given will generally provide the data 
desired. The page numbers for each item are arranged in the order 
of importance of the reference. 



Abrasion Test, 230, 730 

Brick test (brick), 730 

French coefficient, 230, 234 

Percentage of loss (ordinary- 
rocks), 233 
Accidents (First Aid), 460 
Adjustment of Instruments, 343 
Alignment (Minimum Radii), 33-35 

Effect on construction cost, 34 

Grade crossings, 35, 549 

Sight distance, 33, 504 

Switchbacks, 34 
Altitude 

Barometric determination, 283 

Refraction correction solar obser- 
vations, 412 
Amiesite Pavement 

Cost data, 604 

Description, 172 

Materials, amounts required, 606 
Aneroid Barometer, 282-283 
Annual Charges 

Equipment, camp, 438 ^_ 

contractors, 627, 
608-621 

survey, 385 

Maintenance of pavements, 192- 
214. 5. 7 

Renewal of pavements, 190, 5, 7 
Arch Culverts (Examples of), 116, 93 
Areas 

Cross-sections (planimeter) , 512 

Formulae ordinary shapes, 828 
. Rights-of-way parcels (double 
meridian distance method) , 549 
Artillery Loads (Military), 149, 76 
Asphalt Block Pavement 

Cost data, 610, 177 

Description, 176 

Failures, common cause, 187 

Limitations of use, 186, 177, 507 

Maintenance, 209 

Specifications, 790 

Yearly cost, 190 

971 



Asphalt (Kentucky Rock) 

(3ost data, 602 

Description, 172 
Asphalt Pavement (Sheet, Topeka 

Mix, etc.) 
Aggregates, grading of , 678, 781 
Concrete foundation, 761, 677 
Crowns, 36 

Description, general, 171. I73 
Failures, common cause, 187 
Inspection of construction, 

677 
Limitations of use, 186, 163 
Maintenance, 203 
Specifications, 781 
Thickness of surface mix, 171 
Weight of surface mix, 677 
Yearly cost, 190 
Asphaltic Concrete (see Bituminous 

Macadam, Mixing Method) 
Asphalts (see Bitumens) 
Automobiles (Their Effect on De- 
sign) 
Pleasure Cars 

Sight distance, 33 

Skidding, 186 

Traffic rules, 957 
Trucks 

Loads, 150 

Preformance on grades, 17-21 

Traffic regulations, 148, 957 



Banked Curve Sections, 45 

Barometer Altitudes, 283 

Beams 

Formulae for flexure, 952 
Safe loads concrete beams, 566 
'* '* steel beams, 561 
** ** timber beams, 563 

Bench Levels, 325, 388 

Bench Marks, 325 

Bitulithic Pavement (Warren Bros.), 
782, 173 



972 



INDEX 



Bitumens 

Amounts Used 

for Surface applications, 201, 
167. 656. 553 

penetration bituminous ma- 
cadam, 169 
Topeka mix, 781 
Cost of applying as binder, 600 
Cost of applying as surface treat- 
ments, 653-657 
Maintenance use, 210—212 
Properties of, 241-248 
Specifications, 721-729 
Tests and their significance, 248- 

252 
Volume at different temperatures, 
271 
Bituminous Macadam (Mixing 
Method, Open Mix) 
Description, 171 
Specifications, 779 
Bituminous Macadam (Penetration 
Method) 
Amount of bitumen required, 169 
Cost data (see also Cost data in- 
dex), 600, 585-600, 63s 
Crowns, 170, 36 
Description, 169 
Examples of current practice, 47- 

62 
Failures, common cause, 187, 671, 

161-162 
Inspection of construction, 671 
Life of pavement, 190, 6, 7 
Limitations of use, 186, 164, 170, 

507 
Maintenance, 199-214 
Maximum grades, 507, 170 
Specifications, 778 
Thickness required on different 

soils, 152 
Thickness of top course, 169 
Yearly cost of upkeep, 190, 
214. 7 
Bituminous Surfacings 
Amounts of Materials 

Bitumen, 201, 167, 656, 553 
Cover, 202, 656 
Cost data, 653-657 
Description, 201, 167, 168 
Methods, 201-214, 167, 168 



Bituminous Surfacings 

Relative value of materials, 201, 

210-212 
Specifications, 777 
Blasting (Small Boulders), 597 
Bonds (Highway Improvement), 6, i 
Bottom Courses (see Foundations) 
See also Macadam 
Gravel 
Sub-base 
•* *• Telford 
Boulders 

Cost of sledging, 597 
Limitations for crushing, 720 (sec- 
tion 0.29) 
Brick Cube Pavement (McClintock) 
Cost data, 603 
Description, 182 
Brick Pavement (Standard) 
Amounts of Material Required 

Brick, 651 

Expansion joints, 796 

Grout, 650 

Sand cushion, 650 
Cost data (see also Cost data in- 
dex), 647-653 
Crowns, 175, 36 
Cushion 

Cement-sand, 173, 795 

Sand, 173. 719, 792 
Description, general, 173-175 
Edging, 174. 648, 754. 48, 58 
Examples of current practice, 47- 

62 
Expansion joints, 796, 173. i75. 

683, 649, 794 
Failures, common cause, 187, 794, 

679-683 
Inspection of construction, 679-683 
Life of pavement, 190, 6, 7 
Limitations of use, 186, 164, 175. 

507 
Maintenance, 204-214 
Mastic filler, 173, 174, 789 
Specifications 

Cerent-sand cushion type, 794 

Standard type, 791 
Yearly cost of upkeep, 190, 214, 7 
Brick (Paving) 
Hillside, 796, 186 
Properties, 240 



INDEX 



973 



Brick (Paving) 

Sampling, 272 
Specifications, 730, 791 
Tests, 730-734 
Bridges (Small Span) 
Camber, 809, 817 
Design loads (dead), 76, 805 
Design loads Give), 76, 80s, 806, 

109, IIS 
Examples of current practice, 

100-124 
Foundation piles (safe load), 98, 

804, 109 
Foundation soils (safe load), 89, 

811, 808 
Rails and parapets, 219, 216, 100- 

124 
Specifications, 800-824 
Timber floors, 820, 102 
Types used, 77, 80s 
Waterway opening, 75-8S 
Weights of (approximate), 301, 

547, S48 
Widths of roadway, 77, 807 
Burkle-Ziegler Formulse for Runoff, 
79 

Calcium Chloride 

Cost data, 6SS, 661 — 

Description, 166, 202 
Camber, 809, 817 
Camera (Notes on Photography), 

423-435 
Camp Equipment 

Depreciation, 438 

Lists of, 436-444 
Camp Medicine and Hygiene, 445- 

501 
Cast Iron 

Specifications, 736 

Weight, 950 
Cast Iron Pipe 

Culverts, examples of, 89 

Inspection of construction, 683 

Specifications, 736, 738 

Weights and dimensions, 558, 
738 
Catch Basins 

Examples of, 86, 227 

Grates for, 227 
Cattle Guards, 228 



Cement 

Amount required in concrete, 623, 

676, 688-697, 802 
Amount required in grouting, 650 
Cost of handling, 608-621 
Properties, 252 
Specifications, 252, 717 
Tests, 717 
Weight, 950 
Center of Gravity, 954 
Circles, Areas and Circumferences, 

830 
Clearing and Grubbing 
Areas, 297 
Specifications, 742 
Widths, 215 
Columns 

Strength of timber long columns, 
567 
Compass Variation from True North, 

300-308 
Concrete Beams and Slabs 

Safe loads, 564-566 
Concrete Culverts 

Cost, comparative, 87, 88, 298 
Cost data, detail, 621-625 
Design 

Lengths, 77, 807 
Loadings, 76, 805, 806 
Strength of slabs, 564, 565 
Waterway, size of, 75-85 
Discharge capacity, approx., 84 
Examples of current practice, 89- 

97 
Inspection of construction, 683- 

687 
Quantities of concrete, 623, 688- 
697 
Concrete Foundations for Pave- 
ments 
Cost data, detail, 648, 650, 651 
Examples of current practice, 47- 

62 
Inspection, 681 
Specifications, 761 
Concrete (General) 
Aggregates, 253-265 
Cement (see Cement) 
Gravel (see Gravel) 
Sand (see Sand) 
Stone, 254, 719, 802 



974 



INDEX 



Concrete (General) 

Aggregates, Water, 262, 718, 802 

Amounts of material required, 
623, 676, 802 

Cost data (see also Cost data in- 
dex), 621-625 

Finishing, 686, 750 

Forms 

Removal of, 685 
Specifications, 685, 751, 804, 
808 

Inspection, 685-686 

Mixing and placing, 685, 750 

Protection from sun and frost, 
751. 686, 801 

Reinforcement, 555, 736, 803 

Specifications, 749, 801 

Weight of, 950 

Working stresses, 951, 808 
Concrete Guard Rail 
Cost data, 626, 654 
Description, 216 
Concrete Pavement Hassam (see 

Hassam Concrete) 
Concrete Pavement (Standard) 

A mounts of Materials 
Cement, 676 

Expansion joints, 608-621 
Forms. 608-621 
Sand, 676 
Stone, 676 
Water, 674 

Cost data, detail, 608-621 

Crowns, 178, 36 

Description, 177-182 

Examples of current practice, 47- 
62 1 

Failures, common causes, 187 

Inspection of construction, 673- 
677 

Life of, 178, 180, 190, 214 

Limitations of use, 178, 164, 507 

Maintenance, 204-214 

Specifications, 785 

Yearly cost of upkeep and re- 
newal, 190, 214, 210, 208, 6, 7 
Concrete Pipe, 738 
Construction of Roads (Notes on In- 
spection) 

Bituminous applications, 671 

Brick pavement, 679 



Construction of Roads (Notes on 
Inspection) 

Concrete foundations, 681 
Concrete pavement (Hassam), 

672 
Concrete pavement (standard), 

673 
Grading, 664 

Macadam foundations, 667 
Macadam surfaces, 670 
Topeka mix asphalt, 677 
Contractors' Equipment 
Concrete roads, 608-621 
Macadam roads, 627-632 
Conversion Tables 

Cubic feet to cubic yards, 518 

Feet to miles, 538 

General units, 825 

Minutes to decimals of a degree, 

350 
Corrugated Metal Pipe 

Culverts, examples of, 90-91 
Specifications, 739 
Weights and sizes, 559 
Cosecants natural, 868 
Cosines 

Logarithmic, 905 
Natural, 857 
Cost Data (Labor and Materials in 

Detail) 
Amiesite pavement, 604-606 
Asphalt block pavement, 610 
Asphalt Topeka mix, 607 
Brick Pavement 

Edging, 648, 650 

Expansion joints, 649, 650 

Grouting, 649, 650 

Hauling 650 

Laying, 649, 650 

Materials, amount required, 
650, 651 

Sand cushion, 649, 650 

Unloading brick, 650 
Cobble Gutters, 626 
Concrete Culverts 

Forms, 623, 624 

Materials required, 623, 688 

Mixing and placing, 623-625 
Concrete Foundations (Pavement) 

Materials required, 623, 681 

Mixing and placing, 681, 761 



INDEX 



975 



Cost Data (Labor and Materials in 
Detail) 

Concrete Pavement (Hassam), 784, 

672, 607 
Concrete Pavement {Standard) 

Amounts of materials, 608-621, 
676 

Expansion joints, 608-621 

Finishing and curing, 608-621 

Mixing and placing, 608-621 

Plant required and overhead, 
608-621 

Trimming, 608-621 

Water supply, 608-621 
Guard Rail 

Concrete, 626 

Wooden, 625 
Kentucky Rock Asphalt Pavement, 

602 
Macadam Roads 

Contractor's plant, 627-631 

Crushing stone, 593-599 

Excavation, 585 

Hauling, 588 

Loading sand, 590 

Loading stone, 590 

Puddling, 602 

Quantities of materials, 591 

Rolling, 592 - 

Spreading sand filler, 591 

Spreading screenings, 592 

Spreading stone, 590 

Stone fill, 599 

Sub-base (field stone), 600 

Unloading stone from cars, 586 
Maintenance and Repair 

Calcium chloride, 655 

Distribution of maintenance 
costs, 661, 205-214 

Guard rail, resetting, 654 

Oiling, 653-657 

Patrol costs, 660 

Recapping macadam, 655 

Scarifying, 658 
Painting Guard RaiU 626, 654 
Cost (General Comparative) 

Maintenance, 205-214, 190, 5*7 
Office work, 570 
Pavements, 1 88-191 
Preliminary investigations, 266 
Surveys, 333. 385 



Cotangents 

Logarithmic, 905 
Natural, 845 
Cribbing, Log, 741, 100 
Cross -sections 

Areas by planimeter, 512 
Plotting, 506, 572 
Survey methods, 325, 390 
Templets for, 509 
Crowns (see also Respective Type of 
Pavement) 
Maximum and minimum limits, 

36 
Parabolic, 551, 62 
Templets for construction, 674, 
67s 
Crushing Stone 

Cost data, 593-599 
Proportion of screen sizes of out- 
put, 594-599 
Cube Pavements 
Durax, 181 
Kleinpflaster, 181 
McClintock, 182, 603 
Cubes and Cube Roots, 830 
Culling Brick, 682 
Culverts 

Cost comparative, 87, 88, 298 
Design of 
Capacity, 84 
Length, 77, 807 
Loads, 76. 805, 806 
Type, 77. 83, 805 
Waterway, 75-86 
Driveway culverts, 87 
Examples of current practice, 89- 

97 
Inspection of construction, 683- 

687 
Types, 77. 83, 805 
{See also Cast iron pipe) 
" Concrete culverts) 
** Corrugated metal pipe) 
*• Log culverts) 
•* Vitrified pipe) 
Curbs 

Description, 223 
Specifications, 753-754 
Curvature (see Alignment) 
Curves 

Banked, 45, 62 



976 



INDEX 



Curves 

Functions of i** curve (table), 349- 

375 
Length of, 349 

Methods of staking out, 378, 389 
Minimum radii (see Alignment), 

33, 34. 35, 504, 549 
Problems, 380-384 
Radii of (table), 346 
Sharp, avoidance of, 33-35 
Tangent length, 376 
Vertical (^ee Vertical curves), 510-- 

513, 575, 576 
Widening of pavement or section 

at, 45, 62, 71, 34 

Danger Signs, 224, 758 
Declination 

Magnetic, 300-308 
Solar, 414-416 
Deformed Bars (see Reinforcement) 
Depreciation 

Camp equipment, 438 
Contractors' equipment, 627-631 
of Pavements, 190, 7 
Survey equipment. 385 
Depth of Foundations (Small 

Bridges), 808, 810, 117 
Depths of Pavements (Thickness) 
Macadam, on different soils, 152 
Rigid pavements, 188 
(See also Respective type of pave- 
ment) 
Design of Highways 
Cost of office work, 570 
Economic, general summary, 552 
, grading, 509, 26, 16, 29 
" , foundations, 161, 7 
" , pavement selection, 7 
Methods 

Bridges (small span), 74-124 
Culverts, 74-97 
Grading, 509, 577 
Macadam roads, 266-282, 502- 

568 
Rigid pavements, 502-568, 266- 

282 
Pioneer roads, 567-584, 283- 
322 
Speed of office work, 569 
Supplies, cost of for office, 568 



Dickens Formula for Runofif of 

Streams, 82 
Distance Units of Measure, 825 
Ditch Linings (see Gutters), 226 
Ditches 

Dangerous ditches, 38, 67 

Flow of water in, 228 

Functions of, 38 

Intercepting, 66 

Protection of (see Gutters), 226, 
74 

Relief culverts, 74 
Double Meridian Distance Areas, 

549 
Drags (Road Drags), 192-198 
Drainage 

Survey notes, 327, 392 

Underdrains, 125-127, 132 

(See also Culverts and bridges) 
Driveway Culverts, 87 
Drop Inlets, 86, 227 
Ductility (Test), 249, 722 
Duraz Pavement, 181 
Dust Layers, 166 

(See Bitumens) 

(See Calcium chloride) 
Dustless Screenings, 599 

Earth 

Bearing power of , 147, 89, 811, 808 

Shrinkage of, 507, 577 

Weight of, 950, 805 
Earth Excavation 

Amount, variation in, 30-32 

Computation of, 5i5» 283-296 

Inspection, 664, 679 

Slopes, different soils, 41, 36 

Specifications, 743-745 

Tables of amounts and volumes, 
516-537, 285-296 
Earth Roads 

Cost, general comparative, 131 

Crowns, 63, 132 

Description, 130 

Examples of current practice, 55. 
68. 132 

Limitations of use, 128 

Maintenance, 192-197 . 

Specifications, 763 

Yearly cost of upkeep, general, 
comparative, 191, 7 



INDEX 



977 



Edging, Concrete, 174, 648, 754.48,58 
Elasticity, Modulus of, 951 
Embankments 

Inspection of construction, 664, 
680 

Materials suitable for, 665 

Settlement of (shrinkage), 507 

Slopes, 41 

Specifications, 744-745, 764 
Equipment 

Camp, 436-444 

Contractors, 627-631, 608-621 

Survey, 323. 385 
Estimates, Forms for, 632-639, 581 
Excavation (see Earth and Rock 

Excavation) 
Expanded Metal 

Specifications, 736 

Weights and dimensions, 555 
Expansion Joints 

Brick pavements, 796, 173, 175, 
683, 649. 794 

Concrete pavements, 181, 178, 
608-621, 786 

Retaining walls, 219, 220, 222 
Externals 

Of I** curve (table), 349-375 



187. 



161, 



794. 



Failures (Common Causes) 

Asphalt block pavement, 

176 
Asphalt pavement, 187, 677 
Bituminous macadams, 187, 

171 
Brick pavement, 187, 679. 

174 
Concrete pavement (Hassam),672 
Concrete ** (standard), 

187. 673. 177 
Stone block pavement, 187 
Waterbound macadam, 187, 161, 

166 
Fences 

Cattle guards, 228 
Property line, 215 
Snow, 218 
Fillers 

Bituminous for block pavements, 

789. 173. 174 
Cost data {see also Cost data in- 
dex). 590-592 



Fillers 

Grout {see Grout), 650, 649, 719. 

793. 797 
Macadam roads, 240, 590-592, 
162 
Fills (Earth and Stone) 

Inspection of construction, 664 
Materials saitable, 665 
Settlement of (shrinkage), 507, 

577 
Slope stakes, 664 
Slopes (angle of repose), 41 
Specifications, 745, 764 
Financing Highway Improvements 
Bonds, reasonable length of term, 

6. I 
Effect of inadequate funds on de- 
sign, 2 
General requirements to be pro- 
vided for, 6, 7 
First Aid (Accidents), 460 
Flash Point (Test), 722 
Floods (Small Watersheds), 75-83 
Floors, Bridge 
Loading, 76, 806 
Specifications, 806-824 
Foot (Decimals of, in Inches), 

826 
Footing (Safe for Horses or Autos) 
{see also Each type of pave- 
ment) 
Limitations of different pave- 
ments, 507. 186 
Forms 

Concrete roads, 608-621 
Concrete Masonry 
Cost of, 621-625 
Removal of, 685 
Specifications, 749, 808 
Formulae 

Flexure of beams, 952 
Safe loads on piles, 98, 109, 804 
Stream runoff, 82, 79 
Trigo metric, 843 
Foundations 
Depth of (small bridges), 808, 

811, 117 
Pavements 

Concrete foundations, 761, 681, 

47-62, 648, 650, 651 
Macadam and gravel, 147-162 



978 



INDEX 



Foundations 

Piles 
Formula for safe load, 98, 804, 

109 
Limits of loading, 98 
Soils, Bearing Power 
Bridge foundations, 89, 98, 811, 

808 
Pavement foundations, 147 
French Coefficient of Abrasion, 230, 

234 
Functions 

Trigometric, logarithmi-, 905 
" , natural, 845-879 

Geological Classification of Rocks, 

236 
Girder Bridges 

Concrete girder (example of rein- 
forcement), 124, 77. 806-809 

Weights, approximate and speci- 
fications, 547, 548. 813-820 
Glutrin (Sulphite Liquor), 167, 786 
Grade Crossings 

Alignment and grade at, 549. 
35 

Clearance and width (elimina- 
tion), 547. 35 

Elimination of, 35, 547 
Grades 

Adverse grades, 29 

Controlling points, 26 

Economic design, 26, 16, 29, 509, 
577 

Effect on auto trucks, 18-21 

** cost of construction, 24, 
26 
*' " team hauling, 10-17 

Intermediate grades, 26 

Level grades, 28 

Limiting rates on different pave- 
ments, 507 

Maximum grades, 10-26 

Minimum " , 28 

Rolling " ,26, S09 

Ruling " , 10-26 

Grading 

Cost data, 585, 298 

Inspection, 664 

Specifications, 743 
Gratings (Catch Basin), 227 



Gravel for Concrete 

Amount, 623, 676 

Quality, 254, 719, 720 

Sizes, 254, 719, 720 
Gravel Foundations for Pavement 

Amount required, 152, 591 

Loam content, 139, 156 

Manipulation, 139. 156 

Sizing, limitations, 138, 156, 766, 
720 

Specifications, 139, 760 
Gravel Roads 

Cost, general comparative, 143, 
191, 7 

Crowns, 140-142 

Description, 137-143 

Examples of current practice, 140- 
142 

Limitations of use, 128-129 

Maintenance, 197-199 

Sections, 140-142 

Specifications, 139. 760, 763 

Yearly cost of upkeep, general 
comparative, 191, 7 
Gravity 

Center of, 954 

Specific (weights), 950, 233 
Grout 

Amount required, 650 

Inspection, 683 

Sand suitable for, 797. 7I9 

Specifications, 797. 793 
Grubbing (see Clearing) 
Guard Rail 

Concrete, 216, 626, 654 

Wire cable, 218 

Wooden, 216, 625, 654, 756 
Guide Signs, 224, 757 
Gutters 

Brick, 225, 226, 755 

Cobblestone, 225, 226, 626, 754 

Concrete, 225, 226, 755 

Loose stone, 225, 226, 758 

Hassam Concrete Pavement 

Amount of materials required, 

607, 608 
Cost data, 607 
Inspection of, 672 
Maintenance, 209 
Specifications, 784 



INDEX 



979 



Haul 

Computation of length, 539, 641- 

647 
Overhaul, 539. 745 
Hauling 

Cost, 588-590 

Loads on different grades, 15, 16- 
21 
Highway Bonds, 6, i 
Horse Traffic 

Footing safe on grades, 507, 22 
Loads on different grades, 15-17 
Tractive effort long and short 
grades, 16 

Igneous Rocks, 237 

Impact Allowance for, 76, 102, 109 

Inches as Decimals of a Foot, 826 

Inertia, Moments of, 955 

Injuries (First Aid), 460 

Inlets (Drop), 86, 227 

Inspection (Notes of Methods) 

Asphalt pavement, 677-679 

Brick " , 679-683 

Concrete *' , 673-677 

Culverts, 683-687 

Foundation courses, 667-670 

Grading, 664-667 

Macadam surfaces, 670-673 — 
Instruments 

Adjustment of, 343 

Equipment list, 323, 385 
Interest 

On pavement investment, 190 

On plant and payroll, 627-631 
Investigations (Preliminary) 

Cost, 266 

Equipment, 282 

Methods, 266-322 

Sample report, 274-282, 309-320 

Sampling materials, 269 
Iron (see Cast and "Wrought Iron) 

Joists (Bridge Floors) 

Distribution of life loads, 806 
Examples of size and spacing, 100- 

113 
Impact, allowance, 76, 102, 109 
Safe loads steel joists, 561 
Safe loads timber stringers, 563 



Kentucky Rock Asphalt 

Cost data, 602 
Description, 172 
Kleinpflaster (Durax) 
Description, 181 

Land-taking Surveys, 333 

(See also Right-of-way) 
Latitude, Determination of, 413 
Leaching Basins, 227, 746 
Level Adjustments of, 343 
Leveling 

Accuracy required, 325-327. 388- 

390 
Methods, 325-327. 388-390 
Notes, 325, 327, 390, 391 
(See also Surveys) 
Life of Equipment 
Camp, 438 
Contractors, 627-631 
Survey, 385 
Life of Pavements, 190, 7 
Linear Measure, Units of, 825 
Loads 

Beams and Slabs 

Resisting moments, formulae, 

952 
Tables of safe loads, 561-566 
Bridge Design 

Dead loads, 76, 805 

Live loads, 76, 805, 806, 109. 

IIS 
Wind loads, 806 
Columns, Timber^ Safe Loads, 567 
Piles, Formula for Safe Loads, 98, 

804, 109 
Team Loads on Different Grades, 

15-17 
Wheel Loading, Concentrated 
Automobile trucks, 150 
Farm wagons, 150 
Military loads, 149, 76 
Regulation of loads, 148 
Rollers and traction engines, 
148 
Location of Roads (see Survey) 
Log Culverts and Bridges 

Examples of current practice, 97 
Specifications, 740-742 
Logarithms 
Numbers, 880 



980 



INDEX 



Logarithms 

Trigometric functions, 90s 
Logs 

Amount of lumber in, 300 
Lumber, 740, 748 

Macadam (see Waterbound and 

Bituminous Macadam) 
Machinery (Contractors), 627-632, 

608-621 
Magnetic Declination, 300-308 
Maintenance of Highways 

Costs, detail, 653-661 

Costs, general, 192-214, 7 

Materials, 199-212 

Methods, 192-214 
Maps (Plans) 

Preparation of, 502-584 

Scales, 503, S7i 
Masonry 

(See Concrete) 

(See Stone masonry) 
Mass Diagram, 539 
Materials 

Amounts required (see Respective 
material) 

Properties and tests, 229-265 

Reports on location and amount, 
267, 331 

Sampling (instructions for), 269 

Strength of, 951. 810 

Weight of, 950 
Maximum Grades (see Grades) 
McClintock Cube Pavement 

Cost data, 603 

Description, 182 
Measure (Units of), 825 
Medical Notes 

Accidents (first aid), 460-501 

Personal hygiene, 445 

Remedies and doses, 449-455 

Sickness, symptoms and treat- 
ment, 455-460 
Meridian Determination (True 
North) 

Magnetic variation, 300-308 

Polaris meridian, 394-411 

Solar meridian, 402-416 
Meridiograph, 416 
Mesh Reinforcement 

Dimensions and weights, 555 



Mesh Reinforcement 

Specifications, 736 
Metalling (Pavements) 

Thickness required, 152, 188 

Widths of, 188, 42 
Military Road Requirements, 149 
Minimum Radii for Curves 

High type improvements 33 

Mountain conditions, 34 
Modulus of Elasticity, 951 
Moments 

Bending, 952 

Inertia, 955 

Resisting, 953' 
Motor Trucks 

Power on grades, 18, 10 

Regulation of loads, 148, 957 
Mountain Roads 

Alignment, 33 

Grades, 10-32 

Office practice, 569-584 

Preliminary investigations, 282- 
320 

Sections, 63-73 

Surveys, 384-422 

Natural Cement^ 252 

Natural Trigometric Functions, 845- 

879 
North, Magnetic (see Magnetic 

Declination), 300-308 
North, True (see Meridian), 394-416 

Oil and Bitumens, Table of Quanti- 
ties, 553 

(See also Bitumens) 
Oiling (see Bituminous Surfacing) 
Ordinance Loads (Military), 149, 76^ 
Organization 

Office work, 569 

Survey work, 323, 384 
Overhaul, 539, 745 
Overhead Charges (Contract), 627- 

631 

Parabolic Crowns, 551, 62 
Paraffin (Maximum Limit), 725-730 
Parapets (Bridge), 219 
Pavements (General) 

Cost per mile, 188 

Economic selection, 7, 163, 164 

Life of, 190 



INDEX 



981 



Pavements (General) 

Limitations of use, 186, 164, i, 7 
Maintenance, 199-214, 7 
Thickness, 152, 188 
Types (see Respective type name) 
Amiesite 
Asphalt, block 
Asphalt, rock 
Asphalt, sheet 
Bituminous macadam 
Brick 

Concrete Hassam 
Concrete, standard 
Durax 
Gravel 
Kleinpflaster 
McClintock cubes 
Rocmac 
Sand clay 
Stone block 
Waterbound macadam 
Wood block 
Widths, 42, 188 
Paving Pitch 

Expansion joints, 796, 173, 175, 

683. 649, 794 
Mastic filler, 789, 173, 174 
Payroll (Amounts Required), 627 
Petroleum, 243 

Photography (Notes on), 423-435 
Pile Trestles (Examples), 109- 

iiS 
Piles 

Loading, 98, 804, 109 
Specifications, 740 
Use of, 89, 808 
Pipe 

Discharge capacity, 227 
{See also Cast-iron pipe) 
(" " Concrete pipe) 
(" ** Corrugated metal pipe) 
(" " Vitrified pipe) 
Pipe Rail (Bridge), 216 
Pitch (see Paving Pitch) 
Planimeter (Use of), 512 
Plans for Construction, 502-584 
Plants (Contractors), 608-621, 627- 

632 
Pointing Masonry, 753, 228 
Polaris Meridian, 394-411 
Portland Cement (see Cement) 



Posts 

Guard rail, 216 
Sign, 224 
Preliminary Investigations 

Cost, 266 

Equipment, 282 

Methods, 266-322 

Reports, sample, 274-282, 309- 
320 

Sampling materials, 269 
Profile 

Accuracy required, 390 

Arbitrary limitations, 28 

Economic design, 26, 29, 509, 577 

Graphic methods of laying grade 
line, S09, 575, 576 

Plotting, 506, 571, 574 

Rolling grades, 26, 27 

Vertical curves, 510-513. 575, 576 
Puddling Macadam Roads 

Amount of water required, 603' 

Cost data, 602 

Specifications, 775 

Quantities of Materials 

Concrete aggregates, 623, 676, 802 
Concrete in culverts, 688 
Concrete in pavements, 543, 676 
Excavation per 100 feet (side hill 

roads), 285-296 
Macadam in pavements, 543 
Oils and bitumens per 100 feet, 

553 
Stone in macadam, 540 
Surface area of pavements, 543 

Radii of Curves 

Minimum for safety, 33-35 
Table of values for surveys, 346 
Vertical curves for plotting pro- 
files. 513 
Railing 

Bridge, pipe rail, 216, 100-124 
Parapets, solid, 219 
Railroad Crossings 

Alignment restrictions, 549, 35 
Elimination of Grade Crossings, 35, 
547 
Clearance and widths, 547 
Grade restrictions, 549, 35 
Rainfall, 75-78 



982 



INDEX 



Rattler 

Brick test, 730 

Stone " , 230 
Referencing Transit Hubs, 323, 387 
Refraction (Effect on Observed Alti- 
tude), 412 
Reinforcement 

Bars, Steel 
in Slabs and beams, 564, 566, 

IIS. 117 
Specifications, 736 
Weights and sizes, 556 

Mesh 
in Pipe, 738 
*• Slabs, 92 
Specifications, 736 
Weights and sizes, 555 
Repairs (see Maintenance) 
Repointing Masonry, 753. 228 
Reports (Examples of) 

Design report, final, 544 

" ** , preliminary, 274 

Investigation, preliminary, 309 

Survey, 394 
Resurfacing Macadam, 655 
Retaining Walls 

Concrete, 220-222 

Stone masonry, 73, 220-222, 293 
Right-of-way 

Areas, 297, 549 

Fences, 215 

Surveys, 333 

Widths, 215 
Rip Rap 

Necessity for, 98 

Specifications, 749 
Road Materials (see Materials) 
Road Sections, Typical (see Sec- 
tions) 
Roads (General Types) 

Earth roads, 130 

Gravel ** , 137 

Macadam roads, 163 

Pavements, rigid, 173 

Sand-clay roads, 131 
Roadway, Traveled Width of, 37 
Rock Asphalt 

Cost data, 602 

Description, 172 
Rock Excavation 

Specifications, 743-744 



Rockmac, 184 
Rocks 

Geological classification, 236 

Properties, 229-240 

Sampling, 269 

Tests, 230-232 

Weights, 233 

(See also Crushing) 
Rolling, 592, 796 
Roots, Square and Cube, 830 
Ruling Grades (see Grades) 
Runoff (Small Watersheds), 75-85 
Rut Roads, 130 

Safety Measures 

Banked curves, 45 

Crown, one way, 63 

Curves, sharp avoidance of, 33-35 

Grade crossing eliminations, 35, 
547 

Guard rail, 216 

Shoulder slope, 36 

Sight distance, 33-35 

Skidding on pavements, 186 
Sampling Materials, 269 
Sand 

Concrete {see also Concrete), 718, 
253. 623 

Cushion, 719, 649, 682 

Filler for macad-am, 240, 162, 590- 
592 

Grout, 797. 7i9, 650, 649, 793 
Sand-ciay Roads 

Cost, general comparative, 137, 
191 

Description, 131-137 

Limitations of use, 128 

Maintenance, 197 

Sand-clay mixtures, 131, 133 

Sections, 134 

Specifications, 773 
Scarifying Macadam, 658 
Scour 

Rip rap protection (see Rip rap) 

Velocities producing scour, 98 
Screed for Concrete Pavement, 674 
Screenings 

Dustless, 599 

Ordinary, 239, 720, 593*599 

as Sand in concrete, 719 
Secants, Table of, 868 



INDEX 



983 



Sections (Cross-sections) 

Field methocis, 325, 390 

Office *' , 506, 572 

Templets for, 509 
Sections (Typical Examples of Cur- 
rent Practice), 47-73 
Settlement of Fills, 507 
Shoulder 

Slopes, 36 

Stone protection, 42, 204 
Shrinkage of Earthwork, 507, 577 
Sickness (see Medical) 
Side Hill Roads 

Amounts of excavation, 285-296 

Drainage, 74 

Sections, 63-73 

Sight distance, 33-53 
Sight Distance on Curves, 33-35 
Signs 

Danger, 224, 758 

Guide, 224, 757 
Sines 

Logarithmic, 905 

Natural, 856 
Skidding, Automobiles, Effect on 

Design, 186 
Slabs (Culverts and Bridges) 

Effect of depth of fill, 565 

Examples of current practice, 92, 
114, 117, 119 " 

Safe loads, 564 
Slag 

Concrete, 254 

Macadam, 240, 720 
Slipperyness of Pavements (see also 
Each Respective Pavement) 

Limitations on hills for horse 
traffic, 507 
Slopes 

Angle of repose of different soils, 
41 

Slope stakes, 664 
Snow 

Effect on location mountain roads, 
386 

Fences, 218 

Removal from highways, 212 
Soils 

Bearing power, 147, 89, 98, 8ii,8o8 

Shrinkage, 507, 577 

Weight, 950, 805 



Solar Meridian, 402-416 
Specifications 

Bridge, 800-824 

General clauses, 69S-717 

Materials, 717-737 

Methods, 737-800 

{See also Respective item desired) 
Speed of Work 

Construction, 628, 608-621 

Design, 569 

Surveys, 333. 384-393 
Sprinkling, 166 
Square Roots, Table of, 830 
Square Units of Measure (Conver- 
sion), 825 
Square Yards, Table of, 543 
Squares, Table of, 830 
Stadia Measurements, 416-422, 

335 
Stakes 

Grade, 662. 323 

Slope, 664 
Staking Out for Construction, 662 
Steel 

Specifications, 737 
Steel Bar Reinforcement (see Rein- 
forcement) 
Stone 

Concrete, 254, 7i9, 802, 623, 676 

Macadam, 229-240, 540, 720 

(Also see Rocks and crushing) 
Stone Block Pavement 

Crowns, 175 

Description, 175 

Failures, 187 

Life of, 190 

Limitations of use, 190, 188, 186, 
164, 7 

Specifications, 797 

Yearly cost, 190 
Stone Fills, 160, 599, 748 
Stone Masonry, 752 
Stone way 

Depths on different soils, 152 

Widths, 42, 188 
Stream Runoff, 75-85 
Stream Scour, 98 
Strength of Materials 

Beams, safe loads, 561-566 

Columns, ** ** , 567 

Slabs, " " , 564-565 



984 



INDEX 



Strength of Materials 

Working stresses different mate- 
rials, 951, 810 
Sub-base (Foundation Course) 

Amounts of material, 152, 591 

Cost data, 600 

Depth required, 152 

Description, 154 

Fillers, 15S 

Inspection, 667 

Specifications, 759 
Sub-grade, Preparation of, 662-667, 

153. 744 
Sulphite Liquor (Glutrin), 167, 786 
Surface Measures, Units and Con- 
version, 825 
Surgical Supplies, 451 
Surveys 

Cost of, 333. 385 

Equipment, 323, 385 

Methods 

Adjustment of instruments, 343 
Base lines, 323, 387 
Cross-sections, 325, 390 
Curves, 345-384. 389 
Drainage data, 327, 392 
Levels, 388, 325 
Magnetic variation, 300-308 
Materials, sampling, 269, 331 
Meridian determination, 394- 

416 
Stadia work, 416-422, 335 
Topography, 328, 392 
Traffic reports, 329 

Organization, 323, 384 

Preliminary investigations, 266- 
322 

Speed, 333, 384-393 

Tangents 

of 1° curve (table), 349 

Logarithmic, 905 

Natural, 845 
Tar 

Maintenance uses, 200-212 

Properties, 242 

Specifications, 728 
Tar Surfacing (see Bituminous Sur- 
facing) 
Telford Base, 157, 759 
Temperature Units, 825, 672 



Templets 

for Pavement construction, 674 
'* Plotting cross-sections, 509 
Testing Materials 

Methods, 229-265 

Sampling materials, 269 

Significance of tests, 229-265 
Tile, Porous, 125-127, 746 

(See also Vitrified pipe) 
Timber 

Amount in logs, 300 

Beams and columns, safe loads, 
563, 567 

Bridge, floors, 820-824, 100-113 

Bridges (examples of current prac- 
tice), 1 00- 1 13 

Pavements (see Wood block) 

Weight of, per cubic foot, 950 
'* ", *' foot B. M. (treated 
and natural), 805 
Time (Conversion of) 

Determination of local mean time, 
413 

Meantime, local, 401 

Standard times in U. S., 397 
Tires, Wagon 

Allowable load per inch width, 
148-150 

Effect of width on tractive resist- 
ance, 13-15 
Toe Walls, 222 

Top Courses (see Respective Pave- 
ment) 
Topeka Mix (see Asphalt Pavement) 
Topography 

Field methods, 328, 392 

Office methods, 505 
Toughness, Tests for, 231, 722 
Traction Engines, 148, 957-969 
Tractive Power (Horses), 11 
Traffic 

Classification, 164 

Regulation, 148, 957-969 

Reports, 329 
Transit, adjustment of, 343 
Traverse Computations, 334 
Trestles 

Examples of current practice, 109- 
115 
Triangles, Solution of, 843 
Trigometric Formulae, 843 



INDEX 



98s 



Trigometric Functions 

Logarithmic. 905 
Natural, 845-879 
Trucks, Automobile 

Power on grades, 18, 10 
Regulation of, 148, 957-969 

Underdrains 

Porous tile, 125-127, 746 
Stone, 125-127 
Unloading Stone Cost, 586 

Variation (Magnetic Meridian), 300- 

308 
Velocity of Stream Flow 

Formulae for, 98 
Souring action, 98 
Vertical Curves 

Formulae for, 510-513 
Graphic methods, 510, 513. 575 
Radii of, 513 
Vitrified Pipe 

Dimensions and weight, 560 
Discharge capacity, 227 
Specifications, 745 
Voids, Determination of, 180 
Volumes 

Formulae, 828 

Units of measure, 825 

Wagon Loads 

on Different grades, 15 
Farm wagons, 150 
Walls 

Retaining walls, 219-222, 73, 293 
Toe walls, 223 
Warning Signs (see Danger Signs) 
Water 

Amount for concrete, 674, 262 

*' " puddling, 603 

Cost of, 608-621 
Specifications, 718 
Weight of, 950 
Waterbound Macadam 

Depth on different soils, 152 
Foundation courses, 153-162 
Top Course 

Amounts of materials 
Screenings, 591 
Stone, 591 
Water, 603 



Waterbound Macadam 

Top Course 

Cost data, detail, 585-603, 627- 

640 
Cost data, general, 165 
Crowns, 165, 36 
Description, 165 
Examples of current practice, 

47-62 
Failures, common cause, 187, 

161 
Inspection of construction, 670 
Life of, 190, 213 
Limitations of use, 186, 188, 

164, 166, 7 
Maintenance, 199-214 
Maximum grades, 166 
Specifications, 775 
Thickness, 165 

Yearly cost of upkeep, 190, 213 
Waterway of Culverts 

Determination of size, 75-85 
Wear 

Abrasion, percentage of, 230, 233, 

730 
French coefficient, 230, 234 
Weights of Materials 
Bars, steel, 556 
Cast-iron pipe, 558 
Corrugated metal pipe, 559 
Cubic foot various materials, 9So 
Metal mesh, 555 
Rocks, 233 

Timber per foot B. M., 805 
Vitrified pipe, 560 
Wheel Loads 

Farm wagons, 150 
Military ordinance, 149, 76 
Regulation of loads, 148, 957-969 
Rollers, 148 
Trucks, ISO 
Widths 

of Bridges, 77, 807 
of Pavements, 42, 188 
of Sections, 38-72 
of Traveled way, 37 
Wood Block Pavement 

Specifications, 787 
Working Stresses of Materials, 95 r» 

810 
Wrought Iron Specifications, 736 



986 INDEX 

Yearly Charges Yearly Charges 

Camp equipment, 438 Pavements, maintenance and re- 

Contractors* equipment, 627-632, newals, 190, 192-214, 5, 7 

608-621 Survey equipment, 385 



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CONDENSED LIST OF MOST USED DATA 

Page 
First Aid in Case of Accident 4^0 

SURVEY DATA 

Radii of Curves 34^ 

Tangents and Externals 1^ Curve 349 

Conversion Degree of Slope to % of Grade 297 

ESTIMATE AND DESIGN DATA 

Volumes 6O' Cross Sections 516 

Volume of Excavation Side Hill Locations 285-296 

Required Depth of Maeadam on Different Soils 152 

Table of Macadam Quantities 543 

Square Yards of Pavement per 100' 543 

Weights of Cast Iron Pipe. 553 

Weights of Corrugated Iron Pipe 559 

Weights of Vitrified Pipe 560 

Steel Bar Reinforcement 555 

Metal Mesh Reinforcement 555 

Thickness of Concrete Bridge Slabs 666 

Material Requked per Cu. Yd. Concrete 623 

General Tables and Formulae 825-956 



